Answer to Question #331432 in Statistics and Probability for kiel

Question

A researcher claims that the average salary of a private school teacher is greater than P35,000 with

a standard deviation of P7,000. A sample of 35 teachers has a mean salary of P37,000. Test the

claim of the researcher. At 0.05 level of significance, test the claim of the researcher.

Answer 1

$H_0:a=35000$

$H_1:a>35000$

Test statistic: $T={\frac {(X-a)*\sqrt{n}} {\sigma}}={\frac {(37000-35000)*\sqrt{35}} {7000}}= 1.69$

Since the sample size is big (>30), then it is appropriate to use the z-score as the critical value. So, $P(Z>Cr)=\alpha=0.05\implies Cr=1.645$

Since T>Cr, then we should conclude that, based on the given data, there is enough evidence to reject the null hypothesis and admit that average group salary is greater than population's one.