Stat 200 Unit 4 Project Fall 2020
Name:
1. Does increasing the amount of calcium in our diet reduce blood pressure? Examination of a
large sample of people revealed a relationship between calcium intake and blood pressure.
The relationship was strongest for black men. Such observational studies do not establish
causation. Researchers therefore designed a randomized comparative experiment.
The subjects in part of the experiment were 21 healthy men. A randomly chosen group of 10
of the men received a calcium supplement for 12 weeks. The control group of 11 men
received a placebo pill that looked identical. The experiment was double-blind. The response
variable is the decrease in systolic (heart contracted) blood pressure for subject after 12
weeks, in millimeters of mercury. An increase appears as a negative response.
Group 1- Calcium Group
7
-4
18
17
-3
-5
1
5
2
10
11
-2
Group 2- Placebo Group
-1
12
-1
-3
3
-5
-11
-1
-3
a. Is there significant evidence that the blood pressure is different for the calcium and
placebo groups? Perform the appropriate significance test and let 𝛼 = .10.
b. Perform a 90% confidence interval to estimate the difference in the mean decrease in
blood pressure for the calcium and placebo populations.
c. Explain why your confidence interval in part b agrees with your decision in part a.
2. The table below summarizes results from an experiment involving randomly selected
subjects who experience some degree of sleeplessness. Some of the subjects were treated
with a drug, while others were given a placebo.
Experienced Improvement
Did Not Experience Any
Improvement
Treatment Group
10,222
49,875
Placebo Group
10,587
53,252
a. Use the methods of Chapter 11 (Chi-Square) to test for independence between the
treatment and placebo group and whether the subject experienced improvement in the
degree of sleeplessness. What do you conclude? Does it appear that the treatment is
effective? What does the result suggest about the decision to distribute the treatment? Use
(𝛼 = .05).
b. Use the methods of Section 9.4 (inference about two proportions) to test the claim that
the treatment result in a greater rate of improvement that the rate achieved with a placebo.
What do you conclude? Does it appear that the treatment is effective? What does the
result suggest about the decision to distribute the treatment? Use (𝛼 = .05).
c. If you are the chief executive officer of a pharmaceutical company and you are given the
results in the accompanying table, what should you do? Should you market the treatment?
Why or why not?
3. A research wants to determine the effect of smoking on resting heart rate. She randomly
selects individuals from three categories; nonsmokers, light smokers (fewer than 10
cigarettes per day) and heavy smokers (10 or more cigarettes per day) and obtains the
following heart rate data:
Nonsmokers
56
52
53
65
70
58
51
Light smokers
78
62
70
73
67
75
65
Heavy smokers
77
86
65
83
79
80
77
a. Test the hypothesis that the mean resting heart rate is equal for all three groups. Show all
of your work by hand and only check it with the ANOVA calculator function for full
credit. Use (𝛼 = .01).
b. Use the Scheffe follow up test to determine why the null hypothesis in part a was
rejected. Show all work by hand.
c. Draw boxplots of the three treatment levels to support the results (as shown/explained
during Chapter 12 class discussion).