Question

A poll stated that 32% of those polled think the economy is getting worse. An economist wanted to check this claim so she surveyed 750 people and found that 30% of them thought the economy is getting worse. What is the p-value? (α=0.05)

Answer 1

`z=\frac{0.30 -0.32}{\sqrt{(0.32(1-0.32))/(750)}}=-1.174`

The p value for this case would be given by:

`p_v =2*P(z<-1.174)=0.240`

For this case since the p value is higher than the significance level given we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.32 or 32 %

Explanation:

Information given

n=750 represent the random sample taken

`\hat p=0.30` estimated proportion of people who thought the economy is getting worse

`p_o=0.32` is the value that we want to verify

`\alpha=0.05` represent the significance level

z would represent the statistic

`p_v` represent the p value

Hypothesis to test

We want to check if the true proportion of interest is equal to 0.32 or not.:

Null hypothesis:
`p=0.32`

Alternative hypothesis:
`p \\eq 0.32`

The statistic would be given by:

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

Replacing we got:

`z=\frac{0.30 -0.32}{\sqrt{(0.32(1-0.32))/(750)}}=-1.174`

The p value for this case would be given by:

`p_v =2*P(z<-1.174)=0.240`

For this case since the p value is higher than the significance level given we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.32 or 32 %