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

Question

Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 36 of the 41 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 92 of the 106 subjects developed rhinovirus infections. Use a 0.01 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? O B. Ho:p1=p2 HI : pl #p2 0 E. Ho:P1=P2 H1 P1 P2 H1 : P1=P2 H1 : P1 #P2 Identify the test statistic. 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 b. Test the claim by constructing an appropriate confidence interval. | the significance level of = 0.01, so the null hypothesis. There | | sufficient evidence to support the claim that echinacea treatment has an effect. Click to select your answer(s).

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 0

Hypothesis test results:

99% confidence interval results:

Hence,

Hypotheses: Option B is correct.

z = 0.16

p - Value = 0.870

Greater; do not reject; is not

b) 99% confidence interval: -0.146 < (p1 - p2) < 0.167

Includes; Does not; Is not

c) Option B is correct.

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 36 41 92 106 0.010124252 0.061699019 0.16409098 0.8697

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