X2 bar = 76.26
a) Do you agree with the Production Manager that after the adjustment the mean weight is significantly less than the mean weight before the adjustments?
b) Does the new adjustment yield a mean weight within control?
c) The client has sent his Quality Control team to verify the results of the adjustments made. The Quality Control Auditor has issued a report that he is very concerned because the adjustments made to the process yield a significantly larger variability than before the adjustments, and even that the mean weight may have been reduced, the variability of the mean after the adjustments is unacceptable. Perform the appropriate statistical analysis to evaluate the Quality Control Auditor assessment, and draw conclusions.
d) Furthermore, the Quality Control Auditor has stated that also the proportion of the samples with a weight at unacceptable and unsafe limits (more than 85 lbs) has increased significantly after the adjustments. Perform the appropriate test statistics to evaluate the Quality Control Auditor concern. Draw conclusions and build the appropriate confidence interval of the difference in the proportions at unacceptable weight before and after the adjustment.
e) The Quality Auditor has concluded that the variability (not the mean weight) before the adjustment was acceptable (sb). The CEO has instructed you to determine a sample size required to detect an increase of the variability after the adjustment (sa) by 10% (sb = 1.1 sa) with a probability of 90%. What sample size do you recommend to use?