PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers after assembly; results from the past 30 days are given in the worksheet Mower Test in the Performance Lawn Equipment Database. In addition, many in-process measurements are taken to ensure that manufacturing processes remain in control and can produce according to design specifications. The worksheet Blade Weight shows 350 measurements of blade weights taken from the manufacturing process that produces mower blades during the most recent shift. Elizabeth Burke has asked you to study these data from an analytics perspective. Drawing upon your experience, you have developed a number of questions.

1. For the mower test data, what distribution might be appropriate to model the failure of an individual mower?
2. What fraction of mowers fails the functional performance test using all the mower test data?
3. What is the probability of having x failures in the next 100 mowers tested, for x from 0 to 20?
4. What is the average blade weight and how much variability is occurring in the measurements of blade weights?
5. Assuming that the data are normal, what is the probability that blade weights from this process will exceed 5.20?
6. What is the probability that blade weights will be less than 4.80?
7. What is the actual percent of blade weights that exceed 5.20 or are less than 4.80 from the data in the worksheet?
8. Is the process that makes the blades stable over time? That is, are there any apparent changes in the pattern of the blade weights?
9. Could any of the blade weights be considered outliers, which might indicate a problem with the manufacturing process or materials?
10. Is the assumption that blade weights are normally distributed justified?

Summarize all your findings to these questions in a well-written report.

1. What proportion of customers rate the company with “top box” survey responses (which is defined as scale levels 4 and 5) on quality, ease of use, price, and service in the Customer Survey worksheet? How do these proportions differ by geographic region?
2. What estimates, with reasonable assurance, can PLE give customers for response times to customer service calls?
3. Engineering has collected data on alternative process costs for building transmissions in the worksheet Transmission Costs. Can you determine whether one of the proposed processes is better than the current process?
4. What would be a confidence interval for the proportion of failures of mower test performance as in the worksheet Mower Test?
5. For the data in the worksheet Blade Weight, what is the sampling distribution of the mean, the overall mean, and the standard error of the mean? Is a normal distribution an appropriate assumption for the sampling distribution of the mean?
6. How many blade weights must be measured to find a 95% confidence interval for the mean blade weight with a sampling error of at most 0.05? What if the sampling error is specified as 0.02?
7. Elizabeth Burke has identified some additional questions she would like you to answer using the Performance Lawn Equipment Database.
   1. Are there significant differences in ratings of specific product/service attributes in the Customer Survey worksheet?
   2. In the worksheet On-Time Delivery, has the proportion of on-time deliveries in 2018 significantly improved since 2014?
   3. Have the data in the worksheet Defects After Delivery changed significantly over the past five years?
   4. Although engineering has collected data on alternative process costs for building transmissions in the worksheet Transmission Costs, why didn’t they reach a conclusion as to whether one of the proposed processes is better than the current process?
   5. Are there differences in employee retention due to gender, college graduation status, or whether the employee is from the local area in the data in the worksheet Employee Retention?

   Conduct appropriate statistical analyses and hypothesis tests to answer these questions and summarize your results in a formal report to Ms. Burke.