Math 2000 - Solution 3

Fall 2000

Part B

1. The income of teachers could be determined by an observational study. You could survey teachers (perhaps unreliable) or consult public payroll records.

2. This question can be addressed with an experiment. You would make random assignments to a group whose members study while listening to jazz, to a group whose members study while listening to no music, and perhaps to other groups whose members study while listening to other types of music. Such a study could not be single-blind. Notice that this approach has the drawback that there are many other factors that contribute to grades. With different students in different groups, it may be difficult to control for these factors. Instead, the question could also be approached with an experiment in which students who do not ordinarily study to jazz are asked to begin studying while listening to jazz.

3. The question is best answered with a case-control observational study. It would not be appropriate to conduct an experiment and ask some people to ride without helmets. However, it is possible to select a group of bicyclists who by choice do not use helmets and another group of bicyclists who by choice do use helmets. The accident or injury rate of these two groups could then be compared. The question could also be addressed with a pure observational study by looking at medical records of people who have been in bicycle accidents resulting in head injuries. It should be possible to determine whether or not a helmet was used.

4. This question is similar to question 2 above. Some kind of experiment can be used (again, blinding is not possible).

5. This question is best answered by a single-blind experiment in which a control group is given a no treatment, a placebo group is given an aspirin placebo, and a treatment group is given an aspirin a day. This would have to be a long-term study over several years with many participants, so that the incidence of heart attacks in all three groups could be observed and compared.

Part C

Unit 3A

8c. The volume of the human box is (5.5 ft) ´ (1.25 ft) ´ (0.5 ft) = 3.44 ft³.

16b. The number of minutes in a century is

There are about 52 million minutes in a century.

18b. Starting with 1 ft = 12 in, we can cube both sides and find that 1 ft³ = (12 in)³ = 1728 in³.

20b. Use the conversion factor 1 French franc = $0.21:

We see that 25 francs is worth $5.25.

20d. Use the conversion factor 1 mark = $0.72:

We see that $20 is worth 27.78 marks.

Unit 3B

4f. This problem can be worked in units of yards or feet and the result must be the same in the end. Here is a solution using feet. The football field has an area of 100 yd ´ 60 yd = 6000 yd². We have seen that 1 yd² = 9 ft², so the area of the football field is 6000 yd² ´ (9 ft²/yd²) = 54,000 ft². Every 54,000 ft³ of garbage will fill the football field 1 foot deep. Therefore 500,000 ft³ of garbage will fill the field to a depth of 500,000 ft³/54,000 ft² = 9.26 feet.

8a. To convert centimeters to yards, we can proceed in two steps. The conversion factor 1 in = 2.54 cm takes us from centimeters to inches and the conversion factor 1 yd = 36 in takes us from inches to yards. Therefore 105 cm. is equal to

We conclude that 105 centimeters is equal to 1.15 yards.

15c. We need the conversion factors 1 kg = 2.2 lb and 1mark = $0.72. Then we can do the following conversion:

A price of 2 mark/kg is the same as $0.65/lb.