Answer
Firstly, we declare null hypothesis is the percentage of students at your school who hold off-campus jobs is no different from 65% while the alternative hypothesis is the percentage of students at your school who hold off-campus jobs is different from 65%. Secondly, we take the sample size , n=40 . p=0.67. The sample size is large enough to conduct the two-tailed hypothesis testing and np=(40)(0.67) =26.8 and nq=(40)(0.33) =13.2 both are larger than 5. We define the significance level α=0.05 , and we then find the critical value of the test, z=1.96 and compute the sample standard deviation,$σ_p̂$=$\sqrt \frac{0.67*0.33}{40}$=0.0743 and observe z= $\frac{0.67-0.65}{0.0743}$ =0.27 . The observe z is within the non rejection region, therefore we failed to reject the null hypothesis.
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