Question

A random sample of 1005 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 1005 adults​ surveyed, 524 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 ▼ cannot be assumed to be can be assumed to be is stated to not be is stated to be a simple random​ sample, the value of ▼ n ModifyingAbove p with caret 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 is nothing​, which is ▼ less than greater than or equal to ​10, and the ▼ sample size population size population proportion sample proportion ▼ is stated to not be is stated to be cannot be assumed to be can be assumed to be less than or equal to​ 5% of the ▼ population size. sample size. population proportion. sample 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 possible, but not likely 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.)

Answer 1

a)

point estimate for the population proportion=0.521

b)

The sample can be can be assumed to be simple random​ sample, the value of nphat (1-phat)  which is greater than or equal to ​10, and the  sample size can be assumed to be less than or equal to​ 5% of the population size

c)

B. We are 95 % confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.490 and 0.552

d)

because the 95​% confidence interval does not contain 0.60.

e)

. The 95​% confidence interval is 0.448 ; 0.510