1. Hourly wages at Manufacturing Plant A very from worker to worker, with an average hourly wage of $14.18, and a standard deviation of $2.58 per hour, or σPlantA=2.58. 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=2.58. (a) Choose the correct statistical hypotheses. A. H0:μPlantB>14.18HA:μPlantB=14.18 B. H0:μPlantB≥14.18HA:μPlantB<14.18 C. H0:μPlantB=14.18HA:μPlantB≠14.18 D. H0:X―PlantB=14.18HA:X―PlantB>14.18 E. H0:μPlantB=14.18HA:μPlantB>14.18 F. H0:X―PlantB>14.18HA:X―PlantB<14.18 (b) Statistical testing of the null hypothesis is to be carried out by randomly selecting 40 employees at Plant B. If the mean/average hourly wage of these 40 employees is greater than $14.7, 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=40 workers was found to be X―=14.32. 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 hourly wages at Plant B need to be Normally distributed to do the test D. The sample size is too small to conduct a statistical test, so a decision cannot be made (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. 2. The owner of a dry cleaning store believes that the mean amount a customer spends on a dry cleaning order exceeds $22.2. A statistician has said to him that he can be statistically sure that his belief is true if the mean amount of 100 randomly chosen customer bills is greater than $23.09, or X―>23.09. It is assumed that the standard deviation in the bill amounts is $12.72 (σ=12.72). (a) Choose the correct statistical hypotheses. A. H0:X―=22.2,HA:X―>22.2 B. H0:X―>23.09,HA:X―≤23.09 C. H0:X―=22.2,HA:X―≠22.2 D. H0:μ>22.2,HA:μ<22.2 E. H0:μ=22.2,HA:μ≠22.2 F. H0:X―=23.09,HA:X―>23.09 G. H0:μ=22.2HA:μ>22.2 (b) What is the probability of making a Type I error, using the statistician's criterion? Use at least three decimals in your answer. (c) Unknown to anyone, suppose the mean amount spent by all his customers is $21.7. Find the probability that the owner will conclude that the mean amount a customer spends on a dry cleaning order exceeds $22.2 (his original belief) is correct. Use at least three decimals in your answer. (d) Suppose the statistician decides to change the sample size to n=200 and regulate P(TypeI)=0.05. For what values of X― should the null hypothesis in (a) be rejected? A. Reject the null hypothesis if μ>24.29 B. Reject the null hypothesis if μ>43.12 C. Reject the null hypothesis if X―>23.09 D. Reject the null hypothesis if X―>43.12 E. Reject the null hypothesis if X―>22.2 F. Reject the null hypothesis if X―>23.68 G. Reject the null hypothesis if μ>23.68 H. Reject the null hypothesis if X―>24.29