1. Rhinoviruses typically cause common colds. In a test of the effectiveness of
ID: 3364509 • Letter: 1
Question
1. Rhinoviruses typically cause common colds. In a test of the effectiveness of Echinacea, 40 of the 45 subjects treated with Echinacea developed rhinovirus infection. In a placebo group, 88 of the 103 subjects developed rhinovirus infection (based on data from "An Evaluation of Echinacea Angustifolia in Experimental Rhinovirus Infections," by Turner et al, New England Journal of Medicine, vol. 353, No. 4). We want to use a0.05 significance level to test the claim that Echinacea has an effect on rhinovirus infections a. Test the claim using a hypothesis test. In StatCrunch click on Stat> Proportion Stats > Two-Sample> With Summary. Fill in your information and click compute. *State your null and alternative hypothesis . State your Z-Stat . State your P-value Do you "reject" or "Fail to Reject" the null hypothesis b. Test the claim by constructing a 95% confidence interval. If you had just completed part a, you can click options at the top and then edit, to change your information for part b. otherwise follow the steps below. In Statcrunch click on Stat> Proportion Stats > Two-Sample> With Summary Fill in your information, then dlick the box that shows Confidence interval and put in your confidence leve (0 95) and click compute Give the lower and upper values of your conficence incerval I s Based on the resuets to part a and b does Echinaces appear to have any effecs on the infection raze?
Explanation / Answer
a) The StatCrunch output for this part 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:
Hence,
Hypotheses:
H0 : p1 - p2 = 0
HA : p1 - p2 0
Z-Stat = 0.565
P - value = 0.572
Fail to Reject Ho since p - value is greater than 0.05.
b) 95% confidence interval:
Two sample proportion summary confidence interval:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
95% confidence interval results:
Hence,
Lower limit = -0.0798
Upper limit = 0.1489
c) No, it does not appear that Echnacea has any effect on infection rate because we fail to reject the null hypothesis and confidence interval includes 0.
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 40 45 88 103 0.034519957 0.061089174 0.56507486 0.572Related Questions
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