STAT412
Final Exam
Take-Home Part
Name___________________________
Instructions: This is the take-home part of the final exam. Each question is worth 10 points. You are permitted to use
your notes, book, calculator, and statistical software in working this exam. However, you are not permitted to consult with
a fellow student. You are to turn in the finished product when you turn in the in-class part of the final exam. Turn in
computer output and scratch work with your test. Good luck!
1. To test the stimulus effect of caffeine, a double-blind experiment was conducted. Thirty male college students were
randomly assigned to one of three groups of ten students each. Each group was given one of three doses of caffeine (0, 100,
or 200mg) and 2 hours later the students were given a finger tapping exercise. The response is the number of taps per
minute, as shown in the table below.
0 mg Caffeine
242
245
244
248
242
244
246
242
247
248
100 mg Caffeine
248
246
245
247
248
250
247
246
243
244
200 mg Caffeine
246
248
250
252
248
250
246
248
245
250
Analyze the data using =.05.
2. An engineer conducted a study to examine the relationship between the breaking strength, y, of wooden beams and the
specific gravity, x, of the wood. Ten randomly selected beams of the same cross sectional dimensions were stressed until
they broke. The breaking strength and the specific gravity of the wood are shown in the table for each of the ten beams.
Beam 1
1
2
3
4
5
6
7
8
9
10
Breaking Strength
Specific Gravity
12.00
12.74
13.13
11.51
12.38
12.60
11.13
11.70
11.02
11.41
0.488
0.558
0.604
0.441
0.550
0.528
0.418
0.480
0.406
0.467
a. Construct a scatter plot.
b. Calculate the Pearson correlation coefficient.
c. Determine equation of least squares line that can be used for predicting a value of y based on a value of x.
d. Calculate r2 and interpret.
e. Construct a 95% confidence interval for the mean breaking strength of beams that have a specific gravity equal to
.430.
3. According to the U.S. Census Bureau, 69% of houses across the country are occupied by their owners. You randomly
select 50 houses in your community and find that 30 houses are occupied by the owners. Do the data provide sufficient
evidence to conclude that your community differs from the nation as a whole as to the proportion of houses that are owner
occupied. Conduct test using =.05.
4. A random sample of 214 teenagers between the ages of 15 and 19 were questioned regarding their use of alcohol and
their family status. A summary of the responses is shown below.
Upper class
Upper middle class
Lower middle class
Lower class
None
9
15
12
8
Occasional
16
40
47
17
Frequent
10
24
9
7
Do the data provide sufficient evidence to indicate a relationship between family status and the use of alcohol in the
population? Conduct test using =.05.
5. The effect of Benzedrine on the heart rate of dogs (in beats per minute) was examined in an experiment on 14 dogs
chosen for the study. Half of the dogs were assigned to receive Benzedrine during the first study period and the other half
assigned to receive a placebo (saline solution). All dogs were examined to determine the heart rates after 2 hours on the
medication. After 2 weeks in which no medication is given, the regimens for the dogs were switched for the second study
period. The dogs previously on Benzedrine were given the placebo and the others received Benzedrine. Again the rates
were measured after 2 hours. Do the data provide sufficient evidence to conclude that the population mean heart rate when
the placebo is used is less than the population mean heart rate when Benzedrine is used. Conduct hypothesis test using
=.05.
Dog
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Placebo
Benzedrine
250
271
243
252
266
272
293
296
301
298
310
286
306
309
258
285
245
250
268
278
280
305
319
308
320
293
305
313