Answer to Question #202108 in Statistics and Probability for michelle arlac

Question

A researcher reports that the average salary of College Deans is more than P63,000. A sample of 35 College Deans has a mean salary of P65, 700. At , test the claim that the College Deans earn more than P63,000 a month. The standard deviation of the population is P5,250.

Answer 1

actually exact question ;

A researcher reports that the average salary of College Deans is more than P63,000. A sample of 35 College Deans has a mean salary of P65, 700. At $\alpha =0.05$ , test the claim that the College Deans earn more than P63,000 a month. The standard deviation of the population is P5,250.

solution:

given:

$\mu =P63000, \space n=35,\space \bar x =P65700 ,\space \sigma =P5250\\$

since we are given population standard deviation, we use z-test

step1:

state the hypothesis and identify the claim

$H_0 : \mu \leq P63000\\ H_1: \mu > P63000, claim(one-tailed \space right)$

stpe 2:

the level of significance is $\alpha =0.05$

step 3:

determine the critical value using the table

$z_{critical}=+1.645$

step 4:

compute the one sample z test value using the formula

$z_{computed}=\frac{\bar x- \mu}{\frac{\sigma }{\sqrt{n}}}\\ z_{computed}=\frac{65700- 63000}{\frac{5250}{\sqrt{35}}}\\ z_{computed}=\frac{2700}{\frac{5250}{\sqrt{35}}}\\ z_{computed}=\frac{2700}{5250} {\sqrt{35}}\\ z_{computed}=3.043$

step 5:

decision rule ,compare the computed and critical value of z

$3.043>1.645 \\ Reject\space H_0 \space and \space accept \space H_1$

step 6;

There is enough evidence to support the claim that the monthly salary of the college deans is more than P63000