Answer to Question #126555 in Statistics and Probability for jse

Question

An article in Technometrics (1999, Vol. 41, pp. 202–211) studied the capability of a gauge by measuring the weight of paper. The data for repeated measurements of one sheet of paper are in the following table. Construct a 99% one-sided, upper confidence interval for the standard deviation of these measurements. Assume population is approximately normally distributed.

Round your answer to 3 decimal places.

Observations

3.481 3.448 3.485 3.475 3.472

3.477 3.472 3.464 3.472 3.470

3.470 3.470 3.477 3.473 3.474


σ ≤ _____________

Answer 1

sample mean is x=(1/n)$\sum X_i$ =52.08/15=3.472

The sample variance is given as,

s²=(1/(n-1))$\sum (X_i-x)^2=0.000966/14=0.000069$

confidence level, 1-$\alpha$ =99%=0.99

degrees of freedom

df=14

$\chi^2=$ 4.66

A 99% upper confidence bound for the variance is found as follows:

$\sigma^2<(n-1)s^2/\chi^2,$

$\sigma^2<(14)0.000069/4.66;\sigma^2<0.0002073;$ $\sigma<0.0144$