Question

The lifetimes of inexpensive wristwatches of a sample of 21 watches has a standard deviation of 4.9 months. Assume the variable is normally distributed. Use the chi−square distribution table to find any chi−square values to three decimal places. Round your final answers to one decimal place. Part 1 out of 2 Find the 80% confidence interval for the variance and standard deviation.

Answer 1

Solution :

Given that,

n = 21

²_R = ²_/2,df = 28.412

²_L = ²_{1 - /2,df} = 12.443

The 80% confidence interval for variance is,

(n - 1)s² / ²_/2 < ² < (n - 1)s² / ²_{1 - /2}

20 * 24.01 / 28.412 < ² < 20 * 24.01 / 12.443

16.9013 < ² < 38.5932

(16.9013 , 38.5932)

The 80% confidence interval for standard deviation is:  (4.1111 , 6.2123)