Saturday, April 10, 2010

Statistics Assignment #1 [MBA]

The data below were collected using a radar gun to record the speed of bike riders at the bottom of a steep hill in northwest Gainesville. Sorry about the spilled BBQ sauce.

1) If all you had were the mean (18.21) and standard deviation (5.86) of the data set, how would you use them to say something about the speed of all bike riders at the bottom of the hill?

I would choose a few values of interest (speed limit, 5 miles an hour, 10 miles an hour, 20 miles an hour, 30 miles an hour) and compute a probability that a biker was exceeding that speed. For example, using statpad, The probability that a normal random variable with mean 18.21 and standard deviation 5.86 is greater than 5 is: 0.987910287, and The probability that a normal random variable with mean 18.21 and standard deviation 5.86 is greater than 30 is: 0.022112847.

Alternately, we could pick a range of speeds and compute the probability a biker is inside or outside that range. For example, The probability that a normal random variable with mean 18.21 and standard deviation 5.86 is between 10 and 20 is: 0.539388906.

2) For the sample above, would any of the values be considered outliers? (You obviously have to first decide what you can consider an outlier.)

First, I’d use the formula from the book to determine what would be an outlier. A number larger than Upper Quartile + 1.5(Upper Quartile – Lower Quartile) would be considered an outlier and a number smaller than Lower Quartile - 1.5(Upper Quartile – Lower Quartile) would be considered an outlier. Plugging in the information, we’d get 21.25 + 1.5(21.25 – 17.05) = 27.55 and 17.05 - 1.5(21.25 – 17.05) = 10.75.

With this definition, the first three observations (5.6, 8.1, 9.0) would be considered outliers. Perhaps these riders breaked on the way down the hill.

3) In a company with 2000 employees, 70 percent have enrolled in the firm’s group health plan. Fifty-five percent have enrolled in the firm’s group life insurance plan. Of those employees that are NOT in the health plan, 60 percent are also not in the life insurance plan. Use this information to allocate the 2000 employees to the blank cells in the table.


Insurance
Enrollment
No Group Health Ins.
Does Have Group Health

Totals
No Group Life Ins.
360
540
900
Does Have Group Life
240
860
1100
Totals                  
600
1400
2000



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