Question

A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.05 with 90​% confidence if ​(a) she uses a previous estimate of 0.42​? ​(b) she does not use any prior​ estimates?

A television sports commentator wants to estimate the proportion of citizens who​ "follow professional​ football." Complete parts​ (a) through​ (c).

​(a) What sample size should be obtained if he wants to be within 33 percentage points with 95% confidence if he uses an estimate of 48%obtained from a poll

b. They do not use any prior estimates.

Answer 1

1 ) Given : Margin of error = E = 0.05

Significance level=

(a) Since , previous estimate of the proportion = p=0.42

q=1-p=0.58

Therefore , the sample size is ,

(b) Since , the prior estimate of proportion is not known

Assume that p=q=0.5

Therefore , the sample size is ,

2)

Given : Margin of error = E = 0.33

Significance level=

(a) Since , previous estimate of the proportion = p=0.48

q=1-p=0.52

Therefore , the sample size is ,

(b) Since , the prior estimate of proportion is not known

Assume that p=q=0.5

Therefore , the sample size is ,