STATISTICS 2MA3: Test #1A

5 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:

2.2

1.0

0.0

3.0

0.2

Lymphocytes /mm2:

2013

2088

676

2299

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 the probability a child has asthma is 15% if both parents smoke, 13% if only the mother smokes, 5% if only the father smokes, and 4% if neither parent smokes. If 50% of fathers smoke and 40% of mothers smoke but 60% of mothers married to smokers smoke, what percentage of all children will have asthma? What is the probability that two randomly chosen children will both have asthma? What is the probability that two children from the same randomly-chosen family will both have asthma?