Question

A researcher randomly sampled 50 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below. Female MBA graduate: sample mean= $52,500, population standard deviation= 12000, sample size = 25. Male MBA graduates: Sample mean= $56,000, population standard deviation = 13000, sample size = 25

Assuming that the populations are normally distributed, is there evidence of a difference in the average starting salary of the Male MBA graduates and the Female MBA graduates? Use a 0.05 level of significance. Show all details of the Answer

Answer 1

Answer)

Null hypothesis Ho : u1-u2 = 0

Alternate hypothesis Ha : u1-u2 not equal to 0

As the population s.d is known here we can use standard normal z table to conduct the test

Test statistics z = (u1-u2)/standard error

Standard error = √{(s1^2/n1)+(s2^2/n2)}

u1 = 52500, s1 = 12000, n1 = 25

u2 = 56000, s2 = 13000, n2 = 25

After substitution

Z = -0.99

From z table, P(z<-0.99) = 0.1611

But our test is two tailed so, P-Value is = 2*0.1611 = 0.3222

As the obtained P-Value is greater than the given significance level 0.05

We fail to reject the null hypothesis Ho

And we do not have enough evidenve to conclude that there is difference in starting average salary of mba male and female