Question

1- It is believed that the mean μ starting salary for the new KU graduates has increased from last year,s mean of $51 K annually. It is known that the standard deviation of the starting salary is σ = 5 K. To test what you believe, you collect a sample of 15 new graduates and find that the sample mean salary is x= 54 K.

In this question and the next two, we will do a significance test to determine whether the mean starting salary has increased. Here

H0 : μ = 51 HA : μ > 51.

For this question compute the z-value for your collected data.

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Refer to Question 1. Decide if it is a Tow Tail, Left Tail or Right Tail Test and compute the p- value.

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Refer to Question 1. What would be the lowest level of significance, percent among .1, .5, 1 , 2, 3, 4, 5, 6, 7, 8, 9, 10 percent, at which you would accept that the mean starting salary of KU graduates has increased?

Answer 1

Test Statistics

The z-statistic is computed as follows:

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ=51

Ha: μ>51

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

The p-value is p = 0.0101

The lowest level of significance would be >1.01% which is 2% among the above given values. Since p = 0.0101 < 0.02 therefore we would reject the null and conclude that the mean salaries of KU graduates has increased.

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