Question

Hourly wages at Manufacturing Plant A very from worker to worker, with an average hourly wage of $13.86, and a standard deviation of $2.68 per hour, or σPlantA=2.68. 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=2.68


(a) Choose the correct statistical hypotheses.

D. H0:μPlantB=13.86 HA:μPlantB>13.86


(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 $14.65, 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 αα was used here? Enter your answer to at least three decimal places.

(c) The average of the sample of n=44n=44 workers was found to be X⎯⎯⎯⎯=14.08X¯=14.08. What decision can you make from this sample?
A. The hourly wages at Plant B need to be Normally distributed to do the test
B. Employees at Plant B do 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. Employees at Plant B do not earn more on average compared to employees at Plant A.


(d) If the average hourly wage of all workers at Plant B is $14.55, 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 =

Parts: B C D

Answer 1