Use technology to construct the confidence intervals for the population variance sigma^{2} and the population standard deviation sigma. Assume the sam

Question

Use technology to construct the confidence intervals for the population variance

σ^{2}

and the population standard deviation

σ

. Assume the sample is taken from a normally distributed population.

c = 0.99, s = 37, n = 20

The confidence interval for the population variance is (?, ?). The confidence interval for the population standard deviation is (?, ?)

Answer 1

Step 1 Solution: We need to construct the 99% confidence interval for the population variance. We have been provided with the following information about the sample variance and sample size: $s^{2} = 1369$
$n = 20$ Step 2 The critical values for $α = 0.01$ and $d f = 19$ degrees of freedom are $X_{L}^{2} = X_{1 - \frac{α}{2}, n - 1}^{2} = 6.844$ and $X_{U}^{2} = X_{1 - \frac{α}{2}, n - 1}^{2} = 38.5823$ . The corresponding confidence interval is computed as shown below: $C I (V a r i a n c e) = (\frac{(n - 1) s^{2}}{X_{\frac{α}{2}, n - 1}^{2}}, \frac{(n - 1) s^{2}}{X_{1 - \frac{α}{2}, n - 1}^{2}})$
$(\frac{(20 - 1) \times 1369}{38.5823}, \frac{(20 - 1) \times 1369}{6.844}$
$= (674.17, 3800.5711)$ Now that we have the limits for the confidence interval, the limits for the 99% confidence interval for the population standard deviation are obtained by simply taking the squared root of the limits of the confidence interval for the variance, so then: CI(Standard Deviation) $= (\sqrt{674.17}, \sqrt{3800.5711}) = (25.9648, 61.6488)$ Therefore, based on the data provided, the 99% confidence interval for the population variance is $674.17 < σ^{2} < 3800.5711$ , and the 99% confidence interval for the population standard deviation is $25.9648 < σ < 61.6488$ . Step 3 Ci for population variance (674.17 , 3800.57) Ci for population standard deviation ( 25.96 , 61.65)

Use technology to construct the confidence intervals for the population variance sigma^{2} and the population standard deviation sigma. Assume the sam

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