Question

1. A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.05 significance level for both parts.

		Treatment	Placebo
	μ	μ1	μ2
	n	30	36
	x	2.31	2.67
	s	0.92	0.65

a. Test the claim that the two samples are from populations with the same mean.

What are the null and alternative​ hypotheses?

The test​ statistic, t, is ___

The​ P-value is ___

b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

2. A study was done on proctored and nonproctored tests. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.05 significance level for both parts.

	Proctored	Nonproctored
μ	μ1	μ2
n	32	35
x	77.39	84.85
s	11.88	21.23

a. Test the claim that students taking non proctored tests get a higher mean score than those taking proctored tests.

What are the null and alternative​ hypotheses?

The test​ statistic, t, is ___

The​ P-value is ___

b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

3. A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.01 significance level for both parts.

	Men	Women
μ	μ1	μ2
n	11	59
x	97.58 degrees°F	97.31 degrees°F
s	0.77 degrees°F	0.73 degrees°F

a. Test the claim that men have a higher mean body temperature than women.

What are the null and alternative​ hypotheses?

The test​ statistic, t, is ___

The​ P-value is ___

b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

4. Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a

0.01 significance level for both parts.

	Male BMI	Female BMI
μ	μ1	μ2
n	50	50
x	28.3784	25.2079
s	8.961292	4.132129

a. Test the claim that males and females have the same mean body mass index​ (BMI).

What are the null and alternative​ hypotheses

The test​ statistic, t, is ___

The​ P-value is ___

b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

Answer 1

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