MTH 109, Statistics

First test, Chapters 1 - 6, Spring 2001

Be sure to show all your work. Hand in any scrap paper. When you are finished, fold your paper length-wise, and put your name on the outside. Each answer is worth 7 points except part IV, where A and B are worth 10 points each.

(Moved part I to the end)

II. The following table is the average one-way commuting time in minutes for adults who drive or carpool (adapted from USA Snapshots in USA Today, July 13, 1998). The class intervals include the left endpoint, but not the right. You can interpret over 45 minutes as 45 to 75 minutes. About 7 % of those asked did not respond or didn’t know.

Driving time (in min.) / Percent of adults
Under 15 / 39
15 – 20 / 11
20 – 30 / 19
30 – 45 / 13
Over 45 / 11

A. Draw the histogram to the right of the chart.

B. Is the distribution more symmetric or is it skewed? If it is skewed, state the direction.

C. Which is larger, the median or the mean? How do you know?

III. Suppose a cat is weighed 4 times during one trip to the vet, obtaining the following weights (in pounds): 9.25, 9.05, 9.3, and 9.2.

A. What is your best guess for the cat’s actual weight?

B. If the cat were to be weighed one more time, how much chance error would you estimate the scales to have? Or can it be determined? (Tell how and find it, if possible.)

C. How much bias error would you estimate the scales to have, or can it be determined? (Tell how and find it, if possible.)

IV. In a study of aggressive behavior, male white mice, returned to the group in which they live after four weeks of isolation, averaged 19 fights in the first five minutes with a standard deviation of 3 fights. If it can be assumed that the distribution of the number of fights has roughly the shape of a normal distribution, find the following:

A. Estimate the percentage of mice that got into at least 15 fights (in the first five minutes).

B. About how many fights did a mouse have (in the first five minutes) if he is in the 35th percentile?

V. Book question, p. 75, # 7. A study on college students found that the men had an average weight of about 66 kg and an SD of about 9 kg. The women had an average weight of about 55 kg and an SD of 9 kg. If you took the men and women together, would the SD of their weights be smaller than 9 kg, just about 9 kg, or bigger than 9 kg? Why?

I. The following article had the title: “Sleep deprivation is like being drunk” (Winston-Salem Journal, 8/12/97)

After staying awake for 24 hours straight, a person will be about as impaired as if he had had enough alcohol to be legally drunk in most states, a study says. Australian researchers tested 40 people to create a “blood alcohol equivalent” for different levels of impairment from sleeplessness. In one experiment participants stayed awake for 28 hours. In the other, they drank alcohol every half hour until they reached a blood alcohol concentration of 0.10 percent. That’s the drunken-driving standard in most American states (0.08 in North Carolina). Every half hour, the subjects took a computerized test of hand-eye coordination. Results showed that after 24 hours of sleeplessness, participants were about as impaired as they were with at the 0.10 percent level of blood alcohol. After 17 hours, they were about as impaired as they were with an alcohol level of 0.05 percent, which many Western countries define as legally drunk, the researchers said. The work is reported in the July 17 issue of the journal Nature.

A. What kind of study was this? Use All terms that apply: Controlled; Cross-Sectional; Double-Blind; Longitudinal; Observational; Randomized; Single-Blind. Explain your choices.

B. Do you think this was a good study? Why? Back your answer with many supporting details.