Suppose that a random sample of 50 bottles of a particular brand of cough medicine is selected and the alcohol content of each bottle measured. The sample mean alcohol content is 8.6 ml and the standard deviation is 2.99 ml. The standard deviation of the alcohol content is required, by law, to be less than 2.8 ml.A 90% confidence interval for the population variance of the alcohol content is( 6.60 ; 12.91 ).Thus, we can conclude with 90% confidence, that&nbsp;

Question

Suppose that a random sample of 50 bottles of a particular brand of cough medicine is selected and the alcohol content of each bottle measured. The sample mean alcohol content is 8.6 ml and the standard deviation is 2.99 ml. The standard deviation of the alcohol content is required, by law, to be less than 2.8 ml.A 90% confidence interval for the population variance of the alcohol content is( 6.60 ; 12.91 ).Thus, we can conclude with 90% confidence, that&amp;nbsp;

nick1337 · Accepted Answer

To determine the 90% confidence interval for the population variance of the alcohol content, we can use the Chi-square distribution. The formula for the confidence interval is:((n−1)s2χα/2,n−12,(n−1)s2χ1−α/2,n−12),where n is the sample size, s is the sample standard deviation, and χα/2,n−12 and χ1−α/2,n−12 represent the values from the Chi-square distribution with n-1 degrees of freedom corresponding to the lower and upper critical values, respectively.Substituting the given values into the formula, we have:((50−1)·2.992χ0.05/2,50−12},(50−1)·2.992χ1−0.05/2,50−12),where χ0.05/2,50−12 and χ1−0.05/2,50−12 represent the lower and upper critical values from the Chi-square distribution with 49 degrees of freedom at the significance level of 0.05/2 (or 0.025) and 1-0.05/2 (or 0.975), respectively.According to the given information, the 90% confidence interval for the population variance of the alcohol content is (6.60, 12.91).Thus, we can conclude with 90% confidence that the population variance of the alcohol content falls within the interval (6.60, 12.91).

Suppose that a random sample of 50 bottles

Answered question

Answer & Explanation

New Questions in College Statistics