Chapter 8: Q 8.73 (page 331)

Political Prisoners. A. Ehlers et al. studied various characteristics of political prisoners from the former East Germany and presented their findings in the paper "Posttraumatic Stress Disorder (PTSD) Following Political Imprisonment: The Role of Mental Defeat. Alienation, and Perceived Permanent Change". According to the article. the mean duration of imprisonment for 32 patients with chronic PTSD was $33.4$ months. Assuming that $σ = 42$ months, determine a $95 %$ confidence interval for the mean duration of imprisonment, $μ$ . of all East German political prisoners with chronic PTSD. Interpret your answer in words.

Expert verified

$95 %$ confidence interval of $μ$ is $(18.8477, 47.9523)$ .

Step by step solution

It is given that

$σ = 42$

$n = 32$

Sample mean is $33.4$ months.

$\bar{x} = 33.4$

For $95 %$ confidence interval of $μ$ ,

Confidence Level $= 100 \times 0.95 %$

$\Rightarrow 1 - α = 0.95$

$\Rightarrow α = 0.05$

$\Rightarrow z_{\frac{a}{2}} = z_{\frac{0.05}{2}} = z_{0.025} = 1.96$

$95 %$ confidence level of $μ$ is given by

$\bar{x} - z_{0.025} \times \frac{σ}{\sqrt{n}}, \bar{x} + z_{0.025} \times \frac{σ}{\sqrt{n}}$

$= 33.4 - 1.96 \times \frac{42}{\sqrt{32}}, 33.4 + 1.96 \times \frac{42}{\sqrt{32}}$

$= 33.40 - 14.5523, 33.40 + 14.5523$

$= 18.8477, 47.9523$

Hence, $95 %$ confidence level of $μ$ is $(18.8477, 47.9523)$

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