Question

A random sample of 1027 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 1027 adults​ surveyed, 517 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 not be can be assumed to be cannot be assumed to be is stated to be a simple random​ sample, the value of ▼ ModifyingAbove p with caret n ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesis ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesis n n ModifyingAbove p with caret is nothing​, which is ▼ less than greater than or equal to ​10, and the ▼ population proportion sample proportion sample size population size ▼ is stated to not be cannot be assumed to be can be assumed to be is stated to be less than or equal to​ 5% of the ▼ population proportion. population size. sample proportion. sample size. ​(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. 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. ​(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.)

Answer 1

Solution:-

(a) The point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without is 0.5034.

b)

The sample is stated to be a simple random​ sample.

np and np(1-p) are  greater than or equal to ​10, and the sample size population size is stated to to be less than or equal to​ 5% of the population size.

(c) 95​% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without is C.I = ( 0.4728, 0.5339).

C.I = 0.5034 + 1.96*0.015602

C.I = 0.5034 + 0.03058

C.I = ( 0.4728, 0.5339)

d)

p = 0.5034

By applying normal distribution:-

z = 6.19

P(z > 6.19) = less than 0.0001.

It is 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 ( 0.4728, 0.5339)does not contain contains 0.60.