Question

The dean of the 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 that the standard deviation of the collected data from 144 alumni is $3k and the mean is $58k, please estimate the confidence interval of the population’s average salary.

2. The dean wants to know whether there is salary difference between male and female alumni. He knows that the population standard deviation for male is $3k and for female is $4k. The sampled data show that the average salary for 121 male is $60k and the average salary for 100 female is $56k .

(a) What are the null and alternate hypotheses?

(b) Decide on the test statistic and calculate the value of the test statistic?

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

Answer 1

As the test statistic is greater than critical value we have sufficient evidence to reject the null hypothesis