Question

a popular weekly magazine asserts that fewer than 40% of households in the united states have changed their lifestyles because of escalating gas prices. a recent survey of 180 households finds that 67 households have made lifestyle changes due to escalating gas prices.the standard error of p(bar) is:the value of the test statistic is:the pvalue is:at a=0.10 and using the p-valuein light of your conclusion, what test error may happen?

Answer 1

Answer: The null hypothesis is not rejected.

Explanation:

Since we have given that

n = 180

x = 67

So,
`\hat{p}=(x)/(n)=(67)/(180)=0.372`

Hypothesis :

`H_0:\hat{p}\geq 0.4\\\\H_1:\hat{p}<0.4`

So, test statistic value would be

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\\\\z=\frac{0.372-0.4}{\sqrt{(0.4* 0.6)/(180)}}\\\\z=(-0.027)/(0.03645)\\\\z=-0.741`

At 0.01 level of significance, z = -1.28

So, -1.28<-0.741

So, we will not reject the null hypothesis as p - value = 0.2234.

Hence, the null hypothesis is not rejected.