1. Tests of Significance: The Basics BPS chapter 15 © 2006 W.H. Freeman and Company

2. 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) -3.68 oz. c) 4 – 3.68 = 0.32 oz. d) 3.68 – 4 = - 0.32 oz.

3. 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) -3.68 oz. c) 4 – 3.68 = 0.32 oz. d) 3.68 – 4 = - 0.32 oz.

4. 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. The consumer advocate should declare statistical significance only if there is a small probability of a) Observing a sample mean of 3.68 oz. or less when  = 4 oz. b) Observing a sample mean of exactly 3.68 oz. when  = 4 oz. c) Observing a sample mean of 3.68 oz. or greater when  = 4 oz. d) Observing a sample mean of less than 4 oz. when  = 4 oz.

5. 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. The consumer advocate should declare statistical significance only if there is a small probability of a) Observing a sample mean of 3.68 oz. or less when  = 4 oz. b) Observing a sample mean of exactly 3.68 oz. when  = 4 oz. c) Observing a sample mean of 3.68 oz. or greater when  = 4 oz. d) Observing a sample mean of less than 4 oz. when  = 4 oz.

6. 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 0.0048. Her result is a) Statistically significant. b) Not statistically significant.

7. 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 0.0048. Her result is a) Statistically significant. b) Not statistically significant.

8. 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. If the probability described in the previous question is 0.0048, the difference between the observed value and the hypothesized value is a) Small. b) Large.

9. 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. If the probability described in the previous question is 0.0048, the difference between the observed value and the hypothesized value is a) Small. b) Large.

10. 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. If the probability described in the previous question is 0.0048, then the consumer advocate should conclude that the granola is a) Correctly labeled. b) Incorrectly labeled.

11. 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. If the probability described in the previous question is 0.0048, then the consumer advocate should conclude that the granola is a) Correctly labeled. b) Incorrectly labeled.

12. 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)

13. 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)

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

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

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

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

18. 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

19. 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

20. 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

21. 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

22. Conclusions Suppose the P-value for a hypothesis test is 0.304. 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.

23. Conclusions (answer) Suppose the P-value for a hypothesis test is 0.304. 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.

24. Conclusions Suppose the P-value for a hypothesis test is 0.0304. 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.

25. Conclusions (answer) Suppose the P-value for a hypothesis test is 0.0304. 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.

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

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

28. Conclusions Suppose a significance test is being conducted using a significance level of 0.10. 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.

29. Conclusions (answer) Suppose a significance test is being conducted using a significance level of 0.10. 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.

30. 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.

31. 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.

32. 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.

33. 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.

34. 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, 128.86). 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.

35. 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, 128.86). 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.