Question

Have you had a business presentation disturbed by a ringing cell phone? In a poll of 326 business men and women, 303 answered this question “yes” and only 23 answered “no” (“You Say,” Presentations: Technology and Techniques for Effective Communication, January 2003, 18).  Round p-hat to 4 decimal places!  To conduct a follow-up study that would provide 99% confidence that the point estimate is correct to within 0.02 of the population proportion, how large a sample size is required?

		631
		1692
		444
		1088
		269

Answer 1

Solution:

The sample size required to estimate population proportion with 99% confidence level is given as follows:

Where, p̂ is sample proportion, q̂ = 1 - p̂, E is margin of error, n is sample size and Z_(0.01/2) is critical z-value at 99% confidence level.

Sample proportion of respondents who answered yes is given by, p̂ = 303/326 = 0.9294

q̂ = 1 - 0.9294 = 0.0706

Since, we want to estimate correct to within 0.02 of the population proportion, therefore the margin of error is 0.02.

Using Z-table we get, Z_(0.01/2) = 2.58

Hence, required sample size is,

The required sample size is 1088.

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