Question

A random sample of 1021 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1021 adults surveyed, 511 indicated that televisions are a luxury they could do without. Complete parts (a) through (c) below. Click here to view the standard normal distribution table (page 1). LOADING... Click here to view the standard normal distribution table (page 2). LOADING... (a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without. ModifyingAbove p with caretequals nothing (Round to three decimal places as needed.) (b) Construct and interpret a 95 % confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without. Select the correct choice below and fill in any answer boxes within your choice. (Type integers or decimals rounded to three decimal places as needed. Use ascending order.) A. We are nothing % confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between nothing and nothing. B. There is a nothing % chance the proportion of adults in the country who believe that televisions are a luxury they could do without is between nothing and nothing. (c) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely? It is ? possible, but not likely likely not possible that a supermajority of adults in the country believe that television is a luxury they could do without because the 95 % confidence interval ? contains does not contain nothing. (Type an integer or a decimal. Do not round.)

Answer 1

Ans:

a)

Point estimate=511/1021=0.500

b)

95% confidence interval for p

=0.5005+/-1.96*sqrt(0.500*(1-0.500)/1021)

=0.5005+/-0.0307

=(0.470, 0.531)

We are 95% confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.470 and 0.531

c)

It is possible, but not likely possible that a super majority of adults in the country believe that television is a luxury they could do without because the 95 % confidence interval does not contain 0.60.