A recent survey showed that in a sample of 100 elementary school teachers, 15 were single. In a sample of 180 high school teachers, 36 were single. Is the proportion of high school teachers who were single greater than the proportion of elementary teachers who were single? Use α = 0.01.

By using hypothesis test at α = 0.01, we cannot conclude that the proportion of high school teachers who were single greater than the proportion of elementary teachers who were single

Step-by-step explanation:

let p1 be the proportion of elementary teachers who were single

let p2 be the proportion of high school teachers who were single

Then, the null and alternative hypotheses are:

[tex]H_{0}[/tex]: p2=p1

[tex]H_{a}[/tex]: p2>p1

We need to calculate the test statistic of the sample proportion for elementary teachers who were single.

It can be calculated as follows:

[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where

p(s) is the sample proportion of high school teachers who were single ([tex]\frac{36}{180} =0.2[/tex])
p is the proportion of elementary teachers who were single ([tex]\frac{15}{100} =0.15[/tex])

N is the sample size (180)

Using the numbers, we get

[tex]\frac{0.2-0.15}{\sqrt{\frac{0.15*0.85}{180} } }[/tex] ≈ 1.88

Using z-table, corresponding P-Value is ≈0.03

Since 0.03>0.01 we fail to reject the null hypothesis. (The result is not significant at α = 0.01)