The membership director of a national fraternity wanted to do an attitude study

Question

The membership director of a national fraternity wanted to do an attitude study of the fraternity’s 2500 current active members and 12000 alumni.

What sampling frame would likely be available for this study?

Explain the process you would follow to select a simple random sample of current and alumni members?

One question dealt with the proportion of alumni members who attend local chapter meetings. Historically, this proportion has been about 20%. The membership director reasoned that an error of   5% was acceptable for making this estimate. What is the sample size that will yield this quality of estimate at the 95% confidence interval?

Explanation / Answer

Talking about sampling frames, since 2500 members are currently active so they all will definitely available for this study.

Amongst the alumni, you can expect at least 10% of them to be avaiable for study.

So if you are to collect a sample, then sample atleast 200 currently active and 200 alumni members.

Selecting a SRS from active members is very easy. You can choose a systematic SRS method using their membership ID numbers. For the alumni, you first need to consider that particular portion which is expected to be available, depending on their previous activity. Use their membership IDs as well to extract a systematic SRS.

Now, data given is:

p = 0.20

Margin of error, ME = 0.05

Assume that you draw a sample of size 'n' from the alumni.

Margin of error for a 95% CI = 1.96*S

Here, S = Standard error = (p*(1-p)/n)^0.5 = (0.20*(1-0.20)/n)^0.5

So,

1.96*(0.20*(1-0.20)/n)^0.5 = 0.05

Solving we get:

n = 245.86

So you need a sample size of atleast 246.

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