Question

An experiment was conducted to test the effect of a new drug on a viral infection. After the infection was induced in 100 mice, the mice were randomly split into two groups of 50. The first group, the control group, received no treatment for the infection, and the second group received the drug. After a 30-day period, the proportions of survivors, p̂₁ and p̂₂, in the two groups were found to be 0.38 and 0.62, respectively.

(a) Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

(b) Use a 95% confidence interval to estimate the actual difference (p₁ − p₂) in the survival rates for the treated versus the control groups. (Round your answers to two decimal places.)

Answer 1

An experiment was conducted to test the effect of a new drug on a viral infection. After the infection was induced in 100 mice, the mice were randomly split into two groups of 50. The first group, the control group, received no treatment for the infection, and the second group received the drug. After a 30-day period, the proportions of survivors, p̂₁ and p̂₂, in the two groups were found to be 0.38 and 0.62, respectively.

1. Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

One tailed test used.

            

Lower tail test

the test statistic z = -2.40

rejection region: reject Ho if z < -1.645

since test statistic falls in the rejection region, Ho is rejected.

we conclude that new drug on a viral infection is effective.

(b) Use a 95% confidence interval to estimate the actual difference (p₁ − p₂) in the survival rates for the treated versus the control groups. (Round your answers to two decimal places.)

95% CI = (-0.43, -0.05)

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.05
Group 1
Number of Items of Interest	19
Sample Size	50
Group 2
Number of Items of Interest	31
Sample Size	50
Intermediate Calculations
Group 1 Proportion	0.38
Group 2 Proportion	0.62
Difference in Two Proportions	-0.24
Average Proportion	0.5000
Z Test Statistic	-2.4000
Lower-Tail Test
Lower Critical Value	-1.645
p-Value	0.0082
Reject the null hypothesis

Confidence Interval Estimate
of the Difference Between Two Proportions
Data
Confidence Level	95%
Intermediate Calculations
Z Value	-1.9600
Std. Error of the Diff. between two Proportions	0.0971
Interval Half Width	0.1903
Confidence Interval
Interval Lower Limit	-0.4303
Interval Upper Limit	-0.0497