A researcher would like to estimate p, the proportion of U. S. adults who support recognizing civil unions between gay or lesbian couples. If the researcher would like to be 95% sure that the obtained sample proportion would be within 1.5% of p (the proportion in the entire population of U. S. adults), what sample size should be used?

(a) 17,778 (b) 4,445 (c) 1,112 (d) 67 (e) 45

Question

Lilliana Zavala

Mathematics

7 January, 11:54

A researcher would like to estimate p, the proportion of U. S. adults who support recognizing civil unions between gay or lesbian couples. If the researcher would like to be 95% sure that the obtained sample proportion would be within 1.5% of p (the proportion in the entire population of U. S. adults), what sample size should be used?

(a) 17,778 (b) 4,445 (c) 1,112 (d) 67 (e) 45

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Answers (1)

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Madilynn Serrano · Answer 1

(b) 4,445

Step-by-step explanation:

If the researcher would like to be 95% sure that the obtained sample proportion would be within 1.5% of p (the proportion in the entire population of U. S. adults), what sample size should be used?

Given a=0.05, |Z (0.025) |=1.96 (check standard normal table)

So n = (Z/E) ^2*p * (1-p)

= (1.96/0.015) ^2*0.5*0.5

=4268.444

Take n=4269

Answer: (b) 4,445