Question

The number of carbohydrates (in grams) per 8-ounce serving of yogurt for each of a random selection of brands is listed below. Estimate the true population variance and standard deviation for the number of carbohydrates per 8-ounce serving of yogurt with 95% confidence. 17 42 41 20 39 41 35 15 43 25 38 33 42 23 17 25 34

Answer 1

Confidence interval for population variance is given as below:

(n – 1)*S2 / χ2 α/2, n – 1 < σ2 < (n – 1)*S2 / χ2 1 - α/2, n – 1

We are given

Confidence level = 95%

Sample size = n = 17

Degrees of freedom = n – 1 = 16

Sample standard deviation = S = 10.10096

χ2 α/2, n – 1 = 28.8454

χ2 1 - α/2, n – 1 = 6.9077

(By using chi square table)

(n – 1)*S2 / χ2 α/2, n – 1 < σ2 < (n – 1)*S2 / χ2 1 - α/2, n – 1

(17 – 1)* 10.10096^2 / 28.8454 < σ2 < (17 – 1)* 10.10096^2 / 6.9077

56.5939 < σ2 < 236.3274

Lower limit = 56.5939

Upper limit = 236.3274

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 ]

Sqrt(56.5939) < σ < Sqrt(236.327)

7.5229 < σ < 15.3729