Question

# ​(a) Construct a 95​% confidence interval about Mu μ if the sample​ size, n, is 34...

​(a)

Construct a 95​% confidence interval about

Mu μ if the sample​ size, n, is 34

Lower​ bound:

___________

​; Upper​ bound:

______________

​(Use ascending order. Round to two decimal places as​ needed.)

​(b) Construct a 95​% confidence interval about mu μ if the sample​ size, n, is 51.

Lower​ bound:

____________

​; Upper​ bound:

____________

​(Use ascending order. Round to two decimal places as​ needed.)

How does increasing the sample size affect the margin of​ error, E?

A.

The margin of error decreases.

B.

The margin of error does not change.

C.

The margin of error increases.

​(c) Construct a 99​% confidence interval about mu μ if the sample​ size, n, is 34

Lower​ bound:

___________

​; Upper​ bound:

________________

​(Use ascending order. Round to two decimal places as​ needed.)

Compare the results to those obtained in part​ (a). How does increasing the level of confidence affect the size of the margin of​ error, E?

A.

The margin of error decreases.

B.

The margin of error increases.

C.

The margin of error does not change.

​(d) If the sample size is 13

, what conditions must be satisfied to compute the confidence​ interval?

A.

The sample size must be large and the sample should not have any outliers.

B.

The sample must come from a population that is normally distributed and the sample size must be large.

C.

The sample data must come from a population that is normally distributed with no outliers.

a) As xbar and standard deviation is given in the question

Let us take an example:

Xbar = 18.9 standard deviation =4.3

Margin of error = 1.96 * 4.3/sqrt (34) = 1.445

Lower bound = 18.9 - 1.445 = 17.46

Upper bound = 18.9 + 1.445 = 20.25

b)

Margin of error = 1.96 * 4.3/sqrt (51) = 1.18

Lower bound = 18.9 - 1.18 = 17.72

Upper bound = 18.9 + 1.18 = 20.08

The increasing the sample size affect the margin oferror is

Margin of error decreases

c)

Margin of error = 2.575 * 4.3/sqrt (34) = 1.899

Lower bound = 18.9 - 1.889 = 17.01

Upper bound = 18.9 + 1.889 = 20.79

The margin of error increases

d)

For Computing the Confidence Interval sample size must be large.

Hence

The sample must come from a population that is normally distributed and the sample size must be large.

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