The average starting salary of students who graduated from c

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 by $8,000. We want to determine whether or not there has been a significant increase in the starting salaries. a. the null hypothesis is to be tested at 95% confidence level, determine the critical value for this test. b. what do you conclude?

Solution

Set Up Hypothesis
Null Hypothesis H0: U=48400
Alternate Hypothesis H1: U>48400
Test Statistic
Population Mean(U)=48400
Given That X(Mean)=50000
Standard Deviation(S.D)=6000
Number (n)=100
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=50000-48400/(6000/Sqrt(100)
Zo =2.6667
| Zo | =2.6667
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.6667 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 2.6667 ) = 0.0038
Hence Value of P0.05 > 0.0038, Here we Reject Ho