Question

The average starting salary of students who graduated from colleges of Business in 2009 was $48,800. A sample of 100 graduates of 2010 showed an average starting salary of $50,000. Assume the standard deviation of the population is known to be $7000. We want to determine whether or not there has been a significant increase in the starting salaries.

a.	State the null and alternative hypotheses to be tested.
b.	Compute the test statistic.
c.	The null hypothesis is to be tested at the 5% level of significance. Determine the critical value for this test.
d.	What do you conclude from the test?
e.	What does the test result mean in the context of this problem?

Answer 1

Solution:

Part a

Here, we have to use one sample z test for the population mean. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: There is no significant increase in the starting salaries of students who graduated from colleges of business.

Alternative hypothesis: H_a: There is a significant increase in the starting salaries of students who graduated from colleges of business.

H₀: µ = 48800 versus H_a: µ > 48800 (One tailed test)

This is an upper tailed or right tailed test.

Part b

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

We are given

Xbar = 50000

σ = 7000

n = 100

Z = (50000 – 48800)/[7000/sqrt(100)]

Z = 1200/700 = 12/7

Z = 1.7143

Part c

We are given α = 0.05

So, Critical Z value = 1.6449

(by using z-table)

Part d

Test statistic value = 1.7143 > Critical value = 1.6449

So, we reject the null hypothesis at 5% level of significance.

Part e

There is sufficient evidence to conclude that there is a significant increase in the starting salaries of students who graduated from colleges of business.