Question

9.5 A random sample of 100 automobile owners in the state of Virginia shows that an automobile is driven on average 23,500 kilometers per year with a standard de- viation of 3900 kilometers. Assume the distribution of measurements to be approximately normal. (a) Construct a 99% confidence interval for the aver- age number of kilometers an automobile is driven annually in Virginia. • (b) What can we assert with 99% confidence about the possible size of our error if we estimate the aver- age number of kilometers driven by car owners in Virginia to be 23,500 kilometers per year?

Answer 1

n = 100

$\bar{x}$ = 23500

s = 3900

A.

The critical value for a = 0.01 and df = n-1=99 degrees of freedom is to = 21-a/2.n-1 = 2.626. The corresponding confidence interval is computed as shown below: ci = (x-te x 8 + x n ) 23500 - 2.696 3900 23500+ 2.626 3900 V100 V100 = (22475.702, 24524.298)

B.

Only 1% of the times when we calculate confidence interval with 99% confidence, the true population average of the kilometres driven by the car owners won't fall inside the confidence interval.

Please upvote if you have liked my answer, would be of great help. Thank you.