Question

Previous 3 4 Next Question 2 of 4 (1 point) 74 Section Exercise 5 Que A study of life expectancy showed that a sample of 6 states had a standard deviation of 1.3 deaths per year. Find the 90% confidence interval of the variance and standard deviation. Assume the variable is normally distributed. Round your final answers to one decimal place. Check Gui <o?< s! <o< As

Answer 1

Answer:

Given,

sample n = 6

Standard deviation = 1.3

alpha = 0.10

degree of freedom = n - 1 = 6 - 1 = 5

$\chi ^{2}$(1-alpha/2 , df) = 1.14547623

$\chi ^{2}$(alpha/2 , df) = 11.07049769

Consider,

(n-1)s^2/$\chi ^{2}$(alpha/2 , df) < $\sigma ^{2}$ < (n-1)s^2/$\chi ^{2}$(1 - alpha/2 , df)

(6-1)*1.3^2 / 11.0705 < $\sigma ^{2}$ < (6-1)*1.3^2 / 1.1455

0.7633 < $\sigma ^{2}$ < 7.3767

0.8737 < $\sigma$ < 2.7160