Introduction to Inferece BPS chapter 14 © 2010 W.H. Freeman and Company

Statistical Inference What is statistical inference on  ? a) Drawing conclusions about a population mean based on information contained in a sample. b) Drawing conclusions about a sample mean based on information contained in a population. c) Drawing conclusions about a sample mean based on the measurements in that sample. d) Selecting a set of data from a large population.

Statistical Inference (answer) What is statistical inference on  ? a) Drawing conclusions about a population mean based on information contained in a sample. b) Drawing conclusions about a sample mean based on information contained in a population. c) Drawing conclusions about a sample mean based on the measurements in that sample. d) Selecting a set of data from a large population.

Inference The conditions for doing inference on  using the standard normal distribution do NOT include: a) A simple random sample of size n. b) A normal population or sample size large enough to apply the Central Limit Theorem. c) A known value of . d) A known value of .

Inference (answer) The conditions for doing inference on  using the standard normal distribution do NOT include: a) A simple random sample of size n. b) A normal population or sample size large enough to apply the Central Limit Theorem. c) A known value of . d) A known value of .

Inference Why do we need a normal population or large sample size to do inference on  ? a) So that the sampling distribution of is normal or approximately normal. b) So that the distribution of the sample data is normal or approximately normal. c) So that equals . d) So that  is known.

Inference (answer) Why do we need a normal population or large sample size to do inference on  ? a) So that the sampling distribution of is normal or approximately normal. b) So that the distribution of the sample data is normal or approximately normal. c) So that equals . d) So that  is known.

Inference True or False: The condition of known  is often met even when  is unknown. a) True b) False

Inference (answer) True or False: The condition of known  is often met even when  is unknown. a) True b) False

Confidence Intervals The purpose of a confidence interval for  is a) To give a range of reasonable values for the level of confidence. b) To give a range of reasonable values for the sample mean. c) To give a range of reasonable values for the population mean. d) To give a range of reasonable values for the difference between the sample mean and the population mean.

Confidence Intervals (answer) The purpose of a confidence interval for  is a) To give a range of reasonable values for the level of confidence. b) To give a range of reasonable values for the sample mean. c) To give a range of reasonable values for the population mean. d) To give a range of reasonable values for the difference between the sample mean and the population mean.

Confidence intervals The confidence interval formula for  does NOT include a) The sample mean. b) The population standard deviation. c) The z * value for specified level of confidence. d) The margin of error. e) The sample size. f) The population size.

Confidence intervals (answer) The confidence interval formula for  does NOT include a) The sample mean. b) The population standard deviation. c) The z * value for specified level of confidence. d) The margin of error. e) The sample size. f) The population size.

Confidence intervals What do we hope to capture within a confidence interval? a) The unknown confidence level. b) The unknown parameter. c) The unknown statistic. d) The parameter estimate. e) The margin of error. f) The sample size.

Confidence intervals (answer) What do we hope to capture within a confidence interval? a) The unknown confidence level. b) The unknown parameter. c) The unknown statistic. d) The parameter estimate. e) The margin of error. f) The sample size.

Confidence intervals What are the three components of a confidence interval? a) Estimate of confidence level, sample size, and margin of error. b) Mean of sample statistic, confidence level, and margin of error. c) Estimate of population parameter, confidence level, and margin of error.

Confidence intervals (answer) What are the three components of a confidence interval? a) Estimate of confidence level, sample size, and margin of error. b) Mean of sample statistic, confidence level, and margin of error. c) Estimate of population parameter, confidence level, and margin of error.

Confidence intervals Consider the following statement. “The average time a local company takes to process new insurance claims is 9 to 11 days.” Which of the following statements about this confidence interval interpretation is valid? a) This interpretation is incorrect because there is no statement of the true parameter in words. b) This interpretation is incorrect because the interval is not reported. c) This interpretation is incorrect because the confidence level is not reported. d) This is a correct reporting of the confidence interval.

Confidence intervals (answer) Consider the following statement. “The average time a local company takes to process new insurance claims is 9 to 11 days.” Which of the following statements about this confidence interval interpretation is valid? a) This interpretation is incorrect because there is no statement of the true parameter in words. b) This interpretation is incorrect because the interval is not reported. c) This interpretation is incorrect because the confidence level is not reported. d) This is a correct reporting of the confidence interval.

Confidence intervals A very large school district in Connecticut wants to estimate the average SAT score of this year’s graduating class. The district takes a simple random sample of 100 seniors and calculates the 95% confidence interval for the graduating students’ average SAT score at 505 to 520 points. For the sample of 100 graduating seniors, 95% of their SAT scores were between 505 and 520 points. a) Correct interpretation of interval. b) Incorrect interpretation of interval.

Confidence intervals (answer) A very large school district in Connecticut wants to estimate the average SAT score of this year’s graduating class. The district takes a simple random sample of 100 seniors and calculates the 95% confidence interval for the graduating students’ average SAT score at 505 to 520 points. For the sample of 100 graduating seniors, 95% of their SAT scores were between 505 and 520 points. a) Correct interpretation of interval. b) Incorrect interpretation of interval.

Confidence intervals The probability that a 90% confidence interval for a population mean captures  is a) 0. b) c) 1. d) Either 0 or 1—we do not know which.

Confidence intervals (answer) The probability that a 90% confidence interval for a population mean captures  is a) 0. b) c) 1. d) Either 0 or 1—we do not know which.

Confidence intervals What is the confidence level in a confidence interval for  ? a) The percentage of confidence intervals produced by the procedure that contain . b) The probability that a specific confidence interval contains . c) The percentage of confidence interval procedures that will create an interval that contains .

Confidence intervals (answer) What is the confidence level in a confidence interval for  ? a) The percentage of confidence intervals produced by the procedure that contain . b) The probability that a specific confidence interval contains . c) The percentage of confidence interval procedures that will create an interval that contains .

Margin of error Increasing the confidence level will a) Increase the margin of error. b) Decrease the margin of error.

Margin of error (answer) Increasing the confidence level will a) Increase the margin of error. b) Decrease the margin of error.

Margin of error Increasing the sample size will a) Increase the margin of error. b) Decrease the margin of error.

Margin of error (answer) Increasing the sample size will a) Increase the margin of error. b) Decrease the margin of error.

Margin of error Increasing the standard deviation will a) Increase the margin of error. b) Decrease the margin of error.

Margin of error (answer) Increasing the standard deviation will a) Increase the margin of error. b) Decrease the margin of error.

Margin of error Which of the following components of the margin of error in a confidence interval for  does a researcher NOT have the chance to select? a) Confidence level. b) Sample size. c) Population standard deviation.

Margin of error (answer) Which of the following components of the margin of error in a confidence interval for  does a researcher NOT have the chance to select? a) Confidence level. b) Sample size. c) Population standard deviation.

Statistical significance A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews. What is the size of the observed effect? a) 3.68 oz. b) oz. c) 4 – 3.68 = 0.32 oz. d) 3.68 – 4 = oz.

Statistical significance (answer) A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews. What is the size of the observed effect? a) 3.68 oz. b) oz. c) 4 – 3.68 = 0.32 oz. d) 3.68 – 4 = oz.

Statistical significance A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews. Suppose the consumer advocate computes the probability described in the previous question to be Her result is a) Statistically significant. b) Not statistically significant.

Statistical significance (answer) A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews. Suppose the consumer advocate computes the probability described in the previous question to be Her result is a) Statistically significant. b) Not statistically significant.

Stating hypotheses A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews. What alternative hypothesis does she want to test? a) b) c) d) e) f)

Stating hypotheses (answer) A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews. What alternative hypothesis does she want to test? a) b) c) d) e) f)

Statistical significance We reject the null hypothesis whenever a) P-value > . b) P-value  . c) P-value  . d) P-value  .

Statistical significance (answer) We reject the null hypothesis whenever a) P-value > . b) P-value  . c) P-value  . d) P-value  .

Statistical significance The significance level is denoted by a)  b)  c)  d) P-value

Statistical significance (answer) The significance level is denoted by a)  b)  c)  d) P-value

Statistical significance Which of the following is a conservative choice for significance level? a) 0 b) 0.01 c) 0.25 d) 0.50 e) 0.75 f) 1

Statistical significance (answer) Which of the following is a conservative choice for significance level? a) 0 b) 0.01 c) 0.25 d) 0.50 e) 0.75 f) 1

Calculating P-values To calculate the P-value for a significance test, we need to use information about the a) Sample distribution b) Population distribution c) Sampling distribution of

Calculating P-values (answer) To calculate the P-value for a significance test, we need to use information about the a) Sample distribution b) Population distribution c) Sampling distribution of

Conclusions Suppose the P-value for a hypothesis test is Using  = 0.05, what is the appropriate conclusion? a) Reject the null hypothesis. b) Reject the alternative hypothesis. c) Do not reject the null hypothesis. d) Do not reject the alternative hypothesis.

Conclusions (answer) Suppose the P-value for a hypothesis test is Using  = 0.05, what is the appropriate conclusion? a) Reject the null hypothesis. b) Reject the alternative hypothesis. c) Do not reject the null hypothesis. d) Do not reject the alternative hypothesis.

Conclusions Suppose the P-value for a hypothesis test is Using  = 0.05, what is the appropriate conclusion? a) Reject the null hypothesis. b) Reject the alternative hypothesis. c) Do not reject the null hypothesis. d) Do not reject the alternative hypothesis.

Conclusions (answer) Suppose the P-value for a hypothesis test is Using  = 0.05, what is the appropriate conclusion? a) Reject the null hypothesis. b) Reject the alternative hypothesis. c) Do not reject the null hypothesis. d) Do not reject the alternative hypothesis.

P-value True or False: The P-value should be calculated BEFORE choosing the significance level for the test. a) True b) False

P-value (answer) True or False: The P-value should be calculated BEFORE choosing the significance level for the test. a) True b) False

Conclusions Suppose a significance test is being conducted using a significance level of If a student calculates a P-value of 1.9, the student a) Should reject the null hypothesis. b) Should fail to reject the null hypothesis. c) Made a mistake in calculating the P-value.

Conclusions (answer) Suppose a significance test is being conducted using a significance level of If a student calculates a P-value of 1.9, the student a) Should reject the null hypothesis. b) Should fail to reject the null hypothesis. c) Made a mistake in calculating the P-value.

Stating hypotheses If we test H 0 :  = 40 vs. H a :  < 40, this test is a) One-sided (left tail). b) One-sided (right tail). c) Two-sided.

Stating hypotheses (answer) If we test H 0 :  = 40 vs. H a :  < 40, this test is a) One-sided (left tail). b) One-sided (right tail). c) Two-sided.

Stating hypotheses If we test H 0 :  = 40 vs. H a :   40, this test is a) One-sided (left tail). b) One-sided (right tail). c) Two-sided.

Stating hypotheses (answer) If we test H 0 :  = 40 vs. H a :   40, this test is a) One-sided (left tail). b) One-sided (right tail). c) Two-sided.

Using CIs to test A researcher is interested in estimating the mean yield (in bushels per acre) of a variety of corn. From her sample, she calculates the following 95% confidence interval: (118.74, ). Her colleague wants to test (at  = 0.05) whether or not the mean yield for the population is different from 120 bushels per acre. Based on the given confidence interval, what can the colleague conclude? a) The mean yield is different from 120 and it is statistically significant. b) The mean yield is not different from 120 and it is statistically significant. c) The mean yield is different from 120 and it is not statistically significant. d) The mean yield is not different from 120 and it is not statistically significant.

Using CIs to test (answer) A researcher is interested in estimating the mean yield (in bushels per acre) of a variety of corn. From her sample, she calculates the following 95% confidence interval: (118.74, ). Her colleague wants to test (at  = 0.05) whether or not the mean yield for the population is different from 120 bushels per acre. Based on the given confidence interval, what can the colleague conclude? a) The mean yield is different from 120 and it is statistically significant. b) The mean yield is not different from 120 and it is statistically significant. c) The mean yield is different from 120 and it is not statistically significant. d) The mean yield is not different from 120 and it is not statistically significant.