Independent random samples, each containing 50 observations, were selected from
ID: 3218862 • Letter: I
Question
Independent random samples, each containing 50 observations, were selected from two populations. The samples from populations 1 and 2 produced 31 and 20 successes, respectively. Test H_0:(p_1 -p_2) lessthanorequalto 0 against H_alpha = (p_l - p_2) > 0. Use alpha = 0.01 The test statistic is _____________ The P-value is The final conclusion is There is not sufficient evidence to reject the null hypothesis that (p_1 - p_2) = 0. We can reject the null hypothesis that (p_1 - p_2) lessthanorequalto 0 and support that (p_l - p_2) > 0.Explanation / Answer
The statistical software output for this problem is:
Two sample proportion 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
Note: the standard error is calculated using a pooled estimate for the proportion
Hypothesis test results:
a) Test statistic = 2.20044
b) p - value = 0.0139
c) Conclusion: p - value is greater than 0.01 so we do not reject Ho.
Option A is correct.
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 31 50 20 50 0.22 0.099979998 2.2004401 0.0139