Question #4

Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a

0.01 significance level to test for a difference between the measurements from the two arms. What can be concluded?

Right arm	151	141	134	137	139
Left arm	174	167	181	137	134

In this example, _d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the measurement from the right arm minus the measurement from the left arm. What are the null and alternative hypotheses for the hypothesis test?

A. H₀: _d 0

H₁: _d > 0

B. H₀: _d 0

H₁: _d = 0

C. H₀: _d = 0

H₁: _d 0

D. H₀: _d = 0

H₁: ₁ < 0

Identify the test statistic.

t= ____________ (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?

Since the P-value is ____________( A. less, B. greater ) the significance level, __________( A. Fail to reject, B. Reject )the null hypothesis. There ___________ ( A. is not, B. is ) sufficient evidence to support the claim of a difference in measurements between the two arms.

Question #6

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 301 people over the age of 55, 69 dream in black and white, and among 284 people under the age of 25, 11 dream in black and white. Use a 0.01

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 =0.01,

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 98% 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. 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.

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

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

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 cannot be used to verify the cause of such a difference.

Question #9

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	28.2558	24.9116
s	8.050185	5.186586

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

B. Reject 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 is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

D. Reject the null hypothesis. There isnot 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)