Question

The gas mileage for a certain model of car is known to have a standard deviation of 6 mi/gallon. A simple random sample of 64 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gallon. Construct a 97.5% confidence interval for the mean gas mileage for this car model.

Answer 1

Answer: confidence interval = 27.5 +/- 1.68

= ( 25.82, 29.18)

Explanation:

Given;

Number of samples n = 64

Standard deviation r = 6mi/gallon

Mean x = 27.5mi/gallon

Confidence interval of 97.5%

Z' = t(0.0125) = 2.24

Confidence interval = x +/- Z'(r/√n)

= 27.5 +/- 2.24(6/√64)

= 27.5 +/- 1.68

= ( 25.82, 29.18)