## STAT 10

(Sec. 3a-3c)

Introduction to Statistical Reasoning

## Instructor: Ivo Dinov, Asst. Prof.

Departments of Statistics & Neurology
 http://www.stat.ucla.edu/~dinov/

Due Date:

# Friday, Oct. 05, 2001, turn in after lecture

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 intelligence level depends on body weight. 1000 people were selected from a group of volunteers and divided in 4 groups. The first 250 were considered under-weight, second group of 250 were below average weight, another 250 over the average and the last group of 250 over-weight. The subjects underwent a comprehensive cognitive and psychological examination and scores (integer the range 0 to 200) were assigned to all subjects.

Study 2: A technician is interested in the effects of using different baking temperatures on the impact strength of particle board. 20 boards are randomly allocated to 20 different baking temperatures. After the boards are baked, they are sent to a laboratory where the impact strengths are measured.

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 29 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.

• By hand, construct a stem-and-leaf plot of the data using an appropriate scale.
• 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.
• By hand, draw a box plot for this set of data. Show your work.
• Using your plots, in plain English, briefly comment on the data and the story the above summary/plots convey.

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