Question

Compute the value of the test statistic for testing H0: p = 0.1 vs. Ha: p ≠ 0.1 for n = 480, mc061-1.jpg= 0.12.

Answer 1

Given that hypothesis test with

$H_0:p=0.1 \\ H_a:p\neq0.1$

where n = 480 and $\hat{p}=0.12$.

The test statistics is given by

$z= \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} \\ \\ =\frac{0.12-0.1}{\sqrt{\frac{0.1(1-0.1)}{480}}} \\ \\ = \frac{0.02}{\sqrt{\frac{0.1(0.9)}{480}}} = \frac{0.02}{\sqrt{\frac{0.09}{480}}} \\ \\ = \frac{0.02}{\sqrt{0.0001875}} = \frac{0.02}{0.0137} \\ \\ =1.46$