A Gallup Poll asked a sample of 1785 adults, “Did you, yourself, happen to atten

Question

A Gallup Poll asked a sample of 1785 adults, “Did you, yourself, happen to attend church, mosque or synagogue in the last 7 days?” Of the respondents, 750 said “Yes”. Treat Gallup’s sample as an SRS of all American adults.

(a) Give a 99% confidence interval for the proportion of all adults who claim that they attended church, mosque or synagogue during the week preceding the poll.

(b) Do the results of the poll provide good evidence that fewer than half of the popu- lation would claim to have attended church, mosque or synagogue? Clearly explain your answer.

(c) How large a sample would be required to obtain a margin of error of 0.01 in a 99% confidence interval for the proportion of who claim to have attended church, mosque or synagogue? (Use the conservative guess p = 0.5.)

(d) The proportion who actually attended is no doubt lower. Why is this true? Of what is this an example?

Explanation / Answer

here point estimate p=750/1785=0.42

std error =(p(1-p)/n)1/2 =0.0117

for 99% CI, z=2.5758

a) hence confidence interval =point estimate -/+ z*std error =0.3901 ; 0.4503

b)Yes as our interval contains all proportion below 0.5.

c)for sample sizee =p(1-p)(Z/E)2 =16588

d)from above as for margin of error for above sample is 3% which is on higher side for low precision of confidence interval

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