“ top box ” survey responses B u s i n e s s F i n a n c e

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.

- For the mower test data, what distribution might be appropriate to model the failure of an individual mower?
- What fraction of mowers fails the functional performance test using all the mower test data?
- What is the probability of having
*x*failures in the next 100 mowers tested, for*x*from 0 to 20? - What is the average blade weight and how much variability is occurring in the measurements of blade weights?
- Assuming that the data are normal, what is the probability that blade weights from this process will exceed 5.20?
- What is the probability that blade weights will be less than 4.80?
- What is the actual percent of blade weights that exceed 5.20 or are less than 4.80 from the data in the worksheet?
- Is

the process that makes the blades stable over time? That is, are there

any apparent changes in the pattern of the blade weights? - Could

any of the blade weights be considered outliers, which might indicate a

problem with the manufacturing process or materials? - Is the assumption that blade weights are normally distributed justified?

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

- 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? - What estimates, with reasonable assurance, can PLE give customers for response times to customer service calls?
- 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? - What would be a confidence interval for the proportion of failures of mower test performance as in the worksheet
*Mower Test*? - 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? - 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? - Elizabeth Burke has identified some additional questions she would like you to answer using the
*Performance Lawn Equipment Database*.- Are there significant differences in ratings of specific product/service attributes in the
*Customer Survey*worksheet? - In the worksheet
*On-Time Delivery*, has the proportion of on-time deliveries in 2018 significantly improved since 2014? - Have the data in the worksheet
*Defects After Delivery*changed significantly over the past five years? - 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? - 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. - Are there significant differences in ratings of specific product/service attributes in the