This examination is worth 50points. Read each question carefully and be sure to
answer all parts of each question. YOU MUST SHOW ALL WORK AND ROUNDINGS OF
YOUR FINAL ANSWER MUST BE TO 2 DECIMAL PLACES. If you need to continue an
answer on the reverse side of a sheet, please indicate which question and the part
you are answering. You have up to 2 hours to complete the exam. The use of any
form of software including excel is not allowed.
1. It is believed that the lower than normal level of human calcitonin (HCT) in
men with rheumatoid arthritis is a risk factor in developing osteoporosis. In
43 men with rheumatoid arthritis, the observed HCT mean was 33.8pg/mL
with a standard deviation of 23.6. In normal healthy men, the mean was
47.9pg/Ml. From the sample information, can we conclude that the HCT mean
in men with rheumatoid arthritis is less than that in normal men? Assume a
significance level of 0.05.
2. A randomly selected sample of 25 AHS 340 students’ BMI measurements
representing fall 2016 class was found to have an average of 25.6 and a
standard deviation of 5.81.Test at significance level of 0.01 the hypothesis
that the sample’s average is statistically greater than the spring 2016 class
average of 25.3.
3. A study evaluated the serum acid levels in individuals with Down’s syndrome and
normal individuals, the study data are shown below:
Down’s syndrome: = 4.5 = 13 = 1.2
Normal individual: = 3.4 = 16 = 1.5
Test if the mean of serum acid levels in individuals with Down’s
syndrome is greater than normal individuals.
3. Suppose a researcher wants to evaluate the effect of new diet for weight
loss. He randomly selected six subjects and let them use the diet for 2
months; then he compares the weights before and after the diet:
1 100 91
2 89 84
3 83 80
4 95 93
5 109 103
6 94 90
Test at α = 0.05 if there was a statistically significant average decrease in
weight from before diet treatment to 2 months after.
5. Why it is that one person may tend to gain weight, even if he eats no more
and exercises no less than a slim friend? Recent studies suggest that the
factors that control metabolism may depend on your genetic makeup. One
study involved 7 pairs of identical twins fed about 1000 calories per day
more than needed to maintain initial weight. Activities were kept constant,
and exercise was minimal. At the end of the 100 days, the changes in body
weight (in kilograms) were recorded for the 14 twins as shown below.
Pair Twin A
1 4.2 7.3
2 5.5 6.5
3 7.1 5.7
4 8.2 6.4
5 9.1 8.2
6 11.5 6.0
7 13.0 11.0
Using the data shown in the table above:
Assess if there is a linear correlation between changes in the body
weight for the twins, describe the direction and strength.
Test at significance level of 0.01 if the correlation between the
changes in the body weight for the twins is significant.
6. Water samples were taken at four different locations in a river to
determine whether the quantity of dissolved oxygen, a measure of pollution,
varied from one location to another. Data from five water specimens
randomly selected at each location were analyzed using significance level (α)
of 0.01; the result is shown in the output below:
Squares df Mean Square F Sig.
7.8361 3 2.6120 1.81 0.027
23.1151 16 1.4447
Does the data provide sufficient evidence to indicate a difference in the
mean dissolved oxygen contents for the four locations? Explain how you
arrived at your answer.