Section 9.1 Homework

2.  Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea, 34 of the 39 subjects treated with echinacea developed rhinovirus infections. In a placebo​ group, 95 of the 112 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.

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?

Identify the test statistic.

Z=

Identify the​ P-value.

P-value =

What is the conclusion based on the hypothesis​ test?

The​ P-value is _______ the significance level of á=0.05​, so _______ the null hypothesis. There _______ sufficient evidence to support the claim that echinacea treatment has an effect.

Test the claim by constructing an appropriate confidence interval.

The 95​% confidence interval is ____

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits ______​0, there __________ appear to be a significant difference between the two proportions. There _______ evidence to support the claim that echinacea treatment has an effect.

Based on the​ results, does echinacea appear to have any effect on the infection​ rate?

1. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it lowers the infection rate.
2. Echinacea does not appear to have a significant effect on the infection rate.
3. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it increases the infection rate.
4. The results are inconclusive.