Answer:
z = 0.33
Explanation:
The test statistic z can be calculated as:
[tex]z=\frac{p^{\prime}-p}{\sigma}[/tex]
Where p' is the proportion of the sample and p is the value in H0. Additionally, σ is equal to:
[tex]\sigma=\sqrt[]{\frac{p(1-p)}{n}}[/tex]
Where n is the size of the sample.
In this case, we have a sample of 136 subjects, so n = 136 and taking into account H0, p = 0.42. So, replacing the values, we get:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{0.42(1-0.42)}{136}} \\ \sigma=0.0423 \end{gathered}[/tex]
Then, p' is the proportion of the sample, so it is equal to:
p' = 59/136 = 0.4338
Now, replacing p' = 0.4338, σ = 0.0423 and p = 0.42, we get that the test statistic is:
[tex]z=\frac{0.4338-0.42}{0.0423}=0.33[/tex]
Therefore, the answer is:
z = 0.33
