Question

In studying a random sample of 20 automotive​ batteries, the confidence interval ​(0.22​,0.33​) was constructed for the population standard deviation of the​ batteries' reserve capacity in hours. This population standard deviation should be less than 0.26 hour. Does the confidence interval suggest that the variation in the​ batteries' reserve capacities is at an acceptable​ level? Explain your reasoning.

Answer 1

NO.

Explanation:

From the question, we are given a random sample of 20 automotive​ batteries, a confidence interval =(0.22​,0.33​). Also, the population standard deviation is said to be less than 0.26 hour.

The confidence interval does NOT suggest that the variation in the​ batteries' reserve capacities is at an acceptable​ level.

REASON: If you look at the confidence interval, we can see that it contains the value for the standard deviation that is 0.26 and even MORE value than 0.26.

This does not give us any suggestion that the standard deviation is less than 0.26.