The heights of Vulcans - an imaginary humanoid in Star Trek- are normally distributed. Suppose that a simple random sample of 13 Vulcans have a standard deviation of 29.5. Find the confidence Interval for the standard deviation of the entire population with 80% confidence. 1. Find the critical values $\chi_L^2 = \chi_{1-\alpha/2}^2$ and $\chi_R^2 = \chi_{\alpha/2}^2$ that correspond to 80% degree of confidence and the sample size $n = 13$. $\chi_L^2 = \Box$ $\chi_R^2 = \Box$ 2. Find the upper and lower limits of 80% confidence Interval for the standard deviation of the entire population. The lower limit of the 80% confidence interval = $\Box$ The upper limit of the 80% confidence interval = $\Box$
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The confidence level is 80%, so $\alpha = 1 - 0.80 = 0.20$. Then $\alpha/2 = 0.10$ and $1-\alpha/2 = 0.90$. We need to find the critical values $\chi_{0.90}^2$ and $\chi_{0.10}^2$ with $df=12$. Using a chi-square table or calculator, we find: $\chi_{0.90}^2 Show more…
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