The number of hours of reserve capacity of 10 randomly selected aulemotive batte
ID: 2946719 • Letter: T
Question
The number of hours of reserve capacity of 10 randomly selected aulemotive batteries is shown 1 179 187 2 163 176 1.96 135 158 147 2.03 to the right Asume the samtestaken tom anormaitydonated populalon construd 95% confidence intervals tor (a)the population vanance ?2 and(D)the popadon standard deviabon ? (a) The cordidence interval tor the population variance is Round ho three decimal places as neeled) Inberpret the es Select the correct choice below and tin the anower boxes) to complete your choice Round to three decimal places as needed) wth 95%contoen ce, t can be betveen and wth 95% eoenoncercan be tad na ne Popaen vaino nesr OA. be sad that he population rai nce is OB. that the population vanances we, 5%contoence between an Oc.vn, 5% corthdence, tante said that he populaton vanance greater Oo, b The cortidence iterval tor the peopuluation standard devaenD Round to ree decmal places as needed erpret e esuts Seledt the corred choice below and ta in the answer baejes) to complete your choice Cick to select your answes)Explanation / Answer
Solution:- Given that n = 10 , s = 0.2221, p = 0.025
df = n-1 = 9
(X^2)R = 19.02 , (X^2)L = 2.7
(a) The confidence interval for the population variance is (0.023, 0.164)
Formula : ((n-1)*(s^2))/(X^2)R < ?^2 < ((n-1)*(s^2))/(X^2)L
= (9*(0.2221^2)/19.02 < ?^2 < (9*(0.2221^2)/2.7
= 0.023 < ?^2 < 0.164
=> option B.
(b) The confidence interval for the population standard deviation is(0.152, 0.405)
sqrt(((n-1)*(s^2))/(X^2)R) < ? < sqrt(((n-1)*(s^2))/(X^2)L)
sqrt(0.023) < ? < sqrt(0.164)
=> 0.152 < ? < 0.405