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. The following is the setup for this hypothesis test:

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

`\hat p=(92)/(1500)=0.0613` estimated proportion of unemployed

`z=\frac{0.0613 -0.05}{\sqrt{(0.05(1-0.05))/(1500)}}=2.01`

Explanation:

Information given

n=1500 represent the random sample taken

X=92 represent the number of people unemployed

`\hat p=(92)/(1500)=0.0613` estimated proportion of unemployed

`p_o=0.05` is the value to value to test

z would represent the statistic

`p_v` represent the p value

System of hypothesis

We want to test if the true proportion is lower than 0.05 or no and the system of hypothesis are::

Null hypothesis:
`p \geq 0.5`

Alternative hypothesis:
`p < 0.5`

The statistic is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

Replacing the info given we got:

`z=\frac{0.0613 -0.05}{\sqrt{(0.05(1-0.05))/(1500)}}=2.01`