Question

A meat packaging plant uses a machine that packages chicken livers in six pound portions. A sample of 91 packages of chicken livers has a standard deviation of 0.47. Construct the 98% confidence interval to estimate the standard deviation of the weights of the packages prepared by the machine. Round your answers to two decimal places.

Lower endpoint______ Upper endpoint__

Answer 1

To construct the 98% confidence interval to estimate the standard deviation of the weights of the packages, we can use the chi-square distribution.

Step-by-step explanation:

To construct a confidence interval to estimate the standard deviation of the weights of the packages, we will use the chi-square distribution. The formula for the confidence interval is:

Lower endpoint = sqrt((n-1)*s^2/χ^2(df, α/2))

Upper endpoint = sqrt((n-1)*s^2/χ^2(1-α/2, df))

where n is the sample size, s is the standard deviation of the sample, χ^2(df, α/2) is the critical value of the chi-square distribution with df degrees of freedom at α/2 significance level, and χ^2(1-α/2, df) is the critical value of the chi-square distribution with df degrees of freedom at 1-α/2 significance level.

Given that the sample size is 91 and the standard deviation is 0.47, we can calculate the confidence interval:

Lower endpoint = sqrt((91-1)*0.47^2/χ^2(90, 0.01))

Upper endpoint = sqrt((91-1)*0.47^2/χ^2(90, 0.99))

By using the appropriate chi-square values, we can find the lower and upper endpoints of the 98% confidence interval.