Question

a sample of 21 minivan electrical warranty repairs for "loose, not attached" wires (one of several electrical failure categories the dealership mechanic can select) showed a mean repair cost of $45.66 with a standard deviation of $27.79. (a) construct a 95 percent confidence interval for the true mean repair cost. (b) How could the confidence interval be made narrower?

Answer 1

Part a)

Confidence Interval



Lower Limit =
Lower Limit = 33.0101
Upper Limit =
Upper Limit = 58.3099
95% Confidence interval is ( 33.0101 , 58.3099 )

(b) How could the confidence interval be made narrower?

By increasing the sample size we can narrow the confidence interval

For example, n = 21

Width of CI = 58.3099 - 33.0101 = 25.2998

for n = 22

Confidence Interval



Lower Limit =
Lower Limit = 33.3386
Upper Limit =
Upper Limit = 57.9814
95% Confidence interval is ( 33.3386 , 57.9814 )
Width of CI = 57.9814 - 33.3386 = 24.6528

So on, as we increase the sample size we can make the confidence interval narrow.