# Question

Let S2 be the variance of a random sample of size n from N(μ, σ2). Using the fact that (n − 1)S2/σ2 is χ2(n−1), note that the probability

Where

Rewrite the inequalities to obtain

If n = 13 and

Show that [6.11, 24.57] is a 90% confidence interval for the variance σ2. Accordingly, [2.47, 4.96] is a 90% confidence interval for σ.

Where

Rewrite the inequalities to obtain

If n = 13 and

Show that [6.11, 24.57] is a 90% confidence interval for the variance σ2. Accordingly, [2.47, 4.96] is a 90% confidence interval for σ.

## Answer to relevant Questions

A random sample of size 8 from N(μ, 72) yielded = 85. Find the following confidence intervals for μ: (a) 99%. (b) 95%. (c) 90%. (d) 80%. Let X and Y equal the hardness of the hot and cold water, respectively, in a campus building. Hardness is measured in terms of the calcium ion concentration (in ppm). The following data were collected (n = 12 observations of ...An environmental survey contained a question asking what respondents thought was the major cause of air pollution in this country, giving the choices “automobiles,” “factories,” and “incinerators.” Two versions ...Let Y1 < Y2 < · · · < Y8 be the order statistics of eight independent observations from a continuous-type distribution with 70th percentile π0.7 = 27.3. (a) Determine P(y7 < 27.3). (b) Find P(Y5 < 27.3 < Y8). Using the ACT scores in Exercise 6.5-6, find 95% confidence intervals for α, β, and σ2 under the usual assumptions. In Exercise 6.5-6Post your question

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