In: Statistics and Probability
A random sample of 1002 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 1002 adults surveyed, 516 indicated that televisions are a luxury they could do without. Complete parts (a) through (e) 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) Verify that the requirements for constructing a confidence interval about p are satisfied. The sample ▼ is stated to be can be assumed to be is stated to not be cannot be assumed to be a simple random sample, the value of ▼ n ModifyingAbove p with caret n ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesis n ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesis ModifyingAbove p with caret is nothing, which is ▼ less than greater than or equal to 10, and the ▼ population size sample size sample proportion population proportion ▼ is stated to be is stated to not be can be assumed to be cannot be assumed to be less than or equal to 5% of the ▼ sample size. sample proportion. population size. population proportion. (Round to three decimal places as needed.) (c) 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. 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. B. 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. (d) 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 ▼ not possible likely possible, but not likely that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval ▼ does not contain contains nothing. (Type an integer or a decimal. Do not round.) (e) Use the results of part (c) to construct a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a necessity. The 95% confidence interval is ( nothing, nothing). (Round to three decimal places as needed.) Click to select your answer(s).