Question

A random sample of 1012 ts in a certain large country was asked "Do you pretty much think belevisions are a necessity or a luxury you could do without of the 1012 adults surveyed, 537 indicated that televisions are a luxury they could do without Complete parts (a) through to below. Click here to view the standard roma darbo. 1 Cack here to the standardnomalditional Ajotain a pont estimate for the population proportion of buits in the country who ever sons are a luxury they could do wito (Round to three decimal places as needed) 2) Verity that the requirements for constructing a confidence interval about pare satisfied The sample a simple random sample, the value of is which is 10, and the less than or equal to 5% of the Round to three decimal places as needed) (c) Construct and interpreta 95% confidence interval for the population proportion of cuts in the country who believe that televisions are alry they could do without. Select the correct choice below and fill in any answer boxes within you choice (Typengers or decimal rounded to three decimal places as needed. Use wonding order) O A There is probability the proportion of sults in the country who believe that televisions are a ury they could do without is between and OB. We are confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between and () is possible that a supermajority more than 60%) of adults in the country believe that bevision is a luxury they could do without istiky that a supermajority of adults in the country believe that television is a luxury they could do without because the confidence interval (Type an integer or a decimal. Do not found) Use the results of part (e) to construct a 16% confidence interval for the population proportion of adults in the country who believe that televisions werely, Lower bound Upper bound (Round to the decimal places as needed) Click to select your answers

Answer 1

in = lola X -537 Ø - X - = 0.531 537 lola n a} A point estimate for the population propertion is ſ = 10.531 The sample size in ) 1022"]b]The sample List a simple random sample, the value of Lnb (1-6) is 252.027), which is greater than or equal to 10, and the Sample Size) (n = lola) less than or equal to 5% of the population size C) Confidence interwal=0.95 d-1-0.95 = 0:05 xla = 0.025 Z critical Zala 20.025 = + 1,960 (using z-table) 95% Confidence interwal:- = P + Zala + Zum *JF () = 0.531 † 1.960 * 0-531 (1-0.531) lola -0.531+ 0.0307 0.500 3, 0.5617 ~0.501,0.562

option-B. We are 95% confident the proportion of adults in the country who believe that televisions are a lukway they could do without is between [o.sol and 0.562 d) It is not possible that a supermajority of adults in the Country believe that television is a they could do without because the 95% confidence interval does not include 110.6 Lower bound:- 10.501 ubber bound - 0.562 luxary e )