Question

People were polled on how many books they read the previous year. Initial survey results indicate that

sequals=10.6

books. Complete parts ​(a) through ​(d) below.

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Click the icon to view a partial table of critical values.​(a) How many subjects are needed to estimate the mean number of books read the previous year within

four

books with

90​%

​confidence?This

90 %

confidence level requires

nothing

subjects. ​(Round up to the nearest​ subject.)​(b) How many subjects are needed to estimate the mean number of books read the previous year within

two

books with

90%

​confidence?This

90 %

confidence level requires

nothing

subjects. ​(Round up to the nearest​ subject.)

​(c) What effect does doubling the required accuracy have on the sample​ size?

A.

Doubling the required accuracy nearly doubles the sample size.

B.

Doubling the required accuracy nearly quadruples the sample size.

C.

Doubling the required accuracy nearly quarters the sample size.

D.

Doubling the required accuracy nearly halves the sample size.

​(d) How many subjects are needed to estimate the mean number of books read the previous year within

fourfour

books with

99​%

​confidence?This

99%

confidence level requires

nothing

subjects. ​(Round up to the nearest​ subject.)Compare this result to part

​(a).

How does increasing the level of confidence in the estimate affect sample​ size? Why is this​ reasonable?

A.

Increasing the level of confidence decreases the sample size required. For a fixed margin of​ error, greater confidence can be achieved with a smaller sample size.

B.

Increasing the level of confidence decreases the sample size required. For a fixed margin of​ error, greater confidence can be achieved with a larger sample size.

C.

Increasing the level of confidence increases the sample size required. For a fixed margin of​ error, greater confidence can be achieved with a larger sample size.

D.

Increasing the level of confidence increases the sample size required. For a fixed margin of​ error, greater confidence can be achieved with a smaller sample size.

Answer 1

Solution :

a) Z/2 = Z0.05 = 1.645

sample size = n = [Z/2* / E] 2

n = [ 1.645 * 10.6/ 4]2

n = 19.003

Sample size = n = 20

b) Z/2 = Z0.05 = 1.645

sample size = n = [Z/2* / E] 2

n = [ 1.645 * 10.6/ 2]2

n = 76.01

Sample size = n = 77

c) Doubling the required accuracy nearly quadruples the sample size.

d) Z/2 = Z0.005 = 2.576

sample size = n = [Z/2* / E] 2

n = [ 2.576 * 10.6/ 4]2

n = 46.59

Sample size = n = 47

e) C) Increasing the level of confidence increases the sample size required. For a fixed margin of​ error, greater confidence can be achieved with a larger sample size.