1. Slide 10 - 1 Active Learning Questions Copyright © 2009 Pearson Education, Inc. For use with classroom response systems Chapter 10 t Tests, Two-Way Tables, and ANOVA

2. Slide 10 - 2 This partial t-table can be used where necessary.

3. Slide 10 - 3 The t distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population. a.True b.False

4. Slide 10 - 4 The t distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population. a.True b.False

5. Slide 10 - 5 A simple random sample from a normal distribution is taken in order to obtain a 95% confidence interval for the population mean. If the sample size is 12, the sample mean is 32, and the sample standard deviation s is 9.5, what is the margin of error? a.0.604 b.1.74 c.5.98 d.6.04

6. Slide 10 - 6 A simple random sample from a normal distribution is taken in order to obtain a 95% confidence interval for the population mean. If the sample size is 12, the sample mean is 32, and the sample standard deviation s is 9.5, what is the margin of error? a.0.604 b.1.74 c.5.98 d.6.04

7. Slide 10 - 7 A 95% confidence interval for the mean of a normal population is found to be 17.6 <  < 20.8. What is the margin of error? a.0.8 b.0.16 c.1.6 d.16

8. Slide 10 - 8 A 95% confidence interval for the mean of a normal population is found to be 17.6 <  < 20.8. What is the margin of error? a.0.8 b.0.16 c.1.6 d.16

9. Slide 10 - 9 The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 6 and the sample standard deviation did not change, how would the margin of error change? a.It would be smaller b.It would be larger c.It would stay the same d.Cannot be determined

10. Slide 10 - 10 The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 6 and the sample standard deviation did not change, how would the margin of error change? a.It would be smaller b.It would be larger c.It would stay the same d.Cannot be determined

11. Slide 10 - 11 A golfer wished to find a ball that would travel more than 200 yards when hit with his 4-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 9 times at the required speed. State the null and alternative hypotheses for this test. a.H 0 :  = 200; H a :  < 200 b.H 0 :  ≥ 200; H a :  < 200 c.H 0 :  = 200; H a :  > 200 d.H 0 :  ≤ 200; H a :  > 200

12. Slide 10 - 12 A golfer wished to find a ball that would travel more than 200 yards when hit with his 4-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 9 times at the required speed. State the null and alternative hypotheses for this test. a.H 0 :  = 200; H a :  < 200 b.H 0 :  ≥ 200; H a :  < 200 c.H 0 :  = 200; H a :  > 200 d.H 0 :  ≤ 200; H a :  > 200

13. Slide 10 - 13 Data from the test in the previous example resulted in a sample mean of 206.8 yards with a sample standard deviation of 4.6 yards. Assuming normality, find the value of the t statistic. Recall the mean being tested was 200 yards with 9 swings by the robot. a.–4.435 b.–13.304 c.4.435 d.13.304

14. Slide 10 - 14 Data from the test in the previous example resulted in a sample mean of 206.8 yards with a sample standard deviation of 4.6 yards. Assuming normality, find the value of the t statistic. Recall the mean being tested was 200 yards with 9 swings by the robot. a.–4.435 b.–13.304 c.4.435 d.13.304

15. Slide 10 - 15 Data from the test in the previous example resulted in a sample mean of 206.8 yards with a sample standard deviation of 4.6 yards. Assuming normality, find the critical value at the 0.05 significance level. Recall the mean being tested was 200 yards with 9 swings by the robot. a.2.306 b.2.262 c.1.833 d.1.860

16. Slide 10 - 16 Data from the test in the previous example resulted in a sample mean of 206.8 yards with a sample standard deviation of 4.6 yards. Assuming normality, find the critical value at the 0.05 significance level. Recall the mean being tested was 200 yards with 9 swings by the robot. a.2.306 b.2.262 c.1.833 d.1.860

17. Slide 10 - 17 For the previous example, determine the results of a hypothesis test. a.Reject the null hypothesis. The data provide sufficient evidence that the average distance is greater than 200 yards. b.Accept the null hypothesis. The data provide sufficient evidence that the average distance is greater than 200 yards. c.Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 200 yards. d.Accept the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 200 yards.

18. Slide 10 - 18 For the previous example, determine the results of a hypothesis test. a.Reject the null hypothesis. The data provide sufficient evidence that the average distance is greater than 200 yards. b.Accept the null hypothesis. The data provide sufficient evidence that the average distance is greater than 200 yards. c.Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 200 yards. d.Accept the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 200 yards.

19. Slide 10 - 19 One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed. Find the expected value of a male who is not colorblind. a.6.0b.54.0 c.4.0d.36.0 ColorblindNot ColorblindTotal Male95160 Female13940 Total1090100

20. Slide 10 - 20 One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed. Find the expected value of a male who is not colorblind. a.6.0b.54.0 c.4.0d.36.0 ColorblindNot ColorblindTotal Male95160 Female13940 Total1090100

21. Slide 10 - 21 For the previous example, here are the expected values. Find the value of the  2 statistic. a.1.389b.1.0 c.4.167d.4.0 ColorblindNot ColorblindTotal Male6.054.060 Female4.036.040 Total10.090.0100

22. Slide 10 - 22 For the previous example, here are the expected values. Find the value of the  2 statistic. a.1.389b.1.0 c.4.167d.4.0 ColorblindNot ColorblindTotal Male6.054.060 Female4.036.040 Total10.090.0100

23. Slide 10 - 23 State the null and alternative hypothesis for the test associated with the data in the previous example. a.H 0 : Colorblindness and gender are independent H a : Colorblindness and gender are related b.H 0 : Colorblindness and gender are dependent H a : Colorblindness and gender are not related c.H 0 : Colorblindness and gender are related H a : Colorblindness and gender are independent d.H 0 : Colorblindness and gender are nor related H a : Colorblindness and gender are dependent

24. Slide 10 - 24 State the null and alternative hypothesis for the test associated with the data in the previous example. a.H 0 : Colorblindness and gender are independent H a : Colorblindness and gender are related b.H 0 : Colorblindness and gender are dependent H a : Colorblindness and gender are not related c.H 0 : Colorblindness and gender are related H a : Colorblindness and gender are independent d.H 0 : Colorblindness and gender are nor related H a : Colorblindness and gender are dependent

25. Slide 10 - 25 The critical value of  2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the  2 statistic in the previous example had been 4.216, state your conclusion about the relationship between gender and colorblindness. a.Reject H 0. There is insufficient evidence to support the claim that colorblindness and gender are related. b.Accept H 0. There is insufficient evidence to support the claim that colorblindness and gender are related. c.Reject H 0. There is sufficient evidence to support the claim that colorblindness and gender are related. d.Accept H 0. There is sufficient evidence to support the claim that colorblindness and gender are related.

26. Slide 10 - 26 The critical value of  2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the  2 statistic in the previous example had been 4.216, state your conclusion about the relationship between gender and colorblindness. a.Reject H 0. There is insufficient evidence to support the claim that colorblindness and gender are related. b.Accept H 0. There is insufficient evidence to support the claim that colorblindness and gender are related. c.Reject H 0. There is sufficient evidence to support the claim that colorblindness and gender are related. d.Accept H 0. There is sufficient evidence to support the claim that colorblindness and gender are related.

27. Slide 10 - 27 The data given were analyzed using one-way analysis or variance. The purpose of the analysis is to: a.determine whether the groups A, B, and C are independent. b.test the hypothesis that the population means of the three groups are equal. c.test the hypothesis that the population variances of the three groups are equal. d.test the hypothesis that the sample means of the three groups are equal. ABC 292719 262321 252925 282117

28. Slide 10 - 28 The data given were analyzed using one-way analysis or variance. The purpose of the analysis is to: a.determine whether the groups A, B, and C are independent. b.test the hypothesis that the population means of the three groups are equal. c.test the hypothesis that the population variances of the three groups are equal. d.test the hypothesis that the sample means of the three groups are equal. ABC 292719 262321 252925 282117

29. Slide 10 - 29 Here are the results of the ANOVA for the previous example (question on next slide): SUMMARY GroupsCountSumsAverageVariance A4108273.33333 B41002513.33333 C48220.511.66667 SUMMARY Source of VariationSSdfMSFP-valueF crit Between Groups88.7244.34.6940.04014.25649 Within Groups8599.4 Total173.711

30. Slide 10 - 30 If the significance level for the test is 0.05, which conclusion below is correct? a.The data do not provide sufficient evidence to conclude that the population means of groups A, B, and C are related. b.The data do not provide sufficient evidence to conclude that the population means of groups A, B, and C are different. c.The data do not provide sufficient evidence to conclude that the population variances of groups A, B, and C are different. d.The data do not provide sufficient evidence to conclude that the population means of groups A, B, and C are different.

31. Slide 10 - 31 If the significance level for the test is 0.05, which conclusion below is correct? a.The data do not provide sufficient evidence to conclude that the population means of groups A, B, and C are related. b.The data do not provide sufficient evidence to conclude that the population means of groups A, B, and C are different. c.The data do not provide sufficient evidence to conclude that the population variances of groups A, B, and C are different. d.The data do not provide sufficient evidence to conclude that the population means of groups A, B, and C are different.