Question #1

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 0.05 significance level for both parts.

	Male BMI	Female BMI
	1	2
n	49	49
_ x	27.8851	24.4357
s	7.460256	4.331297

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

What are the null and alternative hypotheses?

A. H₀: ₁ = ₂

H₁: _{1 2}

B. H₀: ₁ = ₂

H₁: ₁ > ₂

C. H₀: _{1 2}

H₁: ₁ < ₂

D. H₀: _{1 2}

H₁: ₁ < ₂

The test statistic, t, is _____________. (Round to two decimal places as needed.)

The P-value is ___________. (Round to three decimal places as needed.)

State the conclusion for the test.

A. Reject the null hypothesis. There isnot sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

B. Failtoreject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

C. Failtoreject the null hypothesis. There isnot sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

D. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI.

__________ < _{1 2} < ____________

(Round to three decimal places as needed.)

Does the confidence interval support the conclusion of the test?

_________ ( A. No, B. Yes ) because the confidence interval contains _____________ ( A. only positive values, B. zero, C. only negative values)

Question #3

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 286 people over the age of 55, 70 dream in black and white, and among 281 people under the age of 25, 13 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesis test?

A. H₀: p₁ = p₂

H₁: p₁ p₂

B. H₀: p₁ = p₂

H₁: p₁ < p₂

C. H₀: p₁ p₂

H₁: p₁ = p₂

D. H₀: p₁ p₂

H₁: p₁ p₂

E. H₀: p₁ p₂

H₁: p₁ p₂

F. H₀: p₁ = p₂

H₁: p₁ > p₂

Identify the test statistic.

z= ______________

(Round to two decimal places as needed.)

Identify the P-value.

P-value= ____________

(Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test?

The P-value is ___________ ( A. less than, B. greater than ) the significance level of =0.05,

so ____________ ( A. fail to reject, B. reject ) the null hypothesis. There is ___________ ( A. insufficient, B. sufficient ) evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25.

b. Test the claim by constructing an appropriate confidence interval.

The 90% confidence interval is _________ < ( p₁ p₂ ) < ___________.

(Round to three decimal places as needed.)

What is the conclusion based on the confidence interval?

Because the confidence interval limits ______________ ( A. include, B. do not include )0, it appears that the two proportions are ___________ ( A. not equal B. equal ) Because the confidence interval limits ____________ ( A. only negative, B. positive and negative, C. only positive ) values, it appears that the proportion of people over 55 who dream in black and white is _________________ ( A. not significantly different from, B. greater than, C. lesser than ) the proportion for those under 25.

c. An explanation for the results is that those over the age of 55 grew up exposed to media that was displayed in black and white. Can these results be used to verify that explanation?

A. Yes. The results can be used to verify the given explanation because the difference in proportions is practically significant.

B. Yes. The results can be used to verify the given explanation because the difference in proportions is statistically significant.

C. No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference.

D. No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results are not statistically significant enough to verify the cause of such a difference.

Question #5

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 256 vinyl gloves, 60% leaked viruses. Among 256 latex gloves,

12% leaked viruses. Using the accompanying display of the technology results, and using a

0.10 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1.

View the technology results.

Technology results

Pooled proportion: 0.36

Test statistic, z: 11.3427

Critical z: 1.2816

P-value: 0.0000

80% Confidence interval:

0.4334963 < p₁ p₂ < 0.5274412

What are the null and alternative hypotheses?

A. H₀: p₁ > p₂

H₁: p₁ = p₂

B. H₀: p₁ < p₂

H₁: p₁ = p₂

C. H₀: p₁ = p₂

H₁: p₁ > p₂

D. H₀: p₁ p₂

H₁: p₁ = p₂

E. H₀: p₁ = p₂

H₁: p₁ p₂

F. H₀: p₁ = p₂

H₁: p₁ < p₂

Identify the test statistic.

___________

(Round to two decimal places as needed.)

Identify the P-value.

__________

(Round to three decimal places as needed.)

What is the conclusion for this test?

The P-value is ___________ ( A. less than, B. greater than ) the significance level of ,

so ____________ ( A. fail to reject, B. reject ) the null hypothesis. There is ___________ ( A. insufficient, B. sufficient ) evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.