Fifteen SmartCars were randomly selected and the highway mileage of each was noted. The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per gallon.
Which of the following would represent a 90% confidence interval for the average highway
Mileage of all SmartCars?
A) $47 \pm 1.761 \frac { 5 } { \sqrt { 15 } }$
B) $47 \pm 1.645 \frac { 5 } { \sqrt { 15 } }$
C) $47 \pm 1.345 \frac { 5 } { \sqrt { 15 } }$
D) $47 \pm 1.753 \frac { 5 } { \sqrt { 15 } }$

Question

Fifteen SmartCars were randomly selected and the highway mileage of each was noted. The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per gallon.
Which of the following would represent a 90% confidence interval for the average highway
Mileage of all SmartCars? 
A) $47 \pm 1.761 \frac { 5 } { \sqrt { 15 } }$
B) $47 \pm 1.645 \frac { 5 } { \sqrt { 15 } }$
C) $47 \pm 1.345 \frac { 5 } { \sqrt { 15 } }$
D) $47 \pm 1.753 \frac { 5 } { \sqrt { 15 } }$

Quizplus · Accepted Answer

The correct confidence interval uses the t-distribution since the population standard deviation is unknown and the sample size is small (n < 30). For a 90% confidence interval and 14 degrees of freedom (n-1 = 15-1), the closest t-value from tables is approximately 1.761. Thus, option A correctly applies this t-value in the formula for the confidence interval.

Fifteen SmartCars Were Randomly Selected and the Highway Mileage of Each