Question

A researcher wishes to estimate the proportion of adults who have high-speed internet access. What size sample should be obtained if she wishes the estimate to be within 0.02 with 90% confidence if (a) she uses a previous estimate of 0.52? (b) she does not use any prior estimates?

A. Sample size with prior estimate
B. Sample size without prior estimate
C. Both (a) and (b)
D. Neither (a) nor (b)

Answer 1

To estimate the proportion of adults with high-speed internet access, the researcher can calculate the sample size based on a previous estimate or without any prior estimate.

Step-by-step explanation:

To estimate the proportion of adults with high-speed internet access, the researcher needs to determine the sample size for the desired confidence level and margin of error.

a) With a previous estimate of 0.52, to achieve a 90% confidence level and a margin of error within 0.02, the formula used is:

Sample size = (Z^2 * p * (1-p)) / E^2

Where Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion, and E is the margin of error. Plugging in the values: Sample size = (1.645^2 * 0.52 * (1-0.52)) / 0.02^2

After calculating, the sample size is approximately 753.

b) Without any prior estimate, the formula remains the same. Assuming p=0.5 for maximum uncertainty, the sample size is:

Sample size = (1.645^2 * 0.5 * (1-0.5)) / 0.02^2

After calculating, the sample size is approximately 913.