Question

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

3838

of the

4343

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

8484

of the

9999

subjects developed rhinovirus infections. Use a

0.010.01

significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below.

z value

pvalue
99% confidence interval

Answer 1

Answer:

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

38 of the43 subjects treated with echinacea developed rhinovirus infections. In a placebo group,

84 of the 99 subjects developed rhinovirus infections. Use a0.01significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below.

Upper tail test used.

z value=0.5546

p value=0.2896

99% confidence interval (-0.1212, 0.1917)

calculations:

$z = \frac{ p_1 - p_2}{\sqrt{ P*(1-P)(1/n_1 + 1/n_2) }}$

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.01
Group 1
Number of Items of Interest	38
Sample Size	43
Group 2
Number of Items of Interest	84
Sample Size	99
Intermediate Calculations
Group 1 Proportion	0.8837
Group 2 Proportion	0.8485
Difference in Two Proportions	0.0352
Average Proportion	0.8592
Z Test Statistic	0.5546
Upper-Tail Test
Upper Critical Value	2.3263
p-Value	0.2896
Do not reject the null hypothesis

CI = p1-p2 ± z*se

Standard error of p1-p2= se=

/P1 * (1-p1)/m +Pa * (1-p2) /n2

Confidence Interval Estimate
of the Difference Between Two Proportions
Data
Confidence Level	99%
Intermediate Calculations
Z Value	2.576
Std. Error of the Diff. between two Proportions	0.0607
Interval Half Width	0.1564
Confidence Interval
Interval Lower Limit	-0.1212
Interval Upper Limit	0.1917