June 7, 2019

ANSWERS TO APPLICATION QUESTIONS

22. Here are four populations and a potential sample frame for each one. With each pair,

identify (1) members of the population who are not in the sample frame, and (2)

sample frame items that are not part of the population. Also, for each one, would you

judge the amount of sample frame error to be acceptable or unacceptable?

Population Sample Frame

a. Buyers of Scope mouthwash Mailing list of Consumer Reports

subscribers

Omitted are Scope buyers who do not subscribe to Consumer Reports, a very

considerable number, no doubt. Included are all those who do subscribe but do not

b. Listeners of a particular FM Telephone directory in your city

radio classical music station

Omitted are unlisted and new telephone listings, while included are those with listed

c. Prospective buyers of a new Members of Sales and Marketing Executives

day planner and prospective International (a national organization of

clients tracking kit sales managers)

Omitted are sales persons who do not belong to SMEI, probably a very considerable

proportion of all salespeople in the area. Included are retired salespeople, sales

d. Users of weatherproof decking Individuals’ names registered at a recent

materials (to build outdoor decks) home and garden show

Omitted are all those who did not attend the show plus those who did attend but did

not register. Included are people who have decks, people who do not want a deck, and

23. Here are some numbers that you can use to sharpen your computational skills for

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sample size determination. Crest toothpaste is reviewing plans for its annual survey

of toothpaste purchasers. With each case that follows, calculate the sample size

pertaining to the key variable under consideration. Where information is missing,

provide reasonable assumptions. You can check your computations by using the

sample size calculation feature of the XL Data Analyst.

Key Variable Variability Acceptable

Error

Confidence

Level

Market share of Crest

toothpaste last year

The calculations and rationale for each follow:

Case p q e z Sample size

24. A researcher has the task of estimating how many units of a new, revolutionary

photocopy machine (it does not require ink cartridges and it is guaranteed not to

jam) will be purchased among business firms in Cleveland for the coming annual

sales forecast. She is going to ask the likelihood that they will purchase the new

device and for those that are “very likely” to purchase, she wants the respondents at

the companies to estimate how many machines their company will buy. She has data

that will allow her to divide the companies into small, medium, and large firms based

upon number of employees at the Cleveland office.

What sampling plan should be used? Why?

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example, some small firms may not be able to afford a single machine, but many

large companies may purchase multiple units for multiple locations. Similarly, the

25. Honda USA is interested in learning what its 550 U.S. dealers think about a new

service program Honda USA provided the dealers at the beginning of last year.

Honda USA wants to know if the dealers are using the program and, if so, their likes

and dislikes about the program. Honda USA does not want to survey all 550 dealers

but wants to ensure that the results are representative of all the dealers.

What sampling plan should be used? Why?

Honda dealerships are relatively homogeneous or highly similar, so there is no need

to stratify. Large geographic differences (weather, altitude, typology, etc.) exist, so

For SRS, number the dealers 1 through 550 and use a random number generator to

For a systematic sample, arrange the dealerships alphabetically. Draw a random

number between 1 and 550. Then use the skip interval (550/n) to select the dealers.

26. Applebee’s Restaurants has spent several thousand dollars advertising the restaurant

during the last two years. They wish to have some input into what effect the

advertising has made and they decide to measure TOMA (Top of Mind Awareness). A

TOMA “score” for such a restaurant is the ranking a firm has as a result of asking a

representative sample of consumers in the service area to “Name a non-fast-food

restaurant.” The restaurant that is named by the most persons has the #1 TOMA

score, and so on. It is important that Applebee’s management conduct their TOMA

survey on a representative sample in the metropolitan area.

What sampling plan should be used? Why?

Such surveys are commonly administered by telephone. The strong desire for a

representative sample leads to the use of a probability sample method. A Random

27. We have a 7-point scale to measure the construct: likelihood of buying a new car. We

wish to estimate the mean score on the scale and we want to be 95% confident that

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our sample statistic (mean) is within ±0.5 of a scale point from the true population

parameter.

a. Calculate the required sample size.

This use of the 7-point metric scale means that sample size formula for a mean should

be used. There is no information on the variability, so to estimate “s,” it is advisable

to use the “range/6” approach. Thus, the sample size (n) would be:

Note: This may seem like a small sample size and it is. Why? With a 7-point scale

you have limited variance. It does not require a large sample size to estimate a

b. After you calculate the sample size in 27a, you decide you want to halve the level

of accuracy. What would the new sample size be?

This requires students to think about the concept of accuracy. HALVING accuracy

means to make it LESS accurate so your new e should be set at 1.0 instead of .5.

Alternatively, you may want to ask your students to DOUBLE accuracy. Then, the

28. A plan is set before all state universities to require classes to meet either three or four

days a week in order to make better use of classroom facilities, because currently

classrooms sit empty Friday afternoons and evenings and on Saturday. However,

some schools that have a large percentage of commuter schools are concerned that

this proposal will put a hardship on their commuter students because it will require

more driving to/from the campus. University officials want to estimate the average

number of miles driven, one way, to campus by its commuter students. It is estimated

that some students drive as little as 0 miles to campus while at least one student

reported driving one way as far as 60 miles. University officials want to be 95%

confident that the sample mean is no more than ±2 miles from the real average

number of miles driven in the population.

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a. What is the required sample size?

This use of miles commuted means that sample size formula for a mean should be

used. There is no information on the variability, so to estimate “s,” it is advisable to

use the “range/6” approach. Thus, the sample size (n) would be…

b. After the study is conducted we learn that the standard deviation in the sample

data, which is now our best estimate of s, is actually 12.3. What impact does this

new measure of variation have on the mean number of miles driven that we also

derived from our sample?

The key to understanding this question is to make students think about what they

were doing when they calculated the sample size—they were estimating variance.

However, after the study, we have a representative sample from the population and

we can easily calculate variance in this data. Data from the sample should now be our

best estimate of the actual variance in the population. So, now students need to realize

CASE SOLUTIONS

Case 9.1 Target: Deciding on the Number of Telephone Numbers

Case Objective: With this case students must use the formula for the number of

telephone numbers needed in order to obtain a target final sample size.

Answers to Case Questions

1. With a desired final sample size of 250 for each region, what is the

lowest total number of telephone numbers that should be

purchased for each region?

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2. With a desired final sample size of 250 for each region, what is the

highest total number of telephone numbers that should be

purchased for each region?

The low and high numbers are in the following table. Students must

realize that a low estimated working, incidence, and completion rate

North South East West

3. What is the lowest and highest total number of telephone numbers

to be purchased for the entire survey?

Case 9.2 Integrated Case: Advanced Automobile Concepts

Case Objective: This case requires students to compute sample size

error and to calculate the associate costs of various

sample sizes computed.

Answers to Case Questions

For each of the following possible sample sizes, calculate the

associated expected cost of the panel sample and the sample error.

Using p = q = 50%, the associated errors and costs are below.

Sample

size

Error

(95%)

Cost

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