Section 9.1

Question #8

In a study of treatments for very painful "cluster" headaches, 154 patients were treated with oxygen and 159 other patients were given a placebo consisting of ordinary air. Among the 154 patients in the oxygen treatment group, 112 were free from headaches 15 minutes after treatment. Among the 159 patients given the placebo, 30 were free from headaches 15 minutes after treatment. Use a 0.01 significance level to test the claim that the oxygen treatment is effective. Complete parts (a) through (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of patients treated with oxygen and the second sample to be the sample of patients given a placebo. 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. reject, B. Fail to reject ) the null hypothesis. There is _____________ ( A. is sufficient, B. is not sufficient) evidence to support the claim that the cure rate with oxygen treatment is higher than the cure rate for those given a placebo.

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

The 98% confidence interval is ___________ < ( p₁p₂ ) < ____________.

(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 cure rates are _________________ ( A. equal, B. not equal ) Because the confidence interval limits include ____________ ( A. only positive, B. positive and negative, C. only negative ) values, it appears that the cure rate is _________ ( A. higher, B. the same, C. lower ) for the oxygen treatment than for the placebo.

c. Based on the results, is the oxygen treatment effective?

A. The results suggest that the oxygen treatment is effective in curing "cluster" headaches.

B. The results suggest that the oxygen treatment is not effective in curing "cluster" headaches because the cure rates appear to be the same.

C. The results suggest that the oxygen treatment is not effective in curing "cluster" headaches because the cure rate for the oxygen treatment appears to be lower than that of the placebo.

D. The results are inconclusive.

Question #9

In a random sample of males, it was found that 22 write with their left hands and 216 do not. In a random sample of females, it was found that 62 write with their left hands and

467 do not. Use a 0.01 significance level to test the claim that the rate of left-handedness among males is less than that among females. Complete parts (a) through (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of males and the second sample to be the sample of females. 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. reject, B. Fail to reject ) the null hypothesis. There is _____________ ( A. is sufficient, B. is not sufficient) evidence to support the claim that the rate of left-handedness among males is less than that among females.

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

The 90% confidence interval is ___________ < ( p₁p₂ ) < ____________.

(Round to three decimal places as needed.)

What is the conclusion based on the confidence interval?

Because the confidence interval limits ____________( A. include 0, B. include only negative values ), there _________________ ( A. does not appear, B. appears ) to be a significant difference between the rates of left-handedness among males and females. There ____________ ( A. is sufficient, B. is not sufficient ) evidence to support the claim that the rate of left-handedness among males is less than that among females.

c. Based on the results, is the rate of left-handedness among males less than the rate of left-handedness among females?

A. It is reasonable to conclude that the rate of left-handedness among males is less than the rate of left-handedness among females.

B. It is reasonable to conclude that the rate of left-handedness among males is the same as the rate of left-handedness among females.

C. It isnot reasonable to conclude that the rate of left-handedness among males is less than the rate of left-handedness among females.

D. The assumptions required for the tests are not valid, so the results should not be used for inference.

Question #10

Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 16 having a common attribute. The second sample consists of 1900 people with 1373 of them having the same common attribute. Compare the results from a hypothesis test of p₁ = p₂ (with a 0.05 significance level) and a 95%

confidence interval estimate of p₁ p₂.

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.

_____________

(Round to two decimal places as needed.)

Identify the critical value(s).

_____________, _________

(Round to three decimal places as needed. Use a comma to separate answers as needed.)

What is the conclusion based on the hypothesis test?

The test statistic is ___________ ( A. in, B. not in ) the critical region, so __________ ( A. reject, B. Fail to reject ) the null hypothesis. There is ___________( A. sufficient, B. insufficient ) evidence to conclude that p₁ p₂.

The 99% confidence interval is ___________ < ( p₁p₂ ) < ____________.

(Round to three decimal places as needed.)

What is the conclusion based on the confidence interval?

Since 0 is _________ ( A. included, B. not included ) in the interval, it indicates to ___________ ( A. fail to reject, B. reject ) the null hypothesis.

How do the results from the hypothesis test and the confidence interval compare?

The results are ___________ ( A. different B. the same), since the hypothesis test suggests that p₁ _________ ( A. , B. =, C. < D. >, E. , F. ) p₂, and the confidence interval suggests that p₁ _______( A. , B. =, C. < D. >, E. , F. ) p₂.

Section 9.2

Question #3

	1	2
n	36	36
_ x	0.79216 lb	0.81628 lb
s	0.00446 lb	0.00742 lb

a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.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 support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

B. Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

C. Failtoreject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

D. Reject the null hypothesis. There isnot sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

b. Construct a confidence interval appropriate for the hypothesis test in part (a).

_________ lb < _{1 2} < ______________ lb

(Round to three decimal places as needed.)

Does the confidence interval support the conclusion found with the hypothesis test?

__________ ( A. Yes, B. No ) because the confidence interval contains ___________ ( A. only negative values, B. only positive values, C. Zero )