Question

A researcher is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 92 people are unemployed.
H0 : p= 0.05
Ha : p < 0.05

Required:
Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

Answer 1

Answer:

The test statistic for this hypothesis test for a proportion is z=1.90.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the unemployment rate is less than 5%.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.05\\\\H_a:\pi$

The sample has a size n=1500.

The sample proportion is p=0.061.

$p=X/n=92/1500=0.061$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1500}}\\\\\\ \sigma_p=\sqrt{0.000032}=0.0056$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.061-0.05-0.5/1500}{0.0056}=\dfrac{0.0107}{0.0056}=1.90$