Answer :
Answer:
The value of the standardized z-test statistic is 0.338.
Step-by-step explanation:
We are given the following hypothesis below;
Null Hypothesis, [tex]H_0[/tex] : [tex]p_1=p_2[/tex]
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1\neq p_2[/tex]
The test statistics that will be used here is Two-sample z-test statistics for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of the first sample = [tex]\frac{X_1}{n_1}[/tex] = [tex]\frac{35}{50}[/tex] = 0.70
[tex]\hat p_2[/tex] = sample proportion of the second sample = [tex]\frac{X_2}{n_2}[/tex] = [tex]\frac{40}{60}[/tex] = 0.67
[tex]n_1[/tex] = size of the first sample = 50
[tex]n_2[/tex] = size of the first sample = 60
So, the test statistics = [tex]\frac{(0.70-0.67)-(0)}{\sqrt{\frac{0.70(1-0.70)}{50}+\frac{0.67(1-0.67)}{60}} }[/tex]
= 0.338
Hence, the value of the standardized z-test statistic is 0.338.