Exercise Questions: Chapter 6
Changing the sample size.
Suppose that the sample mean is 50 and the standard
deviation is assumed to be 5. Make a diagram similar to
illustrates the effect of sample size on the width of a 95% interval. Use the following
sample sizes: 10, 20, 40, and 80. Summarize what the diagram shows.
Changing the confidence level.
A study with 36 observations had a mean of 70.
Assume that the standard deviation is 12. Make a diagram similar to
) that illustrates the effect of the confidence level on the width of the interval. Use
80%, 90%, 95%, and 99%. Summarize what the diagram shows.
Mean serum TRAP in young women.
For many important processes that occur in
the body, direct measurement of characteristics of the process is not possible. In many
cases, however, we can measure a
a biochemical substance that is relatively
easy to measure and is associated with the process of interest. Bone turnover is the net
effect of two processes: the breaking down of old bone, called resorption, and the
building of new bone, called formation. One biochemical measure of bone resorption is
tartrate resistant acid phosphatase (TRAP), which can be measured in blood. In a study of
bone turnover in young women, serum TRAP was measured in 31 subjects.
The units are
units per liter (U/l). The mean was 13.2 U/l. Assume that the standard deviation is known
to be 6.5 U/l. Give the margin of error and find a 95% confidence interval for the mean
for young women represented by this sample.
Calories consumed by women in the U.S.
The mean number of calories consumed
by women in the United States who are 19 to 30 years of age is
= 1791 calories per day.
The standard deviation is 31 calories.
You will study a sample of 200 women in this age
range, and one of the variables you will collect is calories consumed per day.
(a) What is the standard deviation of the sample mean
(b) The 68–95–99.7 rule says that the probability is about 0.95 that
is within ________
calories of the population mean
. Fill in the blank.
(c) About 95% of all samples will capture the true mean of calories consumed per day in
plus or minus ________ calories. Fill in the blank.
Required sample size for specifed margin of error.
A new bone study is being
planned that will measure the biomarker TRAP described in
. Using the
given there, 6.5 U/l, find the sample size required to provide an estimate of the
mean TRAP with a margin of error of 2.0 U/l for 95% confidence.
More than one confidence interval.
As we prepare to take a sample and compute a
95% confidence interval, we know that the probability that the interval we compute will
cover the parameter is 0.95. That’s the meaning of 95% confidence. If we use several
such intervals, however, our confidence that
of them give correct results is less than