Question

Note: For this problem, your answer should be rounded to two decimal places. In a particular municipality, it is believed that 25 percent of homes are not properly insulated. In order to test H0:p=.25 vs. HA:p?.25 (where p is the population proportion of homes that are not properly insulated) a random sample of 300 homes was selected. In the sample, it was found that 102 homes were not properly insulated. If the null hypothesis is true, then the z-score for the sample proportion is:

Answer 1

Answer: 3.6

Explanation:

The test statistic for proportion is given by :-

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}`, where p is the population proportion ,
`\hat{p}` is the sample proportion and n is the sample size.

Let p be the population proportion of homes are not properly insulated.

As per given , we have

p= 0.25

Sample size : n= 300

In the sample, it was found that 102 homes were not properly insulated.

Then ,
`\hat{p}=(102)/(300)=0.34`

The test statistic for proportion is given by :-

`z=\frac{0.34-0.25}{\sqrt{(0.25(1-0.25))/(300)}}\\\\=(0.09)/(√(0.000625))\\\\=(0.09)/(0.025)=3.6`

Hence, the z-score for the sample proportion is: 3.6