Question

A random sample of 1008 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 1008 adults​ surveyed, 511 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 caretpequals=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?

is stated to be ?

cannot be assumed to be ?

can be assumed to be ?

a simple random​ sample, the value of

▼

n ModifyingAbove p with caretnp

ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesisp1−p

nn

ModifyingAbove p with caretp

n ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesisnp1−p

is

nothing ​,

which is

▼

less than

greater than or equal to

​10, and the

▼

sample proportion ?

population proportion ?

population size ?

sample size ?

▼

is stated to not be?

can be assumed to be ?

is stated to be ?

cannot be assumed to be?

less than or equal to​ 5% of the

▼

sample proportion. ?

population size. ?

sample 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.

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 ? answer..

and

nothing .? answer...

B.

There is a

answer? ​%

chance the proportion of adults in the country who believe that televisions are a luxury they could do without is between

answer?

and

answer?

​(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

▼

likely ?

not possible ?

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

▼

contains?

does not contain ?

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.)

        More?

                                                        Less?

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 0.5069.

x = 511, n = 1008

b)

The sample can be assumed to be simple random sample.

and are greater than 10.

Sample size can be assumed to be less than or equal to​ 5% of the population size.

c) (A) There is a 95 % chance the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.476 and 0.538.

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 = ( 0.4760, 0.5378).

C.I = 0.5069 + 1.96 × 0.01575

C.I = 0.5069 + 0.030864

C.I = ( 0.4760, 0.5378)

d)

It is possible,  but not likely 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 the 0.60, all the values in the 95% confidence is less than 60%.

​(e) The 95​% confidence interval is ​C.I = ( 0.462, 0.524).

x = 497, n = 1008

C.I = 0.4931 + 1.96 × 0.015747

C.I = 0.4931 + 0.03086

C.I = ( 0.4622, 0.5240)

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