Question

The dean of the a school has observed for several years and found that the probability distribution of the salary of the alumni’s first job after graduation is normal. The college collected information from 144 alumni and finds that the mean of their salary is $58k. Assuming a 95% confidence level, please do the following

1. Suppose the dean believes that the average salary of the population should be about $59k per year, with a standard deviation of $2k. We need to conclude that the mean salary is less than what the dean has believed to be:

(a) What are the null and alternate hypotheses ?

(b) What is the level of significance ?

(c) What is the standard error?

(d) Decide on the test statistic and calculate the value of the test statistic (hint: write the equation and calculate the statistic?

(e) What’s your decision regarding the hypothesis and interpret the result using test-score rejection region rule or p value rule.

Answer 1

Solution :

Given

n = 144 sample size of alumini

. Sample mean

. Population mean

. Population standard deviations

. Level of significance

a ) To test

. Vs.

b ) Here 5% is the level of significance in the problem

Level of significance means probability of rejecting Ho when Ho is true.

c ) The value of the standard error is

S.E = 0.16667

d) Test statistics

Z = - 6.00

Z critical value = 1.96

. From Z table

e) Decision

| Z | that is

6.00

Reject Ho

OR

P value = 0.00001

Reject Ho

Conclusion : we conclude that the average salary of the population is less than $ 59K.