Question

A sample of size 20 from a normal distribution has sample mean 3.5 and sample variance 14.75. Find 90% confidence intervals for the variance and standard deviation of the distribution.

Answer 1

Variance =9.2983, 27.6927

Standard deviation = 3.0493, 5.2624

Explanation:

n = 20

S = 14.75

X² = chisquare

N-1 = degree of freedom

Alpha = 0.1

Alpha/2 = 0.1/2 = 0.05

1-0.1/2 = 0.95

Using statistics table

X² 19,0.05 = 30.14

X² 19, 0.95 = 10.12

A. 19(14.75)/30.14 , 19(14 75)/10.12

= 9.2983, 27.6927 for the variance of the population

B. Standard deviation = square root of variance

= √9.2983, √27.6927

= 3.0493, 5.2624

Please use attachment for better understanding