Question

In order to determine whether there was a difference in the survival rate between females and males, a two-sample proportion test was applied. The following is the output for the test with some entries missing:

Two sample proportion hypothesis test:
p₁ : Proportion of successes (Success = Survived) for Survival where Gender=Female
p₂ : Proportion of successes (Success = Survived) for Survival where Gender=Male
p₁ - p₂ : Difference in proportions
H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ ≠ 0

Hypothesis test results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	Z-Stat	P-value
p1 - p2	25	36	23	53	?	0.10765355	?	?

What is the appropriate conclusion at the 1% significance level based off this data?

Select one:

a. Since P-value < α, reject H₀ and there is sufficient evidence of a difference in survival rate between males and females.

b. Since P-value > α, reject H₀ and there is sufficient evidence of a difference in survival rate between males and females.

c. Since P-value < α, do not reject H₀ and there is insufficient evidence of a difference in survival rate between males and females.

d. Since P-value > α, do not reject H₀ and there is insufficient evidence of a difference in survival rate between males and females.

e. Since P-value > α, do not reject H₀ and there is sufficient evidence of equality in survival rate between males and females.

Answer 1

For sample 1, we have that the sample size is N_1= 36, the number of favorable cases is X_1 = 25, so then the sample proportion is

For sample 2, we have that the sample size is N_2 = 53, the number of favorable cases is X_2 = 23, so then the sample proportion is

The value of the pooled proportion is computed as

Also, the given significance level is α=0.01.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:p1​=p2​

Ha:p1​̸​=p2​

This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the critical value for a two-tailed test is z_c = 2.58

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that |z| = 2.42 < z_c = 2.58 it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p = 0.0155, and since p = 0.0155> 0.01, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p1​ is different than p2​, at the 0.01 significance level.

d. Since P-value > α, do not reject H₀ and there is insufficient evidence of a difference in survival rate between males and females.