Question

Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea, 38 of the 45 subjects treated with echinacea developed rhinovirus infections. In a placebo​ group, 87 of the 101 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.

Identify the test statistic.:

Z equals negative 0.27 ​(Round to two decimal places as​ needed.)

Identify the​ P-value. ​:

P-value equals 0.788 ​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test? The​ P-value is greater than the significance level of a= 0.05​, so fail to 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 less than left parenthesis p 1 minus p 2 right parenthesis less than nothing. :

___<(P1-P2)>___ ?

So what does P1 and P2 equal?

Answer 1

using excel>addin>phstat>two sample test >z test for difference

we have

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0		of the Difference Between Two Proportions
Level of Significance	0.05
Group 1			Data
Number of Items of Interest	38		Confidence Level	95%
Sample Size	45
Group 2			Intermediate Calculations
Number of Items of Interest	87		Z Value	-1.959963985
Sample Size	101		Std. Error of the Diff. between two Proportions	0.064040971
			Interval Half Width	0.125517997
Intermediate Calculations
Group 1 Proportion	0.844444444		Confidence Interval
Group 2 Proportion	0.861386139		Interval Lower Limit	-0.142459692
Difference in Two Proportions	-0.016941694		Interval Upper Limit	0.108576303
Average Proportion	0.856164384
Z Test Statistic	-0.269361521
Two-Tail Test
Lower Critical Value	-1.959963985
Upper Critical Value	1.959963985
p-Value	0.787651494
Do not reject the null hypothesis

the test statistic. Z=- 0.27

the​ P-values = 0.788

The​ P-value is greater than the significance level of alpha equals 0.05​, so fail to 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

-0.1425<(P1-P2) < 0.1086