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 90% confidence that the point estimate is correct to within 0.02 of the population proportion, how large a sample size is required?

		1692
		631
		444
		1088
		269

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 303 / 326 = 0.9294

1 - = 1 - 0.9294 = 0.0706

margin of error = E = 0.02

Z/2 = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.02)2 * 0.9294 * 0.0706

= 444

The sample size is required is 444