Question

The owner of a local golf course wants to determine the average age of the golfers that play on the course in relation to the average age in the area. According to the most recent census, the town has an average age of 21.29. In a random sample of 30 golfers that visited his course, the sample mean was 39.723 and the standard deviation was 8.0282. Using this information, the owner calculated the confidence interval of (35.683, 43.763) with a confidence level of 99%. Which of the following statements is the best conclusion?

a. We are 99% confident that the average age of all golfers that play on the golf course is greater than 21.29
b. We are 99% confident that the average age of all golfers that play on the golf course is less than 21.29
c. We cannot determine the proper interpretation based on the information given.
d. The average age of all golfers does not significantly differ from 21.29.
e. The percentage of golfers with an age greater than 21.29 is 99%.

Answer 1

a. We are 99% confident that the average age of all golfers that play on the golf course is greater than 21.29

Explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

99% confidence interval for the average age of golfers that play on the area is (35.683, 43.763), which means that we are 99% confident that the mean age of all golfers who play in the area is a value in this interval, and the best conclusion is given by option A, as the lower bound of the interval is greater than 21.