Question

An article summarized results from a national survey of 2302 Americans age 8 to 18. The sample was selected in a way that was expected to result in a sample representative of Americans in this age group. (a) Of those surveyed, 1221 reported owning a cell phone. Use this information to construct a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone. (Round your answers to three decimal places.) (b) Of those surveyed, 1529 reported owning an MP3 music player. Use this information to construct a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own an MP3 music player.

An article included the following statement: "Few people believe there's much reality in reality TV: a total of 76% said the shows are either 'totally made up' or 'mostly distorted.'" This statement was based on a survey of 1005 randomly selected adults. Compute a bound on the error (based on 95% confidence) of estimation for the reported proportion of 0.76. (Round your answer to three decimal places.)Interpret the bound. (Round your answers to one decimal place.)We are blank% confident that the proportion of all adults who believe that the shows are either "totally made up" or "mostly distorted" is within blank % of the sample proportion of blank%.

Answer 1

Answer:

1.

a)

x = 1221

n = 2302

p = x/n

p = 1221 / 2302

= 0.53

Here for 90% confidence interval z value = 1.645

Interval = p +/- z*sqrt(p(1-p)/n)

substitute values

= 0.53 +/- 1.645*sqrt(0.53(1-0.53)/2302)

= 0.53 +/- 0.0171

= (0.53 - 0.0171 , 0.53 + 0.0171)

= (0.5129 , 0.5471)

b)

x = 1529

n = 2302

p = x/n

= 1529/2302

= 0.664

Here for 90% confidence interval z value = 1.645

Interval = p +/- z*sqrt(p(1-p)/n)

substitute values

= 0.664 +/- 1.645*sqrt(0.664(1-0.664)/2302)

= 0.664 +/- 0.0162

= (0.664 - 0.0162 , 0.664 + 0.0162)

= (0.6478 , 0.6802)

part 2:

a)

n = 1005

Here for 95% confidence interval z value = 1.96

p = 0.76

Bound on the error = z*sqrt(p(1-p)/n)

substitute values

= 1.96*sqrt(0.76(1-0.76)/1005)

= 0.0264

b)

Here we are 95% confident that the proportion of all adults who believe that the shows are either "totally made up" or "mostly distorted" is within 2.6 % of the sample proportion of 76%.