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I need help with these sample size questions. The questions are answered but could you show the work on how to get to the answers.   

Review Materials ? Sample Size Determination


1. You are working for a large corporation and are in charge of a marketing research project. For this study, your


questionnaire length is 10 minutes and the incidence is 35%, yielding a CPI is $23.00. Your company requires all research


to be at the 95% confidence level, MOE at +/-2%, and to assume a sample statistic of .50 (P and Q = .50). They?ve given


you a budget of $45,000 to complete this survey.


What sample size can you do with this budget, and want is the MOE associated with this sample size? Does this MOE fall


within the parameters of the company requirements? What sample size would you need to stay within the company


MOE requirements for all research studies and how much budget would you need for this study? Please show all your




Answers: n=1957 with MOE of +/- 2.3%.


For a MOE of +/-2% a sample of 2500 would be needed, costing $57,500.


2. You are working with a MOE of +/-4% and a confidence level of 95%. P and Q =.50, and your CPI is $25.00. The


company you work for needs to make a decision as to whether they may need different advertising for men and women.


So, your supervisor wants to know if men and women differ in their response to the company?s advertising. You are in


charge of designing and running this research study.


Given the parameters, what will be your sample size for this study. Now, if you want to assume a MOE of at least +/-4%


for men and for women, how many men and women will you want to interview? What will this particular study cost?


Now, suppose you have a budget of $60,000. Can you do this study with this budget? Please explain your answers.


Answers: n=625. For men and women (625 x 2), 625 of each gender or a total of n=1250 to assure +/-4% in each strata.


$31,250, Stratified Sample , Yes.


3. What is the sample size for studies with MOE of +/-3.5% and +/-2.8%?, with a confidence level of 95%, sample


statistics of .50? Please show your work.


Answers: 816 and 1276


4. Your supervisor comes to you and says she would like to do a marketing research study. She says there is a


budget of $30,000. She would like to conduct a simple random sample of consumers interested in using the


services of the company. She thinks that a sample of 750 would be plenty.


a. Given a confidence level of 95%, and a sample statistic of .50, what will be the MOE for a study of this


type? Answer: +/-3.65% or +/-3.7%


b. If the CPI is $15.75 per completed interview, can you do this study within the given budget?


Answer: $11,811.50, YES this study of 750 at $15.75 CPI can be done within the budget of $30,000.


c. How much more or less sample might you need to spend the entire budget?


Answer: Budget of $30,000 yields sample of 1904, which is 1154 more than 750.


d. What will be the MOE for that study (the one that uses the entire budget)? Answer: n=1904, +/-2.3%


3. What is the sample size for studies with MOE of +/-3.5% and +/-2.8%, with a confidence level of 95%, sample statistics


of .50, and a category population of 7500 (less than 10,000)? Remember the FPC. Please show your work.


Answers; approximately n=736 and n=1091.




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Dec 18, 2020





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