Question

A survey of 1,076 tablet owners was conducted. In response to a survey question about​ shopping, 32​% of tablet owners said they use mobile devices for​ payment, 18​% said they use such devices to make social media comments about their​ purchases, and 13​% said they use such devices to retrieve mobile coupons. Complete parts​ (a) through​ (d) below.

a. Construct a 99​% confidence interval estimate of the population proportion π of tablet owners who said they use mobile devices for payment.

≤ π ≤

​(Round to three decimal places as​ needed.)

b) Construct a 99% confidence interval estimate of the population proportion π of tablet owners who said they use mobile devices to make social media comments about their purchases.

c) Construct a 99% confidence interval estimate of the population proportion π of tablet owners who said they use mobile devices to retrieve mobile coupons.

d) You have been asked to update the results of this study. Determine the sample size necessary to​ estimate, with 99% ​confidence, the population proportions in​ (a) through​ (c) to within plus or minus±0.01.

Answer 1

Ans:

sample proportion=0.32

n=1076

a)99​% confidence interval estimate of the population proportion

=0.32+/-2.576*sqrt(0.32*(1-0.32)/1076)

=0.32+/-0.037

=(0.283, 0.357)

b)

99​% confidence interval estimate of the population proportion

=0.18+/-2.576*sqrt(0.18*(1-0.18)/1076)

=0.18+/-0.030

=(0.150, 0.210)

c)

99​% confidence interval estimate of the population proportion

=0.13+/-2.576*sqrt(0.13*(1-0.13)/1076)

=0.13+/-0.026

=(0.104, 0.156)

d)

sample size required,n=2.576^2*0.32*(1-0.32)/0.01^2=14439

sample size required,n=2.576^2*0.18*(1-0.18)/0.01^2=9794

sample size required,n=2.576^2*0.13*(1-0.13)/0.01^2=7505