Question

A 90 % confidence interval (a t interval) for the mean lives (in minutes) of Kodak AA batteries is ( 380, 460 ). Assume that this result is based on a sample of size 20 .

4) If the confidence interval (385.2962 ,454.7038) is obtained from the same sample data, what is the degree of confidence?
90%
95%
88%
85%

Answer 1

90 % confidence interval (a t interval) for the mean lives (in minutes) of Kodak AA batteries is ( 380, 460 )

and n = 20

X bar = (380+460)/2 = 420

Upper limit = X bar + tc * Sd/SQRT(n)

alpha = 0.1 and df = 19

tc = 1.729 (T.INV.2T(alpha,df)

460 = 420+ 1.729*Sd/SQRT(20)

1.729*Sd/SQRT(20) = 40

Sd/SQRT(20) = 23.1348

Sd = 103.4611

4)

Given, CI = (385.2962 ,454.7038)

CI = X bar +/- tc * Sd/SQRT(n)

Upper limit = X bar + tc * Sd/SQRT(n)

454.7038 = 420 + tc * 103.4611/SQRT(20)

tc * 103.4611/SQRT(20) = 34.7038‬

tc = 1.5001

alpha = 0.15 (T.DIST.2T(1.5001,19))

The degree of confidence = 1-alpha = 1-0.15 = 85%