Question

Following are the numbers of grams of sugar per 100 grams of apple in a random sample of 6 Red Delicious apples. Assume the population is normally distributed. Construct an 80% confidence interval for the standard deviation of the number of grams of sugar. Round the answers to two decimal places. 11.9 12.4 13.2 13.5 12.2 10.4

Answer 1

Confidence interval for population standard deviation is given as below:

Sqrt[(n – 1)*S2 / χ2 α/2, n – 1 ] < σ < sqrt[(n – 1)*S2 / χ2 1 - α/2, n – 1 ]

We are given

Confidence level = 80%

Sample size = n = 6

Degrees of freedom = n – 1 = 5

Sample standard deviation = S = 1.098484

χ2 α/2, n – 1 = 9.2364

χ2 1 - α/2, n – 1 = 1.6103

(By using chi square table)

Sqrt[(n – 1)*S2 / χ2 α/2, n – 1 ] < σ < sqrt[(n – 1)*S2 / χ2 1 - α/2, n – 1 ]

Sqrt[(6 – 1)* 1.098484^2 / 9.2364] < σ < sqrt[(6 – 1)* 1.098484^2 / 1.6103]

0.8082 < σ < 1.9356

Lower limit = 0.81

Upper limit = 1.94