**Explain how the determination of sample size is a ﬁnancial, statistical, and managerial issue.**

The determination of sample size is a financial, statistical and managerial issue. When a sample is determined, researchers need to take care of the sample size because any additional or unneeded sample size would result in extra costs for their study and hence, it becomes a financial issue. Secondly, when the sample size is not determined properly, it results in manipulation of the results and the statistical analysis cannot be carried out properly (Smith, 2013). Lastly, it is also a managerial issue because if it is determined properly, it can be managed easily at organizational level. Simply, it can be said that larger samples cost more money. In terms of statistical issue, the increasing sample size tends to rise on a liner basis while the managerial issues refer to the sample size calculations (McDaniel & Gates, 2013).

**Discuss and give examples of three methods that are used in marketing research for determining sample size.**

Some of the methods that are used in marketing research for determining the sample size include the budget available, the rule of thumb and traditional statistical methods. The budget available method is used to determine sample size, at least indirectly. For example, a brand manager who has 5000$ available in the budget for testing a new product, he will choose sample size based on his budget. In a thumb rule, the clients may specific in their request proposal that they want a sample of 100, 200 or 300. If the researcher finds out that the sample size is not adequate to meet with the objectives of the study, then he is ethically bound to present arguments for a larger sample and ask him to make the final decision (Kadam & Bhalerao, 2010). Other traditional statistical methods for determining sample size include the estimate of population Standard division and the acceptable level of sampling error etc.

**A marketing researcher analyzing the fast-food industry noticed the following: The average amount spent at a fast-food restaurant in California was $3.30, with a standard deviation of $0.40. Yet in Georgia, the average amount spent at a fast-food restaurant was $3.25, with a standard deviation of $0.10. What do these statistics tell you about fast-food consumption patterns in these two states?**

The average amount spent at the fast food restaurants in the California and Georgia followed by a standard division makes it clear that in California the food consumption patterns are a bit higher. The fast food which is consumed in the California usually varies having a standard average amount spent followed by a larger standard division as compared to that of Georgia. While in Georgia, the fast food consumption patterns are a bit stable as the standard deviation was lower over there (Charan & Biswas, 2013).

**Distinguish among population, sample, and sampling distributions. Why is it important to distinguish among these concepts?**

Population distribution is a frequency distribution of all the elements of a population. The sample distribution is the frequency distribution of all the elements of an individual sample while the sampling distribution refers to the probability distribution of a statistic obtained by a large number of samples drawn from a specific population. It is important to distinguish among these concepts because they differentiate between different elements of population, sample and larger number of samples.

**What is the ﬁnite population correction factor? Why is it used? When should it be used?**

Finite population correction factor is also known as FPC and it is an adjustment to needed sample size that is made in such case when the sample is expected to be equal to five percent or more of the total population. It is used in the situations where the sample is large and when the researcher can appropriately reduce the required sample size using it. It should be used when the initially used sample size is not sufficient enough to give appropriate and valid results that might meet with the study objectives.

**Assume that previous fast-food research has shown that 80 percent of the consumers like curly French fries. The researcher wishes to have a standard error of 6 per-cent or less and be 95 percent conﬁdent of an estimate to be made about curly French fry consumption from a survey. What sample size should be used for a simple random sample?**

The samples size that should be used for a simple random sample is this case considering the factors of standard error of 6% and the 95% of an estimate, depends on the population which is being targeted (Binu, Mayya, & Dhar, 2014). However, as the scenario states that the sample size should be for a simple random sample, hence using the sample size formula for proportion and round-off number 2 instead of 1.96:

n= 2^{2}[.8(1-.8)]

.06^{2}

n= 177.8

Thus a sample size of 178 subjects is needed.

**You are in charge of planning a chili cook-off. You must make sure that there are plenty of samples for the patrons of the cook-off. The following standards have been set: a conﬁdence level of 99 percent and an error of less than 4 ounces per cooking team. Last year’s cook-off had a standard deviation in amount of chili cooked of 3 ounces. What is the necessary sample size?**

In this case, using the sample size formula for mean and round-off number 2.6 instead of 2.575,

n= (2.6)^{2}x3^{2}

4^{2}

n=15.21

Thus a sample size of 16 is required.

**Based on a client’s requirements of a conﬁdence interval of 99.74 percent and acceptable sampling error of 2 percent, a sample size of 500 is calculated. The cost is estimated at $20,000. The client replies that the budget for this project is $17,000. What are the alternatives?**

As the budget for the project is 17000 while the estimated costs are 20000$, the client can be asked to use any alternative ways to increase his budget in order to meet with the research objectives. Particularly, client can either change his research objectives a little bit that would reduce the sample size up to 400 people or he needs to increase his budget.

**A marketing researcher must determine how many telephone numbers she needs order from a sample provider to complete a survey of ATM users. The goal is to complete 400 interviews with ATM users. From past experience, she estimates that 60 per-cent of the phone numbers provided will be working phone numbers. The estimated incidence rate (percentage of people contacted who are ATM users) is 43 percent. Finally, she estimates from previous surveys that 35 percent of the people contacted will agree to complete the survey. How many telephone numbers should she order?**

Considering all the factors in mind, it is clear that she needs a total of 4445 phone numbers in order to complete 400 interviews.

From 4445 phone numbers, the 60% will be working = 2667 working phone numbers

43% of 2667 phone numbers are using ATM that is = 1147 Phone numbers

35% of 1147 numbers are ready to participate in survey = 401 persons

# Bibliography

Binu, V. S., Mayya, S. S., & Dhar, M. (2014). Some basic aspects of statistical methods and sample size determination in health science research . *An International Quarterly Journal of Research in Ayurveda, 35*(2), 119-123.

Charan, J., & Biswas, T. (2013). How to Calculate Sample Size for Different Study Designs in Medical Research? . *Indian Journal of Psychological Medicine, 35*(2), 121-126.

Kadam, P., & Bhalerao, S. (2010). Sample size calculation . *International Journal of Ayurveda Research, 1*(1).

McDaniel, C., & Gates, R. (2013). SAmple Size Determination. In *Marketing Research Essentials* (8th Edition ed., pp. 300-323). Hoboken, New Jersey: John Wiley and Sons, Inc.

Smith, S. (2013). Determining Sample Size: How to Ensure You Get the Correct Sample Size. *Qualtrics *.