The personnel manager of a large airline company has declared that, on the avera

Question

The personnel manager of a large airline company has declared that, on the average, workers are asked to work no more than three hours overtime per week. Past studies show standard deviation in overtime hours per week to be 1.2 hours. Suppose the union negotiators wish to test his declaration by sampling payroll records for 250 employees. The negotiators believe that the true mean overtime is more than three hours per week but they want to base their conclusion on the sample results. They decide that the personnel manager’s declaration is likely to be untrue if the sample mean overtime for the 250 employees is over 3.15 hours per week. Given the null and alternative hypotheses to be tested are H0: m and H1: m > 3 respectively.

a) Describe in your own words the meaning of Type I error in the test.

b) Describe in your own words the meaning of Type II error in the test.

Explanation / Answer

Hypothesis testing works pretty much like the court of law, where the Person is question is assumed to be innocent and evidence has to be provided to prove otherwise. Type 1 Error (Alpha)is the situation where Ho rejected when it is true whereas Type 2 error (Beta) is the situation where we fail to reject H0 when H1 is true.

In this situation we are testing H0: m(=3) against the alternative H1: m>3.

Type 1 Error here is we don’t have enough evidence to believe that true mean overtime is 3 hours, when that’s actually true. Reject H0 when is it actually True

Type 2 Error here is we don’t have enough evidence to believe that true mean overtime is greater than 3 hours, when that’s actually true. Fail to Reject H0 when H1 is true

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