1. When You See (This), You Think (That)
AP Stats Exam Review

2. Describe the distribution
When you see….
Describe the distribution

3. You think S O C Shape (say what the shape is) Outliers
(Note: Report results with and without outliers if any exist) C
Center
Mean and Median (and maybe mode--think if it’s important based on context)
Spread
Range, Standard Deviation, IQR (REMEMBER HOW TO CALCULATE IT!!!!!)

4. When you see….
Five Number Summary

5. You think…. Minimum Lower Quartile (Q1) Median Upper Quartile (Q3)
Maximum

6. When you see….
Are there any outliers?

7. You think….
THE OUTLIER TEST!

8. Transforming a distribution
When you see….
Transforming a distribution

9. You think….
Adding/subtracting a constant to every value of a distribution:
Shifts measures of center by that amount
Does not change measures of spread
Does not change shape of the distribution
Multiplying/dividing a constant to every value of a distribution:
Multiplies/Divides measures of center by that constant
Multiplies/Divides most measures of spread by that constant (range, IQR, standard deviation)
Does not change the shape of the distribution

10. When you see….
Normally distributed OR
Normal Distribution

11. You think….
DRAW A PICTURE!

12. Describe the association in the scatterplot
When you see….
Describe the association in the scatterplot

13. You think….
Form
Strength
Direction
Are there any outliers?

14. When you see….
Residual

15. You think….
Residual = Actual - Predicted

16. Interpret the slope of the least- squares line
When you see….
Interpret the slope of the least- squares line

17. You think….
For every (unit increase in the x variable), the predicted (y variable) increases/decreases by (coefficient for slope).

18. Residual Plot for a Linear Regression
When you see….
Residual Plot for a Linear Regression

19. NO PATTERN MEANS NO PROBLEM!
You think….
NO PATTERN MEANS NO PROBLEM!

20. Coefficient of Determination (R-squared)
When you see….
Coefficient of Determination (R-squared)

21. You think…. Two possible explanations:
_____% of the variation in (response variable) can be explained by the variation in (predictor variable).
_____% of the variation in (response variable) can be accounted for by the linear relationship with (predictor variable).

22. When you see….
Perform A Simulation

23. You think….
Specify how to model a component outcome using equally likely/random digits.
Specify how to simulate trials.
Pull it all together to run the simulation.
Analyze the response variable.

24. Are the two events independent?
When you see….
Are the two events independent?

25. You think….
Show that

26. Probability Distribution OR Probability Model
When you see….
Probability Distribution OR
Probability Model

27. List of every outcome and its probability
When you think….
List of every outcome and its probability

28. Expected Value of a Probability Distribution
When you see….
Expected Value of a Probability Distribution

29. You think….

30. Standard Deviation of a Probability Distribution
When you see….
Standard Deviation of a Probability Distribution

31. You think….

32. Transforming a Random Variable
When you see….
Transforming a Random Variable

33. You think…. Adding/subtracting a constant to a random variable:
Shifts the expected value by that amount
Does not change measures of spread (both standard deviation and variance)
Multiplying/dividing a constant to a random variable:
Multiplies/Divides measures of center by that constant
Multiplies/Divides most measures of spread by that constant (range, IQR, standard deviation)
Multiplies/Divides variance by the squared constant

34. Adding/Subtracting Random Variables
When you see….
Adding/Subtracting Random Variables

35. You think….
Variances always add!

36. Binomial Distribution
When you see….
Binomial Distribution

37. You think….
Check assumptions/conditions (BINS!)
Use binompdf(n,p,x) or binomcdf(n,p,x) in your calculator

38. When you see….
“What is the probability that the first success happens before the _____th trial?”

39. Geometric probability distribution!
You think….
Geometric probability distribution!
Use geometricpdf(p, x) or geometriccdf(p, x) in your calculator

40. When you see….
“Can you approximate this binomial distribution with a normal distribution?”

41. Check np and nq (they should be at least 10)
You think….
Check np and nq (they should be at least 10)

42. Sampling Distribution
When you see….
Sampling Distribution

43. You think….

44. Construct a confidence interval
When you see….
Construct a confidence interval

45. You think….

46. When you see….
Margin of Error

47. You think….
Margin of Error = Critical Value x Standard Error

48. “Is there evidence that…”
When you see….
“Test the claim that…” OR
“Is there evidence that…”

49. Create a Null and an Alternative – be sure to define all variables
You think….
Hypothesis Testing
Create a Null and an Alternative – be sure to define all variables

50. What does a p-value even mean in the first place?
When you see….
What does a p-value even mean in the first place?

51. You think….
A p-value is the probability of the observed result occurring GIVEN THAT THE NULL HYPOTHESIS IS TRUE (not the other way around).

52. Type I and Type II Errors
When you see….
Type I and Type II Errors

53. You think…. Type I Error The null hypothesis is true but you reject it
Also known as a false positive
α is the Type I Error Probability
Type II Error
The null hypothesis is false but you fail to reject it
β is the Type II Error Probability

54. Power of a Hypothesis Test
When you see….
Power of a Hypothesis Test

55. You think….
Power = 1 - β
Increasing α will decrease β (and vice versa)
Things that increase power:
Increasing sample size
Increasing α
Decreasing β

56. Degrees of Freedom for Inferences
When you see….
Degrees of Freedom for Inferences

57. You think…. One-Proportion and Two-Proportion: None! One-Sample: n - 1
Two-Sample: (from calculator or technology)
Paired Data: # of differences - 1
Chi-Square Goodness-of-Fit: # of categories - 1
Chi-Square Test for Independence/Homogeneity: (R - 1)(C - 1)
Regression: n - 2

58. Assumptions/Conditions for One-Proportion Inferences
When you see….
Assumptions/Conditions for One-Proportion Inferences

59. You think…. Independent Random/Representative 10% Condition
At least 10 successes and 10 failures (np≥10 and nq≥10)

60. Assumptions/Conditions for Two-Proportion Inferences
When you see….
Assumptions/Conditions for Two-Proportion Inferences

61. You think…. Independent Are data values independent of each other?
Are the two groups independent of each other?
Randomization—check either
Data are sampled or generated at random OR Data are representative of population
10% Condition
Total sample size is no more than 10% of the population size
Enough successes and failures
At least 10 successes and 10 failures for each group
Based on the pooled proportion (but OK if each group has at least 10 successes/failures)

62. Hypothesis Test for the Difference of Two Proportions
When you see….
Hypothesis Test for the Difference of Two Proportions

63. You think…. I should use a pooled proportion!
I should calculate the standard error by using the pooled proportion for both groups!
I shouldn’t use the pooled proportion if I want to calculate a confidence interval.
I should NOT flip out right now.

64. Assumptions/Conditions for One-Sample Inferences for a Mean
When you see….
Assumptions/Conditions for One-Sample Inferences for a Mean

65. You think…. Independent Random/Representative 10% Condition
Nearly Normal Condition (check histogram)

66. Hypothesis Test or Confidence Interval for the Difference of Two Means
When you see….
Hypothesis Test or Confidence Interval for the Difference of Two Means

67. You think….
Should I pair data?

68. When you see….
Assumptions/Conditions for Two-Sample Inferences for a Difference in Means

69. You think…. Data are independent
Data in each group are independent of each other
The two groups are independent of each other
Random/Representative
Data in each group are selected from a random or are representative of the population
10% Condition
Data are no more than 10% of the population
Data in each group come from a distribution that is unimodal and symmetric (AKA the nearly normal condition)

70. Assumptions/Conditions for Paired Data (Mean of Differences)
When you see….
Assumptions/Conditions for Paired Data (Mean of Differences)

71. You think…. Data are independent
Differences (usually people) are independent of each other
Random/Representative
Pairs are selected from a random or are representative of the population
10% Condition
Data are no more than 10% of the population
Differences histogram is unimodal and symmetric (AKA the nearly normal condition)

72. Assumptions/Conditions for Chi-Square Goodness-of-Fit Test
When you see….
Assumptions/Conditions for Chi-Square Goodness-of-Fit Test

73. You think….
Data are counts for the categories of a categorical variable
Counts in cells are independent of each other
Data are either randomly selected or representative of the population of interest
Expected counts should be at least 5 individuals in each cell (use null model to get expected counts)
Data are less than 10% of the population

74. When you see….
Assumptions/Conditions for Chi-Square Test for Independence/Homogeneity

75. You think….
Data are counts for the categories of a categorical variable
Counts in cells are independent of each other
Data are either randomly selected or representative of the population of interest
Expected counts should be at least 5 individuals in each cell (use null model to get expected counts)
Data are less than 10% of the population

76. Assumptions/Conditions for Inferences with Regression
When you see….
Assumptions/Conditions for Inferences with Regression

77. You think…. Linear Enough Independence Normal Population Assumption
Check is scatterplot is linear enough
If not linear enough, considering re-expressing data to make scatterplot more nearly linear
Independence
Individual observations are independent of each other
Check the 10% condition when sampling without replacement
Normal Population Assumption
Residuals follow a normal model (make sure residual plot for unimodal and symmetric)
Can also check normal probability plot for normality
Equal Variance Assumption
Check residual plot for patterns
NO PATTERN, NO PROBLEM! (But don’t get too crazy with looking for patterns)
Random
Data come from a well-designed random sample or randomized experiment