Answer to Question #203562 in Statistics and Probability for Yumi Ramos

Question

A researcher reports that the average salary of College Deans is more than Php 63,000. A sample of 35 College Deans has a mean salary of Php 65,700. At a = 0.01, test the claim that the CollegeDeans earn more than Php 63, 000 a month. The standard deviation of the population is Php 5,250. 

Answer 1

Solution:

Since the population standard deviation is known, one can perform Z test.

The null hypothesis: the average salary of assistant professors is less than or equal to Php 63,000; 

$H_0:\mu\le63,000 .$

The research hypothesis: the average salary of assistant professors is more than Php 63,000;

$H_1: \mu> 63,000$ (represents the claim, right-tailed test).

The test statistic:

$Z=\dfrac{\bar X-\mu}{\sigma/\sqrt{n}}=\dfrac{65700-63000}{5250/\sqrt{35}}=3.042$

Now, p-value$=P(Z>3.04)=1-P(Z\le3.04)=0.00118$

Since, 0.00118<0.01 (alpha value), we can reject the null hypothesis. We have enough evidence to reject null hypothesis. Thus, the average salary of assistant professors is more than Php 63,000