Question

Find the standardized test statistic, z to test the hypothesis that p1 = p2. Use α = 0.05. The sample statistics listed below are from independent samples. Sample statistics: n1 = 50, x1 = 35, and n2 = 60, x2 = 40

Answer 1

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, $H_0$ : $p_1=p_2$  

Alternate Hypothesis, $H_A$ : $p_1\neq p_2$  

The test statistics that will be used here is Two-sample z-test statistics for proportions;

                             T.S.  =  $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }$  ~  N(0,1)

where, $\hat p_1$ = sample proportion of the first sample = $\frac{X_1}{n_1}$ = $\frac{35}{50}$ = 0.70

$\hat p_2$ = sample proportion of the second sample = $\frac{X_2}{n_2}$ = $\frac{40}{60}$ = 0.67

$n_1$ = size of the first sample = 50

$n_2$ = size of the first sample = 60

So, the test statistics =  $\frac{(0.70-0.67)-(0)}{\sqrt{\frac{0.70(1-0.70)}{50}+\frac{0.67(1-0.67)}{60}} }$

                                    =  0.338  

Hence, the value of the standardized z-test statistic is 0.338.