Question

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.

Answer 1

Solution:

For the given scenario, we are given

Sample proportion = P = 0.50

Margin of error = E = 4% = 0.04

Confidence interval = P ± E

Lower limit = P – E = 0.50 – 0.04 = 0.46

Upper limit = P + E = 0.50 + 0.04 = 0.54

Confidence interval = (0.46, 0.54)

If the men and women are not differing in their response, then population proportion for men and women should be 0.5. This means population proportion is considered as 0.5.

The population proportion of 0.5 is included in the above confidence interval, so there is sufficient evidence to conclude that men and women do not significantly differ in their responses to the company’s advertising at 95% confidence level.

Now, we have to find the required sample size for the given scenario. The sample size formula is given as below:

Sample size = n = P*Q*(Z/E)^2

Confidence level = 95%

So, critical Z value = 1.96

(By using z-table or excel)

Sample size = n = 0.5*0.5*(1.96/0.04)^2

Sample size = n = 600.25

Required sample size = 601 individuals

So, this research study will need 601 men and women for interview to get responses for questions regarding company’s advertising.

We are given cost per individual (CPI) = $25

So, cost for 601 persons = $25*601 = $15,025

Budget for this study is given as $60,000.

So, required amount is less than budget amount. This means we can do this study with the given budget.