1. AP Statistics Question Bank
White: Practice AP Statistics test (complied from collegeboard.com)
Blue: 1997 AP Statistics test
Orange: Sample questions from AP Course Description

2. Unit 1: Displaying Univariate Data
3a. Organize data using graphs that are appropriate to the data set, including frequency distributions, stacked line and bar graphs, stem-and-leaf plots, scatter plot, frequency polygon, and histograms. (DOK 2)
4a. Make inferences and predictions from charts, tables, and graphs that summarize data. (DOK 3)
3b. Determine and justify the graph type that best represents a given set of data. (DOK 2)
3c. Create graphs with scales that fairly display the data. (DOK 2)
Types of data (categorical/quantitative)
Pie charts

3. 22) The back-to-back stem-and-leaf plot below gives the percentage of students who dropped out of school at each of the 49 schools in a large metropolitan school district.
0 4 4
Which of the following statements is NOT justified by these data?
A. The drop-out decreased in each of the 49 high schools between the and
B. For the school years shown, most students in the 49 high schools did not drop out of high school.
C. In general, drop-out rates decreased between the and school years.
D. The median drop-out rate of the 49 high schools decreased between the and school years.
E. The spread between the schools with the lowest drop-out rates and those with the highest drop-out rates did not change much between the and school years.

4. 26) A fair coin is flipped 10 times and the number of heads is counted
26) A fair coin is flipped 10 times and the number of heads is counted. The procedure of 10 coin flips is repeated 100 times and the results are placed in a frequency table. Which of the frequency tables below is most likely to contain the results from these 100 trials?
Head
Freq 19 1 12 2 9 3 6 4 5 7 8 14 10 21
Head
Freq 9 1 2 3 4 5 10 6 7 8
Head
Freq 1 2 6 3 9 4 22 5 24 18 7 12 8 10
Head
Freq 7 1 10 2 6 3 11 4 8 5 9 12
Head
Freq 1 2 3 4 24 5 51 6 22 7 8 9 10

5. Unit 2: Describing Univariate Data
2b. Calculate mean, median, mode, standard deviation, z-scores, t-scores, quartiles, and ranges, and explain their applications. (DOK 2)
1a. Describe the comparison of center and spread within groups and between or across group variation. (DOK 2)
4b. Determine the most appropriate measure to describe a data set, including mean, median, mode, standard deviation, and variance. (DOK 2)
Box plots
Empirical rule
Percentiles

6. Consider a data set of positive values, at least two of which are not equal. Which of the following sample statistics will be changed when each value in this data set is multiplied by a constant whose absolute value is greater than 1?
I. The mean
II. The median
III. The standard deviation
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

7. Variable Score N 50
Mean
1045.7
Median
1024.7
TrMean
1041.9
StDev
221.9
SE Mean
31.4
Minimum
628.9
Maximum
1577.1 Q1
877.7 Q3
1219.5
Some descriptive statistics for a set of test scores are shown above. For this test, a certain student has a standardized score of z = What score did this student receive on the test? A B C D E

8. At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scores 81 on the chemistry final and 84 on the calculus final. Relative to the students in each respective class, in which subject did this student do better?
A. The student did better in chemistry.
B. The student did better in calculus.
C. The student did equally well in each course.
D. There is no basis for comparison, since the subjects are different from each other and are in different departments.
E. There is not enough information for comparison, because the number of students in each class is not known.

9. 12) The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachael is at the 99th percentile in height for adult women, then her height, in inches, is closest to A. 60 B. 62 C. 68 D. 70 E. 74

10. 21. Below, the cumulative frequency plot shows height (in inches) of college basketball players.
What is the interquartile range?
(A) 3 inches (B) 6 inches (C) 25 inches (D) 50 inches (E) None of the above

11. The boxplots above summarize two data sets, A and B
The boxplots above summarize two data sets, A and B. Which of the following must be true?
I. Set A contains more data than Set B.
II. The box of Set A contains more data than the box of Set B.
III. The data in Set A have a large range than the data in Set B.
A. I only
B. III only
C. I and III only
D. II and III only
E. I, II, and III

12. **bell curve, **
Which of the following is the best estimate of the standard deviation of the distribution shown in the figure above?
A. 5
B. 10
C. 30
D. 50
E. 60

13. 25. The back-to-back stemplot on the right shows the number of books read in a year by a random sample of college and high school students. Which of the following statements are true? I. One college student read seven books. II. The college median is equal to the high school median. III. The mean is greater than the median in both groups. (A) I only (B) II only (C) I and III only (D) II and III only (E) I, II, and III College High school

14. A company wanted to determine the health care costs of its employees
A company wanted to determine the health care costs of its employees. A sample of 25 employees were interviewed and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expenses in the sample. Which of the following sample statistics must have remained the same after the correction was made?
A. Mean
B. Median
C. Mode
D. Range
E. Variance

15. Gina’s doctor told her that the standardized score (z-score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is Which of the following is the best interpretation of this standardized score?
A. Gina’s systolic blood pressure is 150.
B. Gina’s systolic blood pressure is 1.50 standard deviation above the average systolic blood pressure of women her age.
C. Gina’s systolic blood pressure is 1.50 above the average systolic blood pressure of women her age.
D. Gina’s systolic blood pressure is 1.50 times the average systolic blood pressure for women her age.
E. Only 1.5% of women Gina’s age have a higher systolic blood pressure than she does.

16. 34. Molly earned a score of 940 on a national achievement test
34. Molly earned a score of 940 on a national achievement test. The mean test score was 850 with a standard deviation of 100. What proportion of students had a higher score than Molly? (Assume that test scores are normally distributed.)
(A) (B) (C) (D) (E) 0.90

17. 5. A sample consists of four observations: {1, 3, 5, 7}
5. A sample consists of four observations: {1, 3, 5, 7}. What is the standard deviation? (A) 2 (B) 2.58 (C) 6 (D) 6.67 (E) None of the above

18. 9. A national achievement test is administered annually to 3rd graders
9. A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test?
(A) 82 (B) 88 (C) 100 (D) 112 (E) 118

19. 13. The stemplot below shows the number of hot dogs eaten by contestants in a recent hot dog eating contest.
Which of the following statements are true?
I. The range is 70. II. The median is 46. III. The mean is 47.
(A) I only (B) II only (C) III only (D) I and II (E) I, II, and III

20. 22. Suppose X and Y are independent random variables
22. Suppose X and Y are independent random variables. The variance of X is equal to 16; and the variance of Y is equal to 9. Let Z = X - Y.
What is the standard deviation of Z?
(A) (B) (C) (D) (E) It is not possible to answer this question, based on the information given.

21. 17. Consider the boxplot below.
Which of the following statements are true?
I. The distribution is skewed right. II. The interquartile range is about 8. III. The median is about 10.
(A) I only (B) II only (C) III only (D) I and II (E) II and III

22. Unit 3: Describing Bivariate Data
3a. Organize data using scatter plots. (DOK 2)
2a. Analyze and describe outliers and shape of the data including linearity and correlation across graphs and data sets. (DOK 2)
2d. Use algebraic concepts and methods to determine mathematical models of best fit. (DOK 2)
4c. Use curve-fitting to make predictions from collected data. (DOK 2)
4d. Explain and defend regression models using correlation coefficients and residuals. (DOK 2)
Explanatory v. response variables
Causation, lurking variables
Extrapolation
Transforming data

23. Consider n pairs of numbers (x1, y1), (x2, y2), … , and (xn, yn)
Consider n pairs of numbers (x1, y1), (x2, y2), … , and (xn, yn). The mean and standard deviation of the x-values are meanx = 5 and sx = 4, respectively. The mean and standard deviation of the y-values are meany = 10 and sy = 10, respectively. Of the following, which could be the least squares regression line?
A. y = x
y = 3.0x
y = x
y = x
y = x

24. Exercise physiologists are investigating the relationship between lean body mass (in kilograms) and the resting metabolic rate (in calories per day) in sedetary males.
Based on the computer output above, which of the following is the best interpretation of the value of the slope of the regression line?
For each individual kilogram of lean body mass, the resting metabolic rate increases on average by calories per day.
For each individual kilogram of lean body mass, the resting metabolic rate increases on average calories per day.
For each individual kilogram of lean body mass, the resting metabolic rate increases on average by calories per day.
For each individual calorie per day for the resting metabolic rate, the lean body mass increases on average by kilograms.
For each additional calorie per day for the resting metabolic rate, the lean body mass increases on average by kilograms.
Predictor Constant Mass
Coef
264.0
22.563
StDev
276.9
6,360 T
0.95
3.55 P
0.363
0.005
S = 144.9
R-SQ = 55.7%
R-Sq(adj) = 51.3%

25. **scatterplot***
In the scatterplot of y versus x shown above, the least squares regression line is superimposed on the plot. Which of the following points has the largest residual? A B C D E

26. Job
No job
Total
Juniors 13 5 18
Seniors 26 39 31 57
A survey of 57 students was conducted to determine whether or not they held jobs outside of school. The two-way table above shows the numbers of students by employment status (job, no job) and class (juniors, seniors). Which of the following best describes the relationship between employment status and class?
A. There appears to be no association, since the same number of juniors and seniors have jobs.
B. There appears to be no association, since close to half of the students have jobs.
C. There appears to be an association, since there are more seniors than juniors in the survey.
D. There appears to be an association, since the proportion of juniors having jobs is much larger than the proportion of seniors having jobs.
E. A measure of association cannot be determined from these data.

27. ***graph***
The equation of the least squares regression line for the points on the scatter plot above is y = x. What is the residual for the point (4, 7)?
2.78
3.00
4.00
4.22
7.00

28. There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model
y = x 9 < x < 25
where x is the number of chirps per minute and y is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?
A. 3.3°F
B °F
C °F
D °F
E °F

29. In the context of regression analysis, which of the following statements are true?
I. A linear transformation increases the linear relationship between variables. II. A logarithmic model is the most effective transformation method. III. A residual plot reveals departures from linearity.
(A) I only (B) II only (C) III only (D) I and II (E) I, II, and III

30. In the context of regression analysis, which of the following statements are true?
I. When the sum of the residuals is greater than zero, the model is nonlinear. II. Outliers reduce the coefficient of determination. III. Influential points reduce the correlation coefficient.
(A) I only (B) II only (C) III only (D) I and II (E) I, II, and III

31. 29. A national consumer magazine reported the following correlations.
The correlation between car weight and car reliability is
The correlation between car weight and annual maintenance cost is 0.20.
Which of the following statements are true?
I. Heavier cars tend to be less reliable. II. Heavier cars tend to cost more to maintain. III. Car weight is related more strongly to reliability than to maintenance cost.
(A) I only (B) II only (C) III only (D) I and II (E) I, II, and III

32. Unit 4: Sampling, Experiments
5c. Analyze sources of bias and sampling error(s) in studies. (DOK 3)
5d. Compare and contrast sampling methods, including simple random sampling, stratified random sampling, and cluster sampling with regard to benefits and trade-offs. (DOK 2)
5b. Explain the generalizability of results and types of conclusions that can be drawn from observational studies, empirical experiments, and surveys. (DOK 2)

33. George and Michelle each claimed to have the better recipe for chocolate chip cookies. They decided to conduct a study to determine whose cookies were really better. They each bakes a batch of cookies using their own recipe. George asked a random sample of his friends to taste his cookies and to complete a questionnaire on their quality. Michelle asked a random sample of her friends to complete the same questionnaire for her cookies. They then compared the results. Which of the following statements about this study is false?
Because George and Michelle have a different population of friends, their sampling procedure makes it difficult to compare the recipes.
Because George and Michelle each used only their own respective recipes, their cooking ability is confounded with the recipe quality.
Because George and Michelle each used only the ovens in their houses, the recipe quality is confounded with the characteristics of the oven.
Because George and Michelle used the same questionnaire, their results will generalize to the combined population of their friends.
Because George and Michelle each baked one batch, there is no replication of the cookie recipes.

34. Each person in a simple random sample of 2,000 received a survey, and 317 people returned their survey. How could nonresponse cause the results of the survey to be biased?
Those who did not respond reduced the sample size, and small samples have more bias then large samples.
Those who did not respond caused a violation of the assumption of independence.
Those who did not respond were indistinguishable from those who did not receive the survey.
Those who did not respond represent a stratum, changing the simple random sample into a stratified random sample.
Those who did not respond may differ in some important way from those who did respond.

35. 2. Under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling?
The population can be divided into a large number of strata so that each stratum only contains a few individuals.
The population can be divided into a small number of strata so that each stratum contains a large number of individuals.
The population can be divided into strata so that the individuals in each stratum are as much alike as possible.
The population can be divided into strata of equal size so that each individual in the population still has the same chance of being selected.

36. The student government at a high school wants to conduct a survey of student opinion. It wants to begin with a simple random sample of 60 students. Which of the following survey methods will produce a simple random sample?
A. Survey the first 60 students to arrive at school in the morning.
B. Survey every 10th student entering the school library until 60 students are surveyed.
C. Use random numbers to choose 15 each of first-year, second-year, third-year, and fourth-year students.
D. Number the cafeteria seats. Use a table of random numbers to choose seats and interview the students until 60 have been interviewed.
E. Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey.

37. 18) The Physician’s Health Study, a large medical experiment involving 22,000 make physicians, attempted to determine whether aspirin could help prevent heart attacks. In this study, one group of about 11,000 physicians took an aspirin every other day, while a control group took a placebo. After several years, it was determined that the physicians in the group that took aspirin had significantly fewer heart attacks than the physicians in the control group. Which of the following statements explains why it would not be appropriate to say that everyone should take an aspirin every other day? I. The study included only physicians, and different results may occur in individuals in other occupations. II. The study included only males and there may be different results for females. III. Although taking aspirin may be helpful in preventing heart attacks, it may be harmful to some other aspects of health. A. I only B. II only C. III only D. II and III only E. I, II, and III

38. To check the effect of cold temperature on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a freezer for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before breakage is measured on each rubber band, and the mean for the cold bands is compared to the mean for the others. Is this a good experimental design?
A. No, because the means are not proper statistics for comparison
B. No, because more than two brands should be used.
C. No, because more temperatures should be used.
D. No, because temperature is confounded with brand.
E. Yes

39. 8) Which of the following can be used to show a cause-and-effect relationship between two variables? A. A census B. A controlled experiment C. An observational study D. A sample survey E. A cross-sectional survey

40. 1. Which of the following statements are true? (Check one)
I. Categorical variables are the same as qualitative variables. II. Categorical variables are the same as quantitative variables. III. Quantitative variables can be continuous variables.
(A) I only (B) II only (C) III only (D) I and II (E) I and III

41. 3. An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car buyers. The list includes 2,500 Ford buyers, 2,500 GM buyers, 2,500 Honda buyers, and 2,500 Toyota buyers. The analyst selects a sample of 400 car buyers, by randomly sampling 100 buyers of each brand.
Is this an example of a simple random sample?
(A) Yes, because each buyer in the sample was randomly sampled. (B) Yes, because each buyer in the sample had an equal chance of being sampled. (C) Yes, because car buyers of every brand were equally represented in the sample. (D) No, because every possible 400-buyer sample did not have an equal chance of being chosen. (E) No, because the population consisted of purchasers of four different brands of car.

42. 11. Which of the following statements are true?
I. A sample survey is an example of an experimental study. II. An observational study requires fewer resources than an experiment. III. The best method for investigating causal relationships is an observational study.
(A) I only (B) II only (C) III only (D) All of the above. (E) None of the above.

43. 19. Which of the following statements are true?
I. Random sampling is a good way to reduce response bias. II. To guard against bias from undercoverage, use a convenience sample. III. Increasing the sample size tends to reduce survey bias. IV. To guard against nonresponse bias, use a mail-in survey.
(A) I only (B) II only (C) III only (D) IV only (E) None of the above.

44. With respect to experimental design, which of the following statements are true?
I. Blinding controls for the effects of confounding. II. Randomization controls for effects of lurking variables. III. Each experimental factor has one treatment level.
(A) I only (B) II only (C) III only (D) All of the above. (E) None of the above.

45. 35. Which of the following statements are true?
I. A completely randomized design offers no control for lurking variables. II. A randomized block design controls for the placebo effect. III. In a matched pairs design, subjects within each pair receive the same treatment.
(A) I only (B) II only (C) III only (D) All of the above. (E) None of the above.

46. Unit 5: Probability
1b. Interpret and apply the concept of the Law of Large Numbers. (DOK 2)
1d. Construct and interpret sample spaces, events, and tree diagrams. (DOK 2)
1e. Identify types of events, including mutually exclusive, independent, and complements. (DOK 1)
1g. Create simulations and experiments that correlate to theoretical probability. (DOK 2)
1i. Apply the concept of a random variable to generate and interpret probability distributions. (DOK 2)
1f. Calculate geometric probability using two-dimensional models, and explain the processes used. (DOK 2)
Multiplication, Addition Rules
Discrete v. continuous variables
Expected value, standard deviation of a random variable
Bernoulli trials
Binomial, geometric, and normal models

47. In a certain game, a fair die is rolled and a player gains 20 points if the die shows a “6.” If the die does not show a “6,” the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player?
A gain of about 1,700 points
A gain of about 583 points
A gain of about 83 points
A gain of about 250 points
A loss of about 300 points

48. A summer resort rents rowboats to customers but does not allow more than four people to a boat. Each boat is designed to hold no more than 800 pounds. Suppose the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and a standard deviation of 10 pounds. Is the weights of individual passengers are independent, what is the probability that a group of four adult male passengers will exceed the acceptable weight limit of 800 pounds?
0.023
0.046
0.159
0.317
0.977

49. 3. All bags entering a research facility are screened
3. All bags entering a research facility are screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm. Fifteen percent of the bags that do not contain forbidden material also trigger the alarm. If 1 out of ever 1,000 bags entering the building contains forbidden material, what is the probability that a bag that triggers the alarm will actually contain forbidden material? A B C D E

50. Acme Corporation manufactures light bulbs
Acme Corporation manufactures light bulbs. The CEO claims that an average Acme light bulb lasts 300 days. A researcher randomly selects 15 bulbs for testing. The sampled bulbs last an average of 290 days, with a standard deviation of 50 days. If the CEO's claim were true, what is the probability that 15 randomly selected bulbs would have an average life of no more than 290 days?
(A) (B) (C) (D) (E) .775

51. 26. Suppose a die is tossed 5 times
26. Suppose a die is tossed 5 times. What is the probability of getting exactly 2 fours?
(A) (B) (C) (D) (E) There is not enough information to answer this question.

52. 6. A card is drawn randomly from a deck of ordinary playing cards
6. A card is drawn randomly from a deck of ordinary playing cards. You win $10 if the card is a spade or an ace. What is the probability that you will win the game?
(A) 1/13 (B) 13/52 (C) 4/13 (D) 17/52 (E) None of the above.

53. 2. A coin is tossed three times
2. A coin is tossed three times. What is the probability that it lands on heads exactly one time?
(A) (B) (C) (D) (E) 0.500

54. 30. Bob is a high school basketball player
30. Bob is a high school basketball player. He is a 70% free throw shooter. That means his probability of making a free throw is What is the probability that Bob makes his first free throw on his fifth shot?
(A) (B) (C) (D) (E)

55. An archer claims that 25% of her shots will be in the center of the target (i.e., a bulls-eye). A sports writer plans to test this claim by sampling 300 shots. If the 300 shots result in 60 or fewer bulls-eyes (i.e., 20% bulls-eyes), the writer will reject the archer's claim.
What is the probability that the sports writer will reject the archer's claim, when it is actually true?
(A) (B) (C) (D) (E) 0.16

56. 10. Which of the following is a discrete random variable?
I. The average height of a randomly selected group of boys. II. The annual number of sweepstakes winners from New York City. III. The number of presidential elections in the 20th century.
(A) I only (B) II only (C) III only (D) I and II (E) II and III

57. 14. The number of adults living in homes on a randomly selected city block is described by the following probability distribution.
Number of adults, x : or more
Probability, P(x) : ???
What is the probability that 4 or more adults reside at a randomly selected home?
(A) (B) (C) (D) (E) There is not enough information to answer this question.

58. 18. The number of adults living in homes on a randomly selected city block is described by the following probability distribution.
Number of adults, x:
Probability, P(x):
What is the standard deviation of the probability distribution?
(A) (B) (C) (D) (E) 2.10

59. The XYZ Office Supplies Company sells calculators in bulk at wholesale prices, as well as individually at retail prices. Next year’s sales depend on market conditions, but executives use probability to find estimates of sales for the coming year. The following tables are estimates for next year’s sales.
Wholesale Sales
Retail Sales
What profit does XYZ Office Supplies Company expect to make for the next year if the profit from each calculator sold is $20 at wholesale and $30 at retail?
A. $10,590
B. $220,700
C. 264,750
D. $833,100
E. $1,002,500
Number Sold
2,000
5,000
10,000
20,000
Probability
0.1
0.3
0.4
0.2
Number Sold
600
1,000
1,500
Probability
0.4
0.5
0.1

60. Joe and Matthew plan to visit a bookstore
Joe and Matthew plan to visit a bookstore. Based on their previous visits to this bookstore, the probability distributions of the number of books they will buy are given below.
Assuming Joe and Matthew make their decisions independently, what is the probability that they will purchase no books on this visit to the bookstore? A B C D E
#of books Joe will buy 1 2
Probability
0.50
0.25
# of books Matthew 1 2
Probability
0.25
0.50

61. Every Thursday, Matt and Dave’s Video Venture has “roll the dice” day
Every Thursday, Matt and Dave’s Video Venture has “roll the dice” day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $ If a two and a two are rolled, a second movie may be rented for $ Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15.
If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total amount paid for these second movies will exceed $15.00?
A. 0 B C D E

62. Circuit boards are assembled by selecting 4 computer chips at random from a large batch of chips. In this batch of chips, 90 percent of the chips are acceptable. Let X denote the number of acceptable chips out of a sample of 4 chips from this batch. What is the least probable value of X?
A. 0
B. 1
C. 2
D. 3
E. 4

63. 4) A manufacturer makes lightbulbs and claims that their reliability is 98 percent. Reliability is defined to be the proportion of nondefective items that are produced over the long term. If the company’s claim is correct, what is the expected number of nondefective lightbulbs in a random sample of 1,000 bulbs? 20
200
960
980
1,000

64. 3) A magazine has 1,620,000 subscribers, of whom 640,000 are woman and 980,000 are men. Thirty percent of the women read the advertisements in the magazine and 50 percent of the men read the advertisements in the magazine. A random sample of 100 subscribers is selected. What is the expected number of subscribers in the sample who read the advertisements? 30 40 42 50 80

65. The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal distribution. Based on a very large sample, it was found that 10 percent of the loaves weighed less then ounces, and 20 percent of the loaves weighed more than ounces. What are the mean and standard deviation of the distribution of the weights of the loaves of bread?
A. μ = 15.82, σ = 0.48
B. μ = 15.82, σ = 0.69
C. μ = 15.87, σ = 0.46
D. μ = 15.93, σ = 0.46
E. μ = 16.00, σ = 0.50

66. Unit 6: Sampling Distributions, Confidence Intervals
Normal distributions
Standard error
Central Limit Theorum
Confidence intervals
Margin of error
Critical values

67. Courtney has constructed a cricket out of paper and rubber bands
Courtney has constructed a cricket out of paper and rubber bands. According to the instructions for making the cricket, when it jumps it will land on its feet half of the time and on its back the other half of the time. In the first 50 jumps, Courtney’s cricket landed on its feet 35 times. In the next 10 jumps, it landed on its feet only twice. Based on this experiment, Courtney can conclude that
The cricket was due to land on its feet less than half the time during the final 10 jumps, since it had landed too often on its feet during the first 50 jumps
A confidence interval for estimating the cricket’s true probability of landing on its feet is wider after the final 10 jumps than it was before the final 10 jumps
A confidence interval for estimating the cricket’s true probability of landing on its feet after the final 10 jumps is exactly the same as it was before the final 10 jumps
A confidence interval for estimating the cricket’s true probability of landing on its feet is more narrow after the final 10 jumps than it was before the final 10 jumps
A confidence interval for estimating the cricket’s true probability of landing on its feet based on the initial 50 jumps does not include 0.2, so there must be a defect in the cricket’s construction to account for the poor showing in the final 10 jumps

68. A large company is considering opening a franchise in St
A large company is considering opening a franchise in St. Louis and wants to estimate the mean household income for the area using a simple random sample of households. Based on information from a pilot study, the company assumes that the standard deviation of household incomes is σ = $7,200. Of the following, which is the least number of households that should be surveyed to obtain an estimate that is within $200 of the true mean household income with 95 percent confidence? 75
1,300
5,200
5,500
7,700

69. 11. The Attila Barbell Company makes bars for weight lifting
11. The Attila Barbell Company makes bars for weight lifting. The weights of the bars are independent and are normally distributed with a mean of 720 ounces (45 pounds) and a standard deviation of 4 ounces. The bars are shipped 10 in a box to the retailers. The weights of the empty boxes are normally distributed with a mean of 320 ounces and a standard deviation of 8 ounces. The weights of the boxes filled with 10 bars are expected to be normally distributed with a mean of 7,520 ounces and a standard deviation of
A ounces
ounces
48 ounces

70. 4. Which of the following statements is true. I
4. Which of the following statements is true? I. When the margin of error is small, the confidence level is high. II. When the margin of error is small, the confidence level is low. III. A confidence interval is a type of point estimate. IV. A population mean is an example of a point estimate. (A) I only (B) II only (C) III only (D) IV only (E) None of the above.

71. 7. Which of the following statements is true?
I. The standard error is computed solely from sample attributes. II. The standard deviation is computed solely from sample attributes. III. The standard error is a measure of central tendency.
(A) I only (B) II only (C) III only (D) I and II (E) I and III

72. 8. Nine hundred (900) high school freshmen were randomly selected for a national survey. Among survey participants, the mean grade-point average (GPA) was 2.7, and the standard deviation was 0.4. What is the margin of error, assuming a 95% confidence level? (A) (B) (C) (D) (E) None of the above.

73. 12. Suppose we want to estimate the average weight of an adult male in Dekalb County, Georgia. We draw a random sample of 1,000 men from a population of 1,000,000 men and weigh them. We find that the average man in our sample weighs 180 pounds, and the standard deviation of the sample is 30 pounds. What is the 95% confidence interval?
(A) (B) (C) (D) (E) None of the above.

74. 15. A major metropolitan newspaper selected a simple random sample of 1,600 readers from their list of 100,000 subscribers. They asked whether the paper should increase its coverage of local news. Forty percent of the sample wanted more local news. What is the 99% confidence interval for the proportion of readers who would like more coverage of local news?
(A) 0.30 to (B) 0.32 to (C) 0.35 to (D) 0.37 to (E) 0.39 to 0.41

75. 16. Suppose a simple random sample of 150 students is drawn from a population of 3000 college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 99% confidence interval for the students' IQ score? (A) (B) (C) (D) (E) None of the above.

76. 20. Twenty-two students were randomly selected from a population of 1000 students. The sampling method was simple random sampling. All of the students were given a standardized English test and a standardized math test. Test results are summarized below.
Student
English
Math
Difference, d
(d - d)2 1 95 90 5 16 2 89 85 4 9 3 76 73 92 91 6 53 7 67 68 -1 8 88 -2 75 78 -3 10 -4 25 11 -5 36
Student
English
Math
Difference, d
(d - d)2 12 85 83 2 1 13 87 4 9 14 15 82 3 16 68 65 17 81 79 18 84 19 71 60 11
100 20 46 47 -1 21 75 77 -2 22 80 -3
Σ(d - d)2 = 270 d = 1
What is the 90% confidence interval for the mean difference between student scores on the math and English tests? Assume that the mean differences are approximately normally distributed.
(A) (B) (C) (D) (E)

77. Ten students were randomly selected from a high school students to take part in a program designed to raise their reading comprehension. Each students took a test before and after completing the program. The mean of the differences between the score after the program and the score before the program is 16. It was decided that all students in the school would take part in this program during the next school year. Let uA denote the mean score after the program and uB denote the mean score before the program for all students in the school. The 95 percent confidence interval estimate of the true mean difference for all students Is (9, 23). Which of the following statements is a correct interpretation of this confidence interval?
A. uA > uB with probability 0.95.
B. uA < uB with probability 0.95.
C. uA is around 23 and uB is around 9.
D. For any uA and uB with (uA – uB) ≥ 14, the sample result is quite likely.
E. For any uA and uB with 9 < (uA – uB) < 23, the sample result is quite likely.

78. A random sample of the costs of repair jobs at a large muffler repair shop produces a mean of $ and a standard deviation of $ If the size of this sample is 40, which of the following is an approximate 90 percent confidence interval for the average cost of a repair at this repair shop?
A. $ /= $4.87
B. $ /= $6.24
C. $ /= $7.45
D. $ /= $30.81
E. $ /= $39.53

79. A 95 percent confidence interval of the form p +/= E will be used to obtain an estimate for an unknown population proportion p. If p is the sample proportion and E is the margin of error, which of the following is the smallest sample size that will guarantee a margin of error of at most 0.08?
A. 25
B. 100
C. 175
D. 250
E. 625

80. A survey was conducted to determine what percentage of college seniors would have chosen to attend a different college if they had known what they know now. In a random sample of 100 seniors, 34 percent indicated that they would have attended a different college. A 90 percent confidence interval for the percentage of all seniors who would have attended a different college is
A % to 43.3%
B % to 42.2%
C % to 41.8%
D % to 37.4%
E % to 36.8%

81. USA Today reported that speed skater Bonnie Blair had “won the USA’s heart , according to a poll conducted on the final day of the 1994 Winter Olympics. When asked who was the hero of the Olympics, 65 percent of the respondents chose Blair, who won five fold medals. The poll of 615 adults, done by telephone, had a margin of error of 4 percent. Which of the following statements best describes what is meant by the 4 percent margin of error?
About 4 percent of adults were expected to change their minds between the time of the poll and its publication in USA Today.
About 4 percent of adults did not have telephones.
About 4 percent of the 615 adults polled refused to answer.
Not all of the 615 adults knew anything about the Olympics.
The difference between the sample percentage and the population percentage is likely to be less than 4 percent.

82. A certain country has 1,000 farms
A certain country has 1,000 farms. Corn is grown on 100 of these farms but on none of the others. In order to estimate the total farm acreage of corn for the country, two plans are proposed.
Plan 1: (a) Sample 20 farms at random
(b) Estimate the mean acreage of corn per farm in a confidence interval
(c) Multiply both ends of the interval by 1,000 to get an interval estimate of the total.
Plan 2: (a) Identify the 100 corn-growing farms.
(b) Sample 20 corn-growing farms at random
(c) Estimate the mean acreage of corn for corn-growing farms in a confidence interval.
(d) Multiply both ends of the interval by 100 to get an interval estimate of the total.
On the basis of the information given, which of the following is the better method for estimating the total farm acreage of corn for the country?
A. Choose plan I over plan II.
B. Choose plan II over plan I.
C. Choose either plan, since both are good and will produce equivalent results.
D. Choose neither plan, since neither estimates the total farm acreage of corn.
E. The plans cannot be evaluated from the information given.

83. Unit 7: Hypothesis Testing
2c. Select and use appropriate statistical methods in decision-making and hypothesis testing. (DOK 2)
Significance levels
Types of errors
P-value

84. The mayor of a large city will run for governor if he believes that more than 30 percent of the voters in the state already support him. He will have a survey firm ask a random sample of n voters whether or not they support him. He will use a large sample test for proportions to test the null hypothesis that the proportion of all voters who support him is 30 percent or less against the alternative that the percentage is higher than 30 percent. Suppose that 35 percent of all voters in the state actually support him. In which of the following situations would the power for this test be highest?
The mayor uses a significance level of 0.01 and n = 250 voters.
The mayor uses a significance level of 0.01 and n = 500 voters.
The mayor uses a significance level of 0.01 and n = 1,000 voters.
The mayor uses a significance level of 0.05 and n = 500 voters.
The mayor uses a significance level of 0.05 and n = 1,000 voters.

85. In hypothesis testing, which of the following statements are always true?
I. The P-value is greater than the significance level. II. The P-value is computed from the significance level. III. The P-value is the parameter in the null hypothesis. IV. The P-value is a test statistic. V. The P-value is a probability.
(A) I only (B) II only (C) III only (D) IV only (E) V only

86. 24. Suppose a researcher conducts an experiment to test a hypothesis
24. Suppose a researcher conducts an experiment to test a hypothesis. If she doubles her sample size, which of the following will increase?
I. The power of the hypothesis test. II. The effect size of the hypothesis test. III. The probability of making a Type II error.
(A) I only (B) II only (C) III only (D) All of the above (E) None of the above

87. The Acme Car Company claims that at most 8% of its new cars have a manufacturing defect. A quality control inspector randomly selects 300 new cars and finds that 33 have a defect. Should she reject the 8% claim? Assume that the significance level is 0.05.
(A) Yes, because the P-value is (B) Yes, because the P-value is (C) No, because the P-value is (D) No, because the P-value is (E) There is not enough information to reach a conclusion.

88. A sports writer hypothesized that Tiger Woods plays better on par 3 holes than on par 4 holes. He reviewed Woods' performance in a random sample of golf tournaments. On the par 3 holes, Woods made a birdie in 20 out of 80 attempts. On the par 4 holes, he made a birdie in 40 out of 200 attempts. How would you interpret this result?
(A) The P-value is < 0.001, very strong evidence that Woods plays better on par 3 holes. (B) The P-value is between and 0.01, strong evidence that Woods plays better on par 3 holes. (C) The P-value is between 0.01 and 0.05, moderate evidence that Woods plays better on par 3 holes. (D) The P-value is between 0.05 and 0.10, some evidence that Woods plays better on par 3 holes. (E) The P-value is > 0.10, little or no support for the notion that Woods plays better on par 3 holes.

89. Which of the following would be a reason to use a one-sample t-test instead of a one-sample z-test?
I. The standard deviation of the population is unknown. II. The null hypothesis involves a continuous variable. III. The sample size is large (greater than 40).
(A) I only (B) II only (C) III only (D) I and II (E) I and III

90. 2) An automobile manufacturer claims that the average gas mileage of a new model is 35 miles per gallon (mpg). A consumer group is skeptical of this claim and thinks the manufacturer may be overstating the average gas mileage. If u represents the true average gas mileage for this new model, which of the following gives the null and alternative hypotheses that the consumer group should test?
H0: μ < 35 mpg, Ha: μ ≥ 35 mpg
H0: μ ≤ 35 mpg, Ha: μ > 35 mpg
H0: μ = 35 mpg, Ha: μ > 35 mpg
H0: μ = 35 mpg, Ha: μ < 35 mpg
H0: μ = 35 mpg, Ha: μ ≠ 35mpg

91. In a test of the null hypothesis H0: u = 10 against the alternative hypothesis Ha: u > 10, a sample from a normal population produces a mean of The z-score for the sample is 2.12 and the p-value is Based on these statistics, which of the following conclusions could be drawn?
A. There is no reason to conclude that u > 10.
B. Due to random fluctuation, 48.3 percent of the time a sample produces a mean larger than 10.
C percent of the time, rejecting the alternative hypothesis is in error.
D percent of the time, the mean is above 10.
E percent of the time, the mean is below 10.

92. The process of producing pain-reliever tablets yields tablets with varying amounts of the active ingredient. It is claimed that the average amount of active ingredient per tablet is at least 200 milligrams. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The mean content of the active ingredient for this sample is milligrams, while the standard deviation is 21 milligrams. What is the approximate p-value for the appropriate test? A B C D E

93. In a test of H0: μ = 8 versus Ha: μ ≠ 8, a sample of size 220 leads to a p-value of Which of the following must be true?
A. A 95% confidence interval for μ calculated from these data will not include μ = 8.
At the 5% level is H0 is rejected, the probability of a Type II error is
The 95% confidence interval for μ calculated from these data will be centered at μ = 8.
The null hypothesis should not be rejected at the 5% level.
The sample size is insufficient to draw a conclusion with 95% confidence.

94. Unit 8
Degrees of freedom
T-values
Chi-squared tests

95. 23. Acme Toy Company sells baseball cards in packages of 100
23. Acme Toy Company sells baseball cards in packages of 100. Three types of players are represented in each package -- rookies, veterans, and All-Stars. The company claims that 30% of the cards are rookies, 60% are veterans, and 10% are All-Stars. Cards from each group are randomly assigned to packages.
Suppose you bought a package of cards and counted the players from each group. What method would you use to test Acme's claim that 30% of the production run are rookies; 60%, veterans; and 10%, All-Stars.
(A) Chi-square goodness of fit test (B) Chi-square test for homogeneity (C) Chi-square test for independence (D) One-sample t test (E) Matched pairs t-test

96. 40. A public opinion poll surveyed a simple random sample of voters
40. A public opinion poll surveyed a simple random sample of voters. Respondents were classified by gender (male or female) and by voting preference (Republican, Democrat, or Independent). Results are shown below.
Voting Preferences
If you conduct a chi-square test of independence, what is the expected frequency count of male Independents?
(A) 40 (B) 50 (C) 60 (D) 180 (E) 270
Republican
Democrat
Independent
Row total
Male
200
150 50
400
Female
250
300
600
Column total
450
100
1000

97. 5) When a virus is placed on a tobacco leaf, small lesions appear on the leaf. To compare the mean number of lesions produced by 2 different strains of virus, one strain is applied to half of each of 8 tobacco leaves, and the other strain is applied to the other half of each leaf. The strain that goes on the right half of the leaf is decided by a coin flip. The lesions that appear on each half are then counted. The data are given below.
What is the number of degrees of freedom associated with the appropriate t-test for testing to see if there is a difference between the mean number of lesions per leaf produced by the two strains? 7 8 11 14 16
Leaf 1 2 3 4 5 6 7 8
Strain 1 31 20 18 17 9 10
Strain 2 14 11

98. 6) Which of the following is a criterion for choosing a t-test rather than a z-test when making an inference about the mean of a population?
The standard deviation of the population is unknown.
The mean of the population is unknown.
The sample may not have been a simple random sample.
The population is not normally distributed.
The sample size is less than 100.

99. A candy company claims that 10 percent of its candies are blue
A candy company claims that 10 percent of its candies are blue. A random sample of 200 of these candies is taken, and 16 are found to be blue. Which of the following tests would be most appropriate for establishing whether the candy company needs to change its claim?
A. Matched pairs t-test
B. One-sample proportion test
C. Two-sample t-test
D. Two-sample proportion z-test
E. Chi-squared test of association

100. Aggressive Nonaggressive Total Same colony 40 (33.5) 9 (15.5) 49
An investigator was studying a territorial species of Central American termites, Nasutitermes corniger. Forty-nine termite pairs were randomly selected; both members of each of these pairs were from the same colony. Fifty-five additional termite pairs were randomly selected; the two members in each of these pairs were from different colonies. The pairs were placed in petri dishes and observed to see whether they exhibited aggressive behavior. The results are shown in the table below.
A Chi-squared test for homogeneity was conducted, resulting in X2 = The expected counts are shown in parentheses in the table. Which of the following sets of statements follows from these results?
X2 is not significant at the 0.05 level.
X2 is significant, 0.01 < p < 0.05; the counts in the table suggest that termite pairs from the same colony are less likely to be aggressive than termite pairs from different colonies.
X2 is significant, 0.01 < p < 0.05; the counts in the table suggest that termite pairs from different colonies are less likely to be aggressive than termite pairs from the same colony.
X2 is significant, p < 0.01; the counts in the table suggest that termite pairs from the same colony are less likely to be aggressive than termite pairs from different colonies.
X2 is significant, p < 0.01; the counts in the table suggest that termite pairs from different colonies are less likely to be aggressive than termite pairs from the same colony.
Aggressive
Nonaggressive
Total
Same colony
40 (33.5)
9 (15.5) 49
Different Colonies
31 (37.5)
24 (17.5) 55 71 33
104