Question

In: Statistics and Probability

Faculty members in a state university system who resign within 10 years of initial employment are...

  1. Faculty members in a state university system who resign within 10 years of initial employment are entitled to receive the money paid into a retirement system, plus 4% per year. Unfortunately, experience has shown that the state is extremely slow in returning this money. Concerned about such a practice, a local teachers organization decides to investigate. After a confrontation with the teachers’ union, the state promised to make reimbursements within 60 days. Monitoring of the next 40 resignations yields an average of 61 days, with a standard deviation of 10 days.

    1. (a) Set up the appropriate hypothesis tests for this investigation.

    2. (b) Test the null hypothesis using an α level of 0.01, draw out a graphical representation of the test. Include critical values and test statistic value. What is your conclusion regarding the population parameter μ ( state your answer in the context of the problem).

Solutions

Expert Solution

Since the issue is that the state is slow in returning the money, and that after being informed about the same, they have promised to rectify the situation, and we are now investigating whether the time taken is more than 60 days.

The Hypothesis:

H0: < 60 days

Ha: > 60 days (Claim)

The Test Statistic: Since the population standard deviation is unknown, we use the students t test.

The test statistic is given by the equation:

The p Value: The p value (Right Tail) for t = 0.63, for degrees of freedom (df) = n-1 = 39, is; p value = 0.2662

The Critical Value:   The critical value (Right Tail) at = 0.01, for df = 39, t critical = +2.43

The Decision Rule:   If t observed is > t critical, then Reject H0

Also if P value is < , Then Reject H0.

The Decision:   Since t observed (0.63) is < t critical (2.43), We Fail to Reject H0.

Also since P value (0.2662) is > (0.01) , We Fail to Reject H0.

The Conclusion: There isn’t sufficient evidence at the 99% significance level to support the claim that the mean time for reimbursements takes more than 60 days.

_____________________________________________


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