Question

Given the following values of x, s, and n, form a 90% confidence interval for σ2 a, x = 24, s = 2.9, n = 70 b, xz 0.9, s 0.02, n 16 c. x 162, s-307, n-24 d.x=8.8, s = 1.3, n=4 a. (Round to two decimal places as needed.)

Answer 1

Formula for confidence Interval of variance is,

$\frac{(n-1)s^2}{\chi_{\alpha/2, n-1}^2} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi_{1 - \alpha/2, n-1}^2}$

From the chi-square table we get the value,

$\chi_{0.05, 69}^2 = 50.87924$

$\chi_{0.95, 69}^2 = 89.39121$

Putting the values we get,

$\frac{69 * 2.9^2}{89.39121} \leq \sigma^2 \leq \frac{69 * 2.9^2}{50.87924}$

$6.49 \leq \sigma^2 \leq 11.41$

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