confidence interval of months to months has been found for the mean duration of imprisonment, , 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 months and a % confidence level. (Use months.)d. Find a % confidence interval for the mean duration of imprisonment, , if a sample of the size determined in part (c) has a mean of months.

Complete Question

A 95% confidence interval of 19.3 months to 47.5 months has been found for the mean duration of? imprisonment, ??,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 13 months and a 99% confidence level.? (Use 38 months. for standard deviation )

d. Find a 99% confidence interval for the mean duration of? imprisonment, ??, if a sample of the size determined in part? (c) has a mean of 36.5 months.

a

b

In this context  E tell us that the true mean will lie within E = 14.1 of the sample mean

c

d

Step-by-step explanation:

Considering question a

From the question we are told that

   The upper limit is  U =   47.5 months

    The lower limit is   L = 19.3 months

Generally the margin of error is mathematically represented as

 =>  

 =>  

Considering question b

In this context  E tell us that the true mean will lie within E = 14.1 of the sample mean

Considering question c

Generally the sample size is mathematically represented  as

Here  E is given as  E = 13

Given that the confidence level is  99% then the level of significance is  

=>  

From the normal distribution table  the critical value  of    is  

So

=>    

Considering question d

From the question

   The sample mean is  

Generally the margin of error is mathematically represented as  

=>      

=>          

Generally the 99% confidence interval  for  mean distribution is  mathematically represented as

=>    

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