Question

A school administrator is concerned about the amount of credit card debt that college students have. She wishes to conduct a poll to estimate the percentage of full-time college students who have credit card debt of $2000 or more. What size sample should be obtained if she wishes the estimate to be within 2.5 percentage points with 95% confidence if…

a) A pilot student indicates that the percentage is 34%?

b) No prior estimate were used.

Answer 1

Solution:

Given ,

c = 95% = 0.95

E = 2.5% = 0.025

a)

Here , p = 34% = 0.34

1 - p = 1 - 0.34 = 0.66

Now ,

= 1- c = 1- 0.95 = 0.05

  /2 = 0.025

Using Z table ,

= 1.96

The sample size for estimating the proportion is given by

n =

= (1.96)² * 0.34 * 0.66 / (0.025²)

= 1379.288064

= 1380

n = 1380

b)

Here , no prior information of p is available.

p = 0.5

1 - p = 1 - 0.5 = 0.5

The sample size for estimating the proportion is given by

n =

= (1.96)² * 0.5 * 0.5 / (0.025²)

= 1536.64

= 1537

n = 1537