Math 498
Quiz 5
You should use the inside front and back covers of the textbook as a cheat sheet. You also should use the tables in the back of the textbook.
Justify all answers with neat and organized work. Clearly indicate
your answers.
40 points possible.
For each problem, there is a blank hypothesis testing form on the next page.
1. (10 pts.) Patients with chronic fatigue syndrome were tested, then retested after being
treated with fludrocortisone. Listed below are the changes in fatigue after the treatment
(based on data from ``The Relationship Between Neurally Medicated Hypotension and the Chronic
Fatigue Syndrome'' by BouHolaigah, Rowe, Kan, and Calkins, Journal of the
American Mediacl Association, Vol. 274, No. 12).
A standard scale from -7 to +7 was used, with positive values representing improvements.
Use a = 0.01 to test the claim that the mean change is positive.
Is there evidence that the treatment is effective?
| 6 5 0 5 6 7 3 3 2 6 5 5 0 6 3 4 3 7 0 4 4 |
2. (10 pts.) Samples of 21 filtered kingsize cigarettes and 8 nonfiltered
kingsize cigarettes were measured for nicotine contents. The filtered kings were
found to have a mean nicotine content of 0.94 milligrams with a standard deviation
of 0.31 milligrams. The nonfiltered kings were determined
to have a mean nicotine content of 1.65 milligrams with a standard deviation
of 0.16 milligrams. Use a 0.05 significance level to test the claim that
the filtered and nonfiltered kings have different variances with respect to
nicotine content.
3. (10 pts.) It is a common belief that more fatal car crashes occur
on certain days of the week, such as Friday or Saturday.
A sample of motor vehicle deaths for a recent year in Montana is randomly selected
(based on data from the Insurance Institute for Highway Safety).
The numbers of fatalities for the different days of the week are
listed in the accompanying table. At the a = 0.05 level of significance,
test the claim that accidents occur with equal frequency on the different days.
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4. (10 pts.) Consider a random variable X with p.d.f\. f(x)=0.0008x
for 0 £ x £ 50
and c.d.f\. F(t)=P(X £ t)=0.0004t2 for 0 £ x £ 50.
A computer program is written, and it is hoped that it
will generate random numbers following this distribution.
A sample of 30 numbers is generated (shown below). At a significance level of
0.05, use the data to test
H0: ``the numbers come from a population with p.d.f. f(x)=0.0008x
for 0 £ x £ 50'' versus H1: ``not so.'' Use k=4 classes of equal
probability.
| 31 16 38 47 47 48 6 32 46 18 |
| 24 11 9 20 23 6 26 29 37 30 |
| 30 30 47 34 32 27 49 44 49 24 |