Question

PART I The owner of a local golf course wanted to determine the average age (in...

PART I

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 27 golfers that visited his course, the sample mean was 47 years old and the standard deviation was 5.11 years. Using this information, the owner calculated the confidence interval of (45.3, 48.7) with a confidence level of 90% for the average age. Which of the following is an appropriate interpretation of this confidence interval?

 1) We are 90% confident that the average age of the golfers surveyed is between 45.3 and 48.7 years old.
 2) We are certain that 90% of the average ages of all golfers will be between 45.3 and 48.7 years old.
 3) We are 90% confident that the average age of all golfers that play on the golf course is between 45.3 and 48.7 years old.
 4) We are 90% confident that the proportion of the ages of all golfers is between 45.3 and 48.7 years old.
 5) We cannot determine the proper interpretation of this interval.

PART II

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 64.08. In a random sample of 22 golfers that visited his course, the sample mean was 48.69 and the standard deviation was 8.026. Using this information, the owner calculated the confidence interval of (43.85, 53.53) with a confidence level of 99%. Which of the following statements is the best conclusion?

 1) We are 99% confident that the average age of all golfers that play on the golf course is less than 64.08
 2) We are 99% confident that the average age of all golfers that play on the golf course is greater than 64.08
 3) The average age of all golfers does not significantly differ from 64.08.
 4) The percentage of golfers with an age greater than 64.08 is 99%.
 5) We cannot determine the proper interpretation based on the information given.

PART III

Researchers at a metals lab are testing a new alloy for use in high end electronics. The alloy is very expensive to make so their budget for testing is limited. The researchers need to estimate the average force required to bend a piece of the alloy to a 90 degree angle. From previous tests, the standard deviation is known to be 31.787 Newtons. In order to estimate the true mean within a margin of error of 9.825 Newtons with 90% confidence, how many samples would need to be tested?

 1) 28
 2) 39
 3) We do not have enough information to answer this question since we were not given the sample mean.
 4) 29
 5) 34

I) option 3) is correct

We are 90% confident that the average age of all golfers that play on the golf course is between 45.3 and 48.7 years old.

ii)

option 1) is correct

We are 99% confident that the average age of all golfers that play on the golf course is less than 64.08

iii)

 for90% CI crtiical Z          = 1.645 standard deviation σ= 31.787 margin of error E = 9.825 required sample size n=(zσ/E)2                  = 29

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