STATISTICS 2MA3: Test #1

4 February 1998

Students may bring and use any calculators, one sheet of notes (8.5" x 11", one side only), and any mathematical or statistical tables.

If the tables are in a textbook, elastic bands must be drawn around the remaining pages so that only the tables can be used.

Marks are indicated in the left-hand margin.

[7] 1. Draw a scatter plot and compute the correlation coefficient for the following data. What do you conclude?

Subject:

1

2

3

4

5

% reticulytes:

3.6

2.0

0.3

0.3

0.2

Lymphocytes /mm2:

1700

3078

1820

2706

2086

[8] 2. A tree has 263 peaches and their diameters are independently Normal with mean 3 inches and standard deviation 0.2 inches. If only peaches with diameter greater than 2.5 inches can be marketed, how many peaches would you expect to market from this tree? What is the probability that all 263 peaches will exceed the minimum diameter?

[9] 3. In Assignment 1, you found the following table for children age 2 or younger, with a single infected ear; 13 had been assigned to Antibiotic #1 and 12 to Antibiotic #2. Use the hypergeometric distribution to compute the probability of the infection clearing in at most 2 of the 12 children on Antibiotic #2, given that 6 children did clear and 19 didn't, and assuming that clearance is independent of antibiotic. Compute an odds ratio and risk ratio for the table. What can you conclude?

Antibiotic

#1

#2

14-day clearance

No

9

10

Yes

4

2

[6] 4. Suppose that an influenza epidemic strikes a city. In 8% of families the mother has influenza; in 8% of families the father has influenza; and in 2% of families both the mother and the father have influenza. Are the mother and father independent with respect to influenza? Suppose there is a 20% chance that any one child will get influenza, whereas in 12% of two-child families, both children will get the disease. What is the probability that at least one child in a two-child family will get the disease?