Question

Baylor Athletics plans to conduct a survey among Waco residents to see what proportion of people from outside the Baylor community attends Baylor games. Based on a previous survey, about 25 percent of the residents are expected to attend Baylor games.

1. If Baylor athletics wants the data precision to be +/-3 percent with a 99 percent confidence level, what sample size (i.e. the number of completed survey responses) would you recommend for Baylor Athletics?
2. If the number of Waco residents (not including the Baylor community) is 100,000, do you need to apply the Finite Correction Factor (FCF) to the sample size you estimated and why?

[The Z_B,CLfor 90%, 95% and 99% confidence level are 1.65, 1.96 and 2.58 respectively].

Answer 1

If Baylor athletics wants the data precision to be +/-3 percent with a 99 percent confidence level, what sample size (i.e. the number of completed survey responses) would you recommend for Baylor Athletics?

The sample size formula is given as below:

n = p*q*(Z/E)^2

We are given

p = 0.25

q = 1 – p = 0.75

Confidence level = 99%

Critical Z value = 2.58

(by using z-table)

Margin of error = E = 0.03

The sample size is given as below:

n = p*q*(Z/E)^2

n = 0.25*0.75*(2.58/0.03)^2

n = 1386.75

Required sample size = 1387

If the number of Waco residents (not including the Baylor community) is 100,000, do you need to apply the Finite Correction Factor (FCF) to the sample size you estimated and why?

We are given N = 100000

So, 5% of N = 100,000*0.05 = 5000

So, above sample size n = 1387 is less than 5000, so we don’t need to apply the Finite Correction Factor.