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?
444 |
||
631 |
||
1088 |
||
269 |
||
1692 |
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 = 2.576
sample size = n = (Z / 2 / E )2 * * (1 - )
= (2.576 / 0.02)2 * 0.9294 * 0.0706
= 1088
The sample size is required is 1088
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