Marta Human Resource manager has asserted that Marta workers work, on average, no more than three hours of overtime per week. Let assume that overtime hour is normally distributed with a standard deviation of 1.2 hours. The union leaders believe that this assertion is incorrect and that the actual mean overtime is more than three hours per week. The union leaders decide to test this claim and claim their conclusion on the sample result. They conduct a study on a sample of payroll records for 250 employees.   1. State the study, null, and alternative hypotheses, and Describe in your own words the meaning of Type I type II error in the context of this case.

Question
Marta Human Resource manager has asserted that Marta workers work, on average, no more than three hours of overtime per week. Let assume that overtime hour is normally distributed with a standard deviation of 1.2 hours. The union leaders believe that this assertion is incorrect and that the actual mean overtime is more than three hours per week. The union leaders decide to test this claim and claim their conclusion on the sample result. They conduct a study on a sample of payroll records for 250 employees.
 
1. State the study, null, and alternative hypotheses, and Describe in your own words the meaning of Type I type II error in the context of this case.
 
2. Establish the appropriate decision rule if the union leaders want to have no more than a 0.01 chance of a Type I error.
 
3. The payroll records produced a sample mean of 3.15 hours. Do the union leaders have a basis for a grievance against Marta? Support your answer with a relevant statistical procedure.

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