FOR 6520 Winter 2003

Alliant International University

Research II: Data Analysis & Advanced Statistics

http://www.stat.ucla.edu/~dinov/courses_students.html

HOMEWORK 1

Due Date:

Saturday, Feb. 01, 2003

Please, submit your homework right after lecture on the due date. See the HW submission rules. On the front page include the following header.

(HW_1_1) Consider the following four studies:

Study 1: A researcher was interested in whether pain tolerance levels were related to hair color. 80 people were selected from a group of volunteers, 20 with light blonde hair, 20 with dark blond hair, 20 brunettes and 20 redheads. The subjects underwent a series of tests and pain tolerance scores (on a scale of 0 to 100) were assessed.

Study 2: A forensic scientist is interested in the effects of age on the quality of finger prints. 20 random individuals of different ages are selected and their finger prints are obtained using the same protocol. A laboratory assessments of the quality of the obtained finger prints is performed.

Study 3: The manager of an auto repair shop is interested in whether using a new diagnostic machine will speed up the regular servicing of cars. There are two mechanics working on regular services, one with 8 years experience while the other mechanic had only 2 years experience. One mechanic was told to use the diagnostic machine on the next 10 cars she serviced, but not use it on the following 10 cars. The other mechanic was told not to use the diagnostic machine on the next 10 cars he serviced, but to use it on the following 10 cars. Each mechanic recorded the time it took to complete the services for each of these jobs.

Study 4: A sociologist is interested in comparing the exam results for male and female students on 10 different subjects. The proper authority was contacted to obtain the numbers of male and female students who took the exam and the numbers of male and female students who got each of the grades A, B, C and D.

For each study, describe what treatment is being compared and what response is being measured to compare the treatments.
Which of the studies would be described as experiments and which would be described as observational studies?
For the studies that are observational, could an experiment have been carried out instead? If not, briefly explain why not.
For the studies that are experiments, briefly discuss what forms of blinding would be possible to be used.
In which of the studies has blocking been used? Briefly describe what was blocked and why it was blocked.

(HW_1_2) The following data represent the daily number of parking tickets given out on UCLA campus over a period of 30 days.

42	47	46	35	43	39	38	40	50	37	68	37	47	44	49
41	34	38	41	36	42	38	38	58	34	32	42	49	52	54

Calculate the five number summary for the data (min, lower quartile, median, upper quartile and max). Note: If there are x indices of numbers below the median then the (x+1)/2 -st number in the ordered observations, see stem-and-leaf plot, gives you the value of the lower quartile. The upper quartile is computed identically as the lower quartile, except that you take the value of the observation half-way between the median and the max-observation.
Draw a box plot for this set of data. Show your working.
Using your plots, in plain English, briefly comment on the data and the story the above summary/plots convey.

(HW_1_3) Assume the distribution of human blood types in one geographic region is: 30% type A; 11% type B; 49% type O and; 10% type AB. Suppose we select one married couple at random, with the husband and the wife following this blood type distribution.

If the wife has type B blood, what is the probability that the husband has blood type B?
What is the probability that both husband and wife have type A blood?
What is the probability that at least one of them has blood type AB?
What is the probability that they have the same blood type?

(HW_1_4) Suppose that X ~ Normal(μ=3, σ²=16) compute the Z-scores for the following numbers and state how many SD's each of these numbers is away from μ:

-5
11
5
1.4
What is the probability P(-3 ≤ X ≤ -1)? Is it different from P(-3 < X < -1)? Why?

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Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology, UCLA School of Medicine

42	47	46	35	43	39	38	40	50	37	68	37	47	44	49
41	34	38	41	36	42	38	38	58	34	32	42	49	52	54

42	47	46	35	43	39	38	40	50	37	68	37	47	44	49
41	34	38	41	36	42	38	38	58	34	32	42	49	52	54

42	47	46	35	43	39	38	40	50	37	68	37	47	44	49
41	34	38	41	36	42	38	38	58	34	32	42	49	52	54