Question

An educational researcher wants to investigate the percentage of high school teachers in the district of Blueville who have been in their teaching job for more than 5 years. The researcher predicts that more than 45% of high school teachers in Blueville have been in their teaching job for more than 5 years. A random sample of high school teachers in Blueville was obtained and each teacher in the sample was asked how long they have been in their teaching job (‘5 years or less’ or ‘more than 5 years’).

What hypothesis test would be appropriate to investigate the researchers prediction? Specifically any kind of t-test? or what kind of test?

Answer 1

Sol:

Here z test for proportion to be conducted

Null hypothesis,Ho:p=0.45

Alternative Hypothesis,Ha:p>0.45

Right tail z test for proportion

set alpha=0.05

compute sample proportion of teachers who are more than 5 yrs

p^=x/n=how many are 5 years are kore/Total sample size

z=p^-p/sqrt(p*(1-p)/n)

p is popualtion proportion=0.45

and then calculate p value

if p<0.05

Reject Ho

Accept Ha

Then there will be suffcient statistcal evidence at 5% level of significance to support the claim that

more than 45% of high school teachers in Blueville have been in their teaching job for more than 5 years.

And if you get p>0.05

Do not Reject Ho

Accept H0

Then there will be no suffcient statistcal evidence at 5% level of significance to support the claim that

more than 45% of high school teachers in Blueville have been in their teaching job for more than 5 years.