Question

Construct a 98% confidence interval for the population standard deviation σ of a random sample of 20 crates which have a mean weight of 154.2 pounds and a standard deviation of 9.4 pounds. Assume the population is normally distributed. The confidence interval is: Group of answer choices between 6.52 and 15.02 between 6.81 and 14.83 between 42.51 and 225.60 between 46.39 and 219.94

Answer 1

From chi-square table,

Chi-square critical values at 0.02 significance level with 19 df = 7.633 ,36.191

98% confidence interval for $\sigma$ is

sqrt [ (n -1 ) * S² / $\chi^2$ U ] < $\sigma$ < sqrt [ (n -1 ) * S² / $\chi^2$ UL]

sqrt [ (20 - 1) * 9.4² / 36.191 ] < $\sigma$ ​​​ < sqrt [ (20 - 1) * 9.4² / 7.633 ]

6.81 < $\sigma$ < 14.83

Between 6.81 and 14.83