Question

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).

Answer 1

n(1-p) 1002 x (1-0.515) 485.97 and n(1-p)2 10 The assumption is approximate p by a normal distribution is np 2 10 with n 1002 is satisfied c) A 95% confidence interval for the population proportion of adults in the country who ethtelviionsaea ury they could do without s From the standard normal table, the z-critical value at 95% confidence is 1.96. p(l - p) 95% CI. = p±zeX -0.515 1.96x 0.515(1-0.515) 1002 0.484 to 0.546 A 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without is 0.484 to 0.546

p(l- p) 95% C.1-pt/c × -0.600 1.96x 0.6000-0.600) 0.570 to 0.630 V1002 A 95% confidence interval for the population proportion of adults in the country who believe that televisions are a necessity is 0.570 to 0.630