Quiz 9: Determining Sample Size and the Sample Plan

Indicate the sample frame error typically found in the households listing of a telephone book.

Explain why the Literary Digest survey of the Landon/ Roosevelt election was so incorrect.

What is meant by accuracy of a sample and what is the formula to measure it?

What is the formula for estimating a percentage in the population? Explain what the variables z, p, q, and e represent.

What does p, q measure and what relationship does this have to the size of the sample, given all else is equal?

What do we mean by "level of confidence" and how is it expressed in the sample size formula?

What is the formula for estimating a mean in the population? Explain how its components are different/like the components in the formula for estimating a percentage.

What are three methods for estimating the variance in the population using the formula to calculate the sample size for estimating a mean?

Explain how you would use XL Data Analyst to calculate the desired sample size to estimate a percentage in the population.

How do probability samples differ from nonprobability samples and what is the significance of this difference?

What is simple random sampling and when would you use it?

What is systematic sampling and when would you use it?

What is cluster sampling and when would you use it?

What is stratified sampling and when would you use it?

How would you use XL Data Analyst to generate random numbers?

Explain how you would use the skip interval in a systematic sample if you had to draw a sample from your city telephone directory.

Would you use a proportionate or disproportionate stratified sample? Why?

Describe the four types of nonprobability samples.

What are the drawbacks of using a nonprobability sample and why are they used?

Briefly explain the three techniques presented in the chapter for online sampling.

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?

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

Aresearcher 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?

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?

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 top of mind awareness (TOMA). 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?

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 our sample statistic (mean) is within ± 0.5 of a scale point from the true population parameter. a. Calculate the required sample size. 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?

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 Saturdays. 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 mile 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. a. What is the required sample size? 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?

Target: Deciding on the Number of Telephone Numbers Target is a major retail store chain specializing in goodquality merchandise and good values for its customers. Currently, Target operates about 1,700 stores, including over 200 Super Targets, in major metropolitan areas of forty-eight of the U.S. states. One of the core marketing strategies employed by Target is to ensure that the shopper has a special experience every time he or she shops at Target. This special shopping experience is enhanced by Target's department arrangements that are intuitive (e.g., toys are next to sporting goods). Another shopping experience feature is the "racetrack" or extra wide center aisle that helps shoppers navigate the store easily and quickly. A third feature is the aesthetic appearance of its shelves, product displays, and seasonal specials. Naturally, Target continuously monitors the opinions and satisfaction levels of its customers because competitors are constantly trying to outperform Target, and/or customers' preferences change. Target management has committed to an annual survey of 1,000 of its customers to determine these very issues and to provide for a constant tracking and forecasting system of its customers' opinions. The survey will include customers of Target's competitors such as Wal-Mart, K-Mart, and Sears. In other words, the population under study is all consumers who shop in mass merchandise stores through Target's geographic markets. The marketing research project director has decided on the use of a telephone survey to be conducted by a national telephone survey data collection company, and he is currently working with Survey Sampling International (SSI) to purchase the telephone numbers of consumers residing in Target's metropolitan target markets. The SSI personnel have informed him of the basic formula they use to determine the number of telephone numbers needed. The formula is as follows: Telephone numbers needed = Completed interviews/(Working phone rate × Incidence × Completion rate) Where: Working phone rate _ percent of telephone numbers that are "live" Incidence = percentage of those reached that will take part in the survey Completion rate = percentage of those willing to take part in the survey that actually complete the survey As a matter of convenience, Target identifies four different regions that are roughly equal in sales volume: North, South, East, and West. 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?

Target: Deciding on the Number of Telephone Numbers Target is a major retail store chain specializing in goodquality merchandise and good values for its customers. Currently, Target operates about 1,700 stores, including over 200 Super Targets, in major metropolitan areas of forty-eight of the U.S. states. One of the core marketing strategies employed by Target is to ensure that the shopper has a special experience every time he or she shops at Target. This special shopping experience is enhanced by Target's department arrangements that are intuitive (e.g., toys are next to sporting goods). Another shopping experience feature is the "racetrack" or extra wide center aisle that helps shoppers navigate the store easily and quickly. A third feature is the aesthetic appearance of its shelves, product displays, and seasonal specials. Naturally, Target continuously monitors the opinions and satisfaction levels of its customers because competitors are constantly trying to outperform Target, and/or customers' preferences change. Target management has committed to an annual survey of 1,000 of its customers to determine these very issues and to provide for a constant tracking and forecasting system of its customers' opinions. The survey will include customers of Target's competitors such as Wal-Mart, K-Mart, and Sears. In other words, the population under study is all consumers who shop in mass merchandise stores through Target's geographic markets. The marketing research project director has decided on the use of a telephone survey to be conducted by a national telephone survey data collection company, and he is currently working with Survey Sampling International (SSI) to purchase the telephone numbers of consumers residing in Target's metropolitan target markets. The SSI personnel have informed him of the basic formula they use to determine the number of telephone numbers needed. The formula is as follows: Telephone numbers needed = Completed interviews/(Working phone rate × Incidence × Completion rate) Where: Working phone rate _ percent of telephone numbers that are "live" Incidence = percentage of those reached that will take part in the survey Completion rate = percentage of those willing to take part in the survey that actually complete the survey As a matter of convenience, Target identifies four different regions that are roughly equal in sales volume: North, South, East, and West. 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?

Target: Deciding on the Number of Telephone Numbers Target is a major retail store chain specializing in goodquality merchandise and good values for its customers. Currently, Target operates about 1,700 stores, including over 200 Super Targets, in major metropolitan areas of forty-eight of the U.S. states. One of the core marketing strategies employed by Target is to ensure that the shopper has a special experience every time he or she shops at Target. This special shopping experience is enhanced by Target's department arrangements that are intuitive (e.g., toys are next to sporting goods). Another shopping experience feature is the "racetrack" or extra wide center aisle that helps shoppers navigate the store easily and quickly. A third feature is the aesthetic appearance of its shelves, product displays, and seasonal specials. Naturally, Target continuously monitors the opinions and satisfaction levels of its customers because competitors are constantly trying to outperform Target, and/or customers' preferences change. Target management has committed to an annual survey of 1,000 of its customers to determine these very issues and to provide for a constant tracking and forecasting system of its customers' opinions. The survey will include customers of Target's competitors such as Wal-Mart, K-Mart, and Sears. In other words, the population under study is all consumers who shop in mass merchandise stores through Target's geographic markets. The marketing research project director has decided on the use of a telephone survey to be conducted by a national telephone survey data collection company, and he is currently working with Survey Sampling International (SSI) to purchase the telephone numbers of consumers residing in Target's metropolitan target markets. The SSI personnel have informed him of the basic formula they use to determine the number of telephone numbers needed. The formula is as follows: Telephone numbers needed = Completed interviews/(Working phone rate × Incidence × Completion rate) Where: Working phone rate _ percent of telephone numbers that are "live" Incidence = percentage of those reached that will take part in the survey Completion rate = percentage of those willing to take part in the survey that actually complete the survey As a matter of convenience, Target identifies four different regions that are roughly equal in sales volume: North, South, East, and West. What is the lowest and highest total number of telephone numbers to be purchased for the entire survey?

Your Integrated Case Advanced Automobile Concepts As you know, Nick Thomas, CEO of Advanced Automobile Concepts, has agreed with Cory Rogers of CMG Research to use an online method of survey. In particular, the decision has been made to purchase panel access, meaning that the online survey, developed with the use of Qualtrics, will be completed by individuals who have joined the ranks of the panel data company and agreed to periodically answer surveys online. Even though these individuals are compensated by their panel companies, the companies claim that their panel members are highly representative of the general population. Also, because the panel members have provided extensive information about themselves such as demographics, lifestyles, and product ownership that is stored in the panel company data banks, a client can purchase this data without the necessity of asking these questions on its survey. Rogers's CMG Research team has done some investigation and they have concluded that there are several panel companies that can provide a representative sample of U.S. households. Rogers decides to purchase the sample from a company that can provide a probability sample of U.S. households. The company provides blended data, which is a combination of stored database information on the panel members and answers to online survey questions. The cost will be based on the number of respondents. Rogers knows that his Advanced Automobile Concepts client is operating under two constraints. First, Zen Motors top management has agreed to a total cost for all of the research, and it is up to Thomas to spend this budget prudently. If a large portion of the budget is expended on a single activity, such as paying for an online panel sample, then there are less funds available for other research activities. Second, Rogers knows from his extensive experience with clients that both Thomas and Zen Motors top management will expect this project to have a large sample size. Of course, as a marketing researcher, Rogers realizes that large sample sizes are generally not required from a sample error standpoint, but he must be prepared to respond to any questions, reservations, or objections from Thomas or Zen Motors top management when the sample size is proposed. As preparation for the possible need to convince top management that Rogers's recommendation is the right decision for the sample size for the Advanced Automobile Concepts survey, he decides to make a table that specifies sample error and cost of the sample. For each of the following possible sample sizes, calculate the associated expected cost of the panel sample and the sample error. 1. 20,000 2. 10,000 3. 5,000 4. 2,500 5. 1,000 6. 500