A 95% confidence interval of 17.6 months to 49.2 months has been found for the mean duration of imprisonment, mu, 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 11 months and a 99% confidence level. (Use sigmaequals45 months.) d. Find a 99% confidence interval for the mean duration of imprisonment, mu, if a sample of the size determined in part (c) has a mean of 36.5 months.

a)

b) For this case we have 95% of confidence that the true mean would be between units respect the true mean.

c)

So the answer for this case would be n=112

d)    

Step-by-step explanation:

Part a

For this case we know that the cinfidence interval for the true mean is given by:

Where E represent the margin of error. For this case we have the confidence interval at 95% of confidence and we can estimate the margin of error like this:

Part b

For this case we have 95% of confidence that the true mean would be between units respect the true mean.

Part c

The margin of error is given by this formula:

   (a)

And on this case we have that ME =11 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

  (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The critical value would be , replacing into formula (b) we got:

So the answer for this case would be n=112

Part d

The confidence interval for the mean is given by the following formula:

  (1)

Replcaing the info given we got:

add 5 subtract 1

step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.