# Chapter 8 & 9 Case Study

Chapter 8 & 9 Case Study

October 20, 2009

Chapter 8 9 Case StudyISQS 5345: Business Statistics

Team 4:

Kyle Lock

Jeff Morris

Derrick Plunk

Brian Wilder

10/20/2009

Page 4

Chapter 8 & 9 Case Study

October 20, 2009

**Table of Contents**

Chapter 8 Case Study 3

Question 1 3

Question 2 3

Question 3 3

Question 4 3

Chapter 9 Case Study 4

Question 1 4

Question 2 4

Question 3 4

Question 4 4

Question 5 4

Page 4Chapter 8 & 9 Case Study

October 20, 2009

## Chapter 8 Case Study

### Question 1

*Do you agree that drawing a second sample was a good idea?*

Certainly not the way they did it! Because they did not get responses from the entire first 400, they chose 200 more people at random. Was this a sampling with replacement, or a sampling without replacement? If it was a sampling with replacement, you may be using data from one person twice, which would not help to produce a representative sample. Drawing a second sample would have been a good idea only if the purpose of the second sample was to get the number of respondents up to n, and only if those selected were truly selected at random and not repeated from the first sample.

### Question 2

*Do you agree that the follow-up mailings were a good idea?*

I think the timing of the follow-up mailings is important. If they were sent after the second sample was already mailed out (which I think is what the text is saying), then the responses of the follow-ups should not matter. Also, it doesn't say in the book, but shouldn't these responses be independent and submitted without being influenced, even by something as innocuous as a dollar?

### Question 3

*How might you explain differences among averages in the results?*

Obviously, someone in the Pilot study is doing an ungodly amount of spending that has skewed the average and standard deviation beyond a reasonable amount. The total spending of that one company must be an outlier and the pilot study should probably not be used. However, the average and standard deviation of the first, second and combined samples seem to be somewhat uniform.

### Question 4

*Are there useful results here? Which ones are useful? Are they sufficient, or is further study needed?*

The company initially set n at 400 and even with all the respondents accounted for including the pilot study with the questionable respondent, the total respondents only amounts to 348. My advice would be to start over using the random numbers table, select 400 new numbers between 1 and 8,391 and allow those respondents to give you your sample data.

## Chapter 9 Case Study

### Question 1

*Is it proper to multiply the average order size, $53.94, by the number of addresses (1,300,000) in the target mailing?*

No, the average $53.94 is the sample average used in the random sample. Multiplying this average by the target mailing addresses produces false and skewed results.

In addition, this $53.94 average is the result of 9 respondents out of 74 returned. The other 65 respondents may not be interested in purchasing out of the specialty catalog at all, so why are we applying a $53.94 average charge to them?

### Question 2

*Is it better, as suggested, to multiply the endpoints of the confidence interval by the target mailing size?*

No. The target interval is wrong as well since the sample average is skewed.

### Question 3

*Would it be better to multiply by the size of the frame used to compute the random sample?*

Yes, it would be better to multiply the frame by sample size instead of the population size. This will give more accurate confidence intervals. Lastly, it would be better, but it still wouldn't be great!

### Question 4

*Should anything else trouble you about this situation?*

Yes, according to the study the random sample is 600,000 of well off people. In the target addresses is there a low income and middle income bracket? If so they needed to included in the random sample.

In addition, I would think it would be a mistake to base a calculation on what 1,300,000 people will do with only 9 dollar amounts. Wasn't n supposed to equal 600?!

### Question 5

*What is your best estimate, with confidence limits, for potential catalog sales?*

The potentials sales are between $-2.97 and $110.85.

Lower Limit:

n=9 / t=2.306 / x=53.94 / x-t(Sx) / .5394-(2.306*.2468) / .5394-.5691=-0.0297

Upper Limit:

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