Question

I just need the answer for question D, please show all your work, thank you.

I

(1 point) Hourly wages at Manufacturing Plant A very from worker to worker, with an average hourly wage of $14.09, and a standard deviation of $2.3 per hour, or σ/YanIA-2.3. 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 ơPlantB (a) Choose the correct statistical hypotheses A. Ho . Įị Plant B > 14.09 HA : μΡ1amB-14.09 14.09 HA HPlant B < C. Ho : μ Plant B-14.09 HA : μ Planı B + 14.09 D. 11() : X Plant B > 14.09 HA-X Plant B < 14.09 E. Ho : HPlanB HA F. Ho : X 14.09 HA : μΡ1anı B > ! в = 14.09 HA . XPlantB > 14.09 14.09 PlantB - (b) Statistical testing of the null hypothesis is to be carried out by randomly selecting 37 employees at Plant B. If the mean/average hourly wage of these 37 employees is greater than $14.67, 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 a was used here? Enter your answer to at least three decimal places. 0.06253 (c) The average of the sample of n - 37 workers was found to be X - 14.41. What decision can you make from this sample? A. Employees at Plant B do earn more on average compared to employees at Plant A e sample size is too small to conduct a statistical test, so a decision cannot be made o C. Employees at Plant B do not earn more on average compared to employees at Plant A. 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 $14.55, 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 Answer0.1158

Answer 1

d)

for P(plant B is not greater than plant A)=P(Xbar<14.67)=P(Z<(14.67-14.55)*sqrt(37)/2.3)

=P(Z<0.3174)=0.62452