Question

# A 95​% confidence interval of 16.6 months to 49.6 months has been found for the mean...

A

95​%

confidence interval of

16.6

months to

49.6

months has been found for the mean duration of​ imprisonment,

muμ​,

of political prisoners of a certain country with chronic PTSD.

a. Determine the margin of​ error, E.

b. Explain the meaning of E in this context in terms of the accuracy of the estimate.

c. Find the sample size required to have a margin of error of

12

months and a

99​%

confidence level.​ (Use

sigmaσequals=42

​months.)d. Find a

99​%

confidence interval for the mean duration of​ imprisonment,

μ​,

if a sample of the size determined in part​ (c) has a mean of

36.1

months.

a. The margin of error is

nothing

months.

​(Type an integer or a​ decimal.)

b. Choose the correct answer below.

A.One can be

95​%

confident that the interval

16.6

months to

49.6

months contains the mean duration of​ imprisonment,

μ​,

of the prisoners.

B.One can be

95​%

confident that the minimum error made in estimating

muμ

by

x overbarx

is as found in part​ (a).

C.One can be

95​%

confident that the maximum error made in estimating

muμ

by

x overbarx

is as found in part​ (a).

D.

The average duration of imprisonment is as found in part​ (a).

c. The required sample size to have a margin of error of

12

months with a

99​%

confidence level is

nothing

prisoners.

​(Round up to the nearest whole​ number.)

d. The

99​%

confidence interval for the mean duration of​ imprisonment,

μ​,

is from

nothing

months to

nothing

month