The owner of a local golf course wanted to determine the average age (in years) of the golfers that played on the course. In a random sample of 20 golfers that visited his course, the sample mean was 41.6 years old, and the standard deviation was 7.81 years. Using this information, the owner calculated the confidence interval of (38.6, 44.6) with a confidence level of 90% for the average age. Which of the following is an appropriate interpretation of this confidence interval?

A. We are certain that 90% of the average ages of all golfers will be between 38.6 and 44.6 years old.

B. We are 90% confident that the average age of the golfers surveyed is between 38.6 and 44.6 years old.

C. We cannot determine the proper interpretation of this interval.

D. We are 90% confident that the proportion of the ages of all golfers is between 38.6 and 44.6 years old.

E. We are 90% confident that the average age of all golfers that play on the golf course is between 38.6 and 44.6 years old.

Question

30-11-2024
Mathematics

College

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The owner of a local golf course wanted to determine the average age (in years) of the golfers that played on the course. In a random sample of 20 golfers that visited his course, the sample mean was 41.6 years old, and the standard deviation was 7.81 years. Using this information, the owner calculated the confidence interval of (38.6, 44.6) with a confidence level of 90% for the average age. Which of the following is an appropriate interpretation of this confidence interval?

A. We are certain that 90% of the average ages of all golfers will be between 38.6 and 44.6 years old.

B. We are 90% confident that the average age of the golfers surveyed is between 38.6 and 44.6 years old.

C. We cannot determine the proper interpretation of this interval.

D. We are 90% confident that the proportion of the ages of all golfers is between 38.6 and 44.6 years old.

E. We are 90% confident that the average age of all golfers that play on the golf course is between 38.6 and 44.6 years old.

Answer :

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joaobezerra joaobezerra · Answer 1 · 2023-08-21T04:49:37-04:00

Answer:

e. We are 90% confident that the average age of all golfers that play on the golf course is between 38.6 and 44.6 years old.

Step-by-step 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:

90% confidence interval for the average age of golfers in the course is of (38.6, 44.6). This means that we are 90% sure that the true average age of all golfers in the course is between these two values, that is, the correct answer is given by option e.