Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 35 of the 42 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 85 of the 99 subjects developed rhinovirus infections. Use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with 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 α=0.05, so ___________ ( A. reject, B. Fail to reject ) the null hypothesis. There ___________ ( A. is, B. is not) sufficient evidence to support the claim that echinacea treatment has an effect. b. Test the claim by constructing an appropriate confidence interval. The 95% 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, there ______________ ( A. does not, B. does) appear to be a significant difference between the two proportions. There _____________ ( A. is not, B. is ) evidence to support the claim that echinacea treatment has an effect. c. Based on the results, does echinacea appear to have any effect on the infection rate? A. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it increases the infection rate. B. Echinacea does not appear to have a significant effect on the infection rate. C. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it lowers the infection rate.
Section 9.1
Question #7
Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 35 of the 42 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 85 of the 99 subjects developed rhinovirus infections. Use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below.
a. Test the claim using a hypothesis test.
Consider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with 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 α=0.05, so ___________ ( A. reject, B. Fail to reject ) the null hypothesis. There ___________ ( A. is, B. is not) sufficient evidence to support the claim that echinacea treatment has an effect.
b. Test the claim by constructing an appropriate confidence interval.
The 95% 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, there ______________ ( A. does not, B. does) appear to be a significant difference between the two proportions. There _____________ ( A. is not, B. is ) evidence to support the claim that echinacea treatment has an effect.
c. Based on the results, does echinacea appear to have any effect on the infection rate?
A. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it increases the infection rate.
B. Echinacea does not appear to have a significant effect on the infection rate.
C. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it lowers the infection rate.
D. The results are inconclusive.
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