Question

4. A random sample of 1003 adult Americans was asked, "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1003 adults surveyed, 521 indicated that televisions are a luxury they could do without (A) Obtain a point estimate for the population proportion of adult Americans who believe that televisions are a luxury they could do without. (B) Verify that the requirements for constructing a confidence interval about p are satisfied. (C) Construct and interpret a 95% confidence interval for the population proportion ofadult Americans who believe that televisions are a luxury they could do without.

Answer 1

Given that: - n = 1003 X = 521 (A) Point estimate (p) = X/n = 521/1003 p = 0.52 (B) (1) Large sample size (2) Sample proportion given (Point estimate) (C) The 95 % confidence interval for P [P plusminus Z_alpha/2 squareroot P(1 - P)/n [0.52 plusminus 1.96 squareroot 0.52 times 0.48/1003] [0.52 plusminus 1.96 times 0.01578] [0.52 plusminus 0.0309] rightarrow (0.4891, 0.5509)