Determining sample size for fast food restaurant visit frequency survey

Marketing Analysis

Management needs to estimate how many times the average fast food restaurant user visits a fast food restaurant in an average month. Management needs this information to make a decision regarding a new promotional campaign that is being developed. A year ago, a similar study was conducted and the standard deviation in that study for the variable, "average number of times a fast food restaurant was visited in the past 30 days," was 1.39. The marketing research manager, Bill, intends to survey a random sample of fast food users using telephone interviewing and the random digit dial method. The managers believe a high degree of accuracy is needed which the marketing research manager takes to mean that the estimate should be within one-tenth (0.10) of a visit of the true population value. Bill wants to be 95% confident that the true population mean falls in the interval defined by the sample mean, plus or minus the error just defined. Previous studies have recorded a typical sample response rate in similar telephone interviews of 35%. What size of sample is necessary to meet the requirements outlined? Show all calculations.

Sample Size for Frequency in a Population

Population size (for finite population correction factor or fpc)(N):

Hypothesized % frequency of outcome factor in the population (p):

Confidence limits as % of 100(absolute +/- %)(d):

Design effect (for cluster surveys-DEFF):

Sample size n = [DEFF*Np (1-p)] / [(d2/Z21-?/2*(N-1)+p*(1-p)]

Sample Size (n) for Various Confidence Levels

Source: Mathsoft.com equations

Confidence

Level (%)

Sample Size

Question Two manufacturer would like to survey users to determine the demand potential for a new power press. The new press has a capacity of 500 tons and costs $225,000. It is used for forming products from light- and heavy-weight steel and can be used by automobile, construction equipment, and major appliance manufacturers.

A a) Identify the population and sampling frame that could be used.

This specific research needs to include manufacturing, operations, and financial senior managers and executives from the automobile, construction equipment and major appliance or durable goods industries. These specific sets of executives need to be included in the population as each department represented have different needs and requirements for the power press. The needs of manufacturing executives include the integrate the power press into existing manufacturing processes and workflows, in addition to understanding how the specific aspects of the press will need to potentially be integrated into other machinery. The operations executives need to be involved to understand how maintenance, repair and overhaul schedules will need to be specifically be handled for the new power press. Finally, as the press costs $225,000, the financial analysis will need to be completed most likely by the Chief Financial Officers' (CFO)s' office. The sampling frame will include all those manufacturing companies in each of the specific segments listed above (automobile, construction equipment and major appliance) and their VP-level and C-level executives who have P&L responsibility for each of the respective functions they represent.

A b) Describe how a simple random sample can be drawn using the identified sampling frame.

After first creating a listing of all manufacturers that are part of the population, the technique of simple random sampling (SRS) can next be used to select manufacturers to participate in the survey. As a prerequisite to defining the specific list of manufacturers, the functional areas of manufacturing, operations, and finance need to be verified as departments in the list of companies that are part of the total population. Providing this prerequisite is met, the population from which the sample is chosen will be truly representative of the eventual customer base targeted for purchasing the new power press.

Could a stratified sample be used? If so, how?

Yes, a stratified random sampling technique could also be used as the specific companies that comprise the population could be stratified or layered by their specific criteria. The most common one used is revenues, yet spending on capital equipment, or the number of production plants could also be used to stratify the sample. Of these, financial measures are the most basis of stratification in research populations.

A e) Which sampling technique would you recommend? Why?

Of all techniques, a stratified random sample based on revenues is the best approach as there will be major differences in the approaches these companies take in funding a new power press. There will be differences in the approaches each of these stratified samples have in terms of how they also track and report Return on Invested Capital (ROIC), and their approaches to managing the financial evaluation process for new equipment.

A f) Identify two possible nonsampling research errors that might occur in the sampling plan you recommended. Explain how you would deal with these nonsampling errors.

Using a stratified random sampling technique based on revenue could provide two nonsampling research errors. The first would be that the assumption of purchasing processes varying significantly by size of company based on revenue could prove to be erroneous, yet sample means testing would bring this out quickly during a preliminary statistical analysis of the results. A second error could potentially be the lack of ROI activity across both groups, a fact that would not emerge until after the analysis was completed. The first problem could be alleviated through the use of a set of screening criteria applied to the entire research population prior to the survey being completed to ensure the hypothesis of processes being different actually exist. The second error could be alleviated through speaking with industry research firms who possibly have secondary data in the form of ROI analyses in the industries of interest. Specifically, industry associations for automobile, construction equipment and major appliance or durable goods industries could be contacted to see if they have any visibility into the ROI processes in place by size of company.

Question Three

Refer to the Pella Satisfaction Questionnaire. Identify what meaningful and useful analyses you would like to conduct and why: What cross-tabulations for which variables?

Cross-tabs need to include Question 1 on customer satisfaction by questions 3, 4, 5, 6, and both 7a and 7b. These cross-tabs will explain the specific attributes that lead to greater customer satisfaction from a sales cycle execution standpoint, product features, performance and perception of them by owners as