Independent random samples, each containing 700 observations, were selected from
ID: 3361121 • Letter: I
Question
Independent random samples, each containing 700 observations, were selected from two binomial populations. The samples from populations 1 and 2 produced 314 and 410 successes, respectively.
(a) Test H0:p1=p2 against H1:p1p2. Use =0.08
test statistic =
rejection region |z| >
The final conclustion is
A. We can reject the null hypothesis that p1=p2 and accept that p1p2.
B. There is not sufficient evidence to reject the null hypothesis that p1=p2.
(b) Test H0:p1=p2 against H1:p1>p2 Use =0.08
test statistic =
rejection region z>
The final conclustion is
A. There is not sufficient evidence to reject the null hypothesis that p1=p2.
B. We can reject the null hypothesis that p1=p2 and accept that p1>p2.
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:
Hence,
Test statistic = -5.134
Rejection Region: |z| > 1.75
Final Conclusion: We can reject the null hypothesis that p1=p2 and accept that p1p2.
b) Test statistic = -5.134
Rejection region z > 1.405
Final conclusion: There is not sufficient evidence to reject the null hypothesis that p1=p2.
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 314 700 410 700 -0.13714286 0.026710411 -5.1344345 <0.0001