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

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

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<0.05`

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{(\pi(1-\pi))/(n)}=\sqrt{(0.05*0.95)/(1500)}\\\\\\ \sigma_p=√(0.000032)=0.0056`

Then, we can calculate the z-statistic as:

`z=(p-\pi-0.5/n)/(\sigma_p)=(0.061-0.05-0.5/1500)/(0.0056)=(0.0107)/(0.0056)=1.90`