Reference no: EM132856525

Hourly wages at Manufacturing Plant A very from worker to worker, with an average hourly wage of $13.66, and a standard deviation of $2.41 per hour, or σPlantA=2.41. In an attempt to attract new employees, a newly constructed Manufacturing Plant B claims that its employees will be paid, on average, more than than employees at Manufacturing Plant A. Assume that the standard deviation in hourly wages at Plant B is the same as at Plant A, or σPlantB=2.41.

(a) Choose the correct statistical hypotheses.

H0:X¯PlantB=13.66HA:X¯PlantB>13.66

(b) Statistical testing of the null hypothesis is to be carried out by randomly selecting 44 employees at Plant B. If the mean/average hourly wage of these 44 employees is greater than $14.69, then there is enough statistical evidence to indicate that the mean hourly wage of employees at Plant B is greater than the mean hourly wage of employees at Plant A.

What level of α was used here? Enter your answer to at least three decimal places.

(c) The average of the sample of n=44

n=44 workers was found to be X=14.15

X¯=14.15. What decision can you make from this sample?

A. Employees at Plant B do earn more on average compared to employees at Plant A

B. Employees at Plant B do not earn more on average compared to employees at Plant A.

C. The sample size is too small to conduct a statistical test, so a decision cannot be made

D. The hourly wages at Plant B need to be Normally distributed to do the test

(d) If the average hourly wage of all workers at Plant B is $14.52, what is the probability of concluding using the decision criteria outlined in part (b) that the mean hourly wage of all employees at Plant B is not greater than the mean hourly wage of all employees at Plant A? Enter your answer to at least three decimals.

Answer =