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?





3)

We do not have enough information to answer this question since
we were not given the sample mean. 




