Question

The average starting salary of students who graduated from colleges of Business in 2009 was $48,400. 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 $8000. We want to determine whether or not there has been a significant increase in the starting salaries. Step 1. Statement of the hypothesis (1.5 marks) Step 2. Standardized test statistic formula (1 mark) Step 3. State the level of significance (1 mark) Step 4. Decision Rule (Draw a bell to show rejection zone) Step 5. Calculation of the statistic Step 6. Conclusion (1.5 marks)

Answer 1

Sol:

Step 1. Statement of the hypothesis (1.5 marks)

Null hypothesis:

There is no increase in salary from the hypothesized value of 48400

Ho:Mu=48400

Alternative hypothesis:

There is an increase in salary from the hypothesized value of 48400

Ha:Mu>48400

Step 2. Standardized test statistic formula (1 mark)

z=xbar-mu/sigma/sqrt(n)

xbar=sample mean

mu=population mean

sigma=population standard deviation

n=sample size

Step 3. State the level of significance (1 mark)

alpha=5%=0.05

Step 4.

z crit=NORM.S.INV(0.05)=1.644853627

that z crit ar 5%=1.645

RIght side is critical region

if Zo>1.645,reject Ho

Else accept Ho

Step-5:

z=xbar-mu/sigma/sqrt(n)

z=(50000-48400)/(8000/sqrt(100))

Z=2

Step 6. Conclusion (1.5 marks)

z =2>1.645

Reject Ho

There is sufficient statistical evidence at 5% level of significance to conclude that

there has been a significant increase in the starting salaries