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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:

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JeanaShupp

Answer: 3.6

Step-by-step explanation:

The test statistic for proportion is given by :-

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex], where p is the population proportion , [tex]\hat{p}[/tex] 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 , [tex]\hat{p}=\dfrac{102}{300}=0.34[/tex]

The test statistic for proportion is given by :-

[tex]z=\dfrac{0.34-0.25}{\sqrt{\dfrac{0.25(1-0.25)}{300}}}\\\\=\dfrac{0.09}{\sqrt{0.000625}}\\\\=\dfrac{0.09}{0.025}=3.6[/tex]

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

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