A simple random sample of size n is drawn from a population that is normally distributed. The sample mean,

x overbar

,

is found to be

108

,

and the sample standard deviation, s, is found to be

10

.

(a) Construct

a

90

%

confidence interval about

mu

if the sample size, n, is

24

.

(b) Construct

a

90

%

confidence interval about

mu

if the sample size, n, is

19

.

(c) Construct

an

80

%

confidence interval about

mu

if the sample size, n, is

24

.

(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?

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Part 1

(a) Construct

a

90

%

confidence interval about

mu

if the sample size, n, is

24

.

Lower bound:

104.5

;

Upper bound: 111.5

(Use ascending order. Round to one decimal place as needed.)

Part 2

(b) Construct

a

90

%

confidence interval about

mu

if the sample size, n, is

19

.

Lower bound:

104.02

;

Upper bound: 112.0

(Use ascending order. Round to one decimal place as needed.)

Part 3

How does

decreasing

the sample size affect the margin of error, E?

A.

As the sample size

decreases

,

the margin of error stays the same.

B.

As the sample size

decreases

,

the margin of error

decreases

.

C.

As the sample size

decreases

,

the margin of error

increases

.

Part 4

(c) Construct

an

80

%

confidence interval about

mu

if the sample size, n, is

24

.

Lower bound:

105.31

;

Upper bound: 110.7

(Use ascending order. Round to one decimal place as needed.)

Part 5

Compare the results to those obtained in part (a). How does

decreasing

the level of confidence affect the size of the margin of error, E?

A.

As the level of confidence

decreases

,

the size of the interval

increases

.

B.

As the level of confidence

decreases

,

the size of the interval

decreases

.

C.

As the level of confidence

decreases

,

the size of the interval stays the same.

Part 6

(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?

A.

No, the population needs to be normally distributed.

B.

No, the population does not need to be normally distributed.

C.

Yes, the population needs to be normally distributed.

D.

Yes, the population does not need to be normally distributed.