Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 43 of the 49 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 79 of the 96 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: p1p2 Identify the test statistic. z=nothing (Round to two decimal places as needed.) Identify the P-value. P-value=nothing (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is ▼ greater than less than the significance level of α=0.05, so ▼ fail to reject reject the null hypothesis. There ▼ is 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 nothing

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea,

of the

subjects treated with echinacea developed rhinovirus infections. In a placebo group,

of the

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?

H0:

p1≤p2

H1:

p1≠p2

H0:

p1=p2

H1:

p1<p2

H0:

p1≠p2

H1:

p1=p2

H0:

p1=p2

H1:

p1≠p2

H0:

p1≥p2

H1:

p1≠p2

H0:

p1=p2

H1:

p1>p2

Identify the test statistic.

z=nothing

(Round to two decimal places as needed.)

Identify the P-value.

P-value=nothing

(Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test?

The P-value is

▼

greater than

less than

the significance level of

α=0.05,

▼

fail to reject

reject

the null hypothesis. There

▼

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

nothing<p1−p2<nothing.

(Round to three decimal places as needed.)

What is the conclusion based on the confidence interval?

Because the confidence interval limits

▼

include

do not include

0, there

▼

does not

does

appear to be a significant difference between the two proportions. There

▼

is not

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?

Echinacea does appear to have a significant effect on the infection rate. There is evidence that it increases the infection rate.

Echinacea does not appear to have a significant effect on the infection rate.

Echinacea does appear to have a significant effect on the infection rate. There is evidence that it lowers the infection rate.

The results are inconclusive.

Click to select your answer(s).

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