TVs in America: Necessity or Luxury? A Statistical Insight

Chapter 5, Problem 27

(choose chapter or problem)

QUESTION:

Luxury or Necessity? 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 of adult Americans who believe that televisions are a luxury they could do without.

(d) Is it possible that a supermajority (more than 60% ) of adult Americans believe that television is a luxury they could do without? Is it likely?

(e) Use the results of part (c) to construct a 95 confidence interval for the population proportion of adult Americans who believe that televisions are a necessity.

Questions & Answers

QUESTION:

(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 of adult Americans who believe that televisions are a luxury they could do without.

(d) Is it possible that a supermajority (more than 60% ) of adult Americans believe that television is a luxury they could do without? Is it likely?

(e) Use the results of part (c) to construct a 95 confidence interval for the population proportion of adult Americans who believe that televisions are a necessity.

ANSWER:

Step 1 of 3

Given, in a survey 1003 adults, 521 indicated that televisions are a luxury they could do without.

a) The sample proportion is