Answer to Question #203563 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

$\mu=63000 \\ n= 35 \\ \bar{x}=65700 \\ \sigma=5250 \\ H_0: \mu ≤ 63000 \\ H_1: \mu > 63000$

The level of significance is $\alpha=0.01$

$z _{crit}=2.326$

The test statistic:

$z=\frac{\bar{x}-\mu}{\sigma / \sqrt{n}} \\ = \frac{65700-63000}{5250/ \sqrt{32}} \\ = 3.043 \\ Z=3.043>Z_{crit}=2.326$

So, we reject H₀ and accept H₁.

There is evidence to support the claim that the monthly salary of the college dean is more than P63,000