MONT 106N – Identifying Patterns Midterm Exam – October 19, 2009

Directions

Do all work in the blue exam booklet or on the graph paper provided. Be sure to provide explanations for your answers if that is asked for. There are 100 possible points.

I. The following quotation is taken from an article that appeared in the New York Times on December 3, 1991.

“... new research also demonstrates that spanking, which remains parents’ main disciplinary weapon, is not only useless in the long run but also potentially harmful to the child’s emerging personality. In experimental studies with toddlers placed in a room with their mothers and breakable objects they were told not to touch, the children who were frequently spanked were less obedient than the children who were disciplined in nonphysical ways.”

A) (5) True or False: The author is claiming that the studies show that children who are spanked frequently tend to become more disobedient than children who are disciplined in nonphysical ways.

B) (10) What questions should one ask about the way these studies were performed before deciding whether they provide good evidence for a relation between spanking and obedience? Explain.

II. A study of grand juries in Alameda County, California, compared the demographic characteristics of grand jurors in one year with the general population. Here are the results for age. Only persons 21 years and older are included.

Age  Countywide Percentages Number of Grand Jurors
20 < age ≤ 40  42  5
40 < age ≤ 50  23  9
50 < age ≤ 60  16  19
60 < age ≤ 80  19  33
Totals  100%  66 jurors

A) (15) Construct two age histograms, one for the countywide population and one for

the actual grand jurors. (Use the graph paper provided.) B) (5) By comparing your histograms, what appears to be true about the age distributions

of the two groups?

III. The grades in a large university calculus class were normally distributed with an average of 68 (out of a possible 100 points) and an SD of 10. A) (15) If 400 students took the test, estimate how many scored between 58 and 83

inclusive. Show all work and draw normal curves as needed.

B) (15) The professor decided to set the cutoff numerical grade for an A letter grade at the 90th percentile of the grade distribution. What grade did a student need in order to earn an A in calculus?

IV. The US Department of Justice made a study of civil cases during the year 1992. Juries awarded money damages to the plaintiffs in 5949 of the cases. The median damage award was $50,000 and the average damage award was $450,000. A) (10) Sketch a possible (smoothed) histogram of the damage awards. Does your his-

togram have a long left tail, a long right tail, or is it symmetric? B) (5) Which is larger, the difference between the award at the 10th percentile and the

median award, or the difference between the median award and the award at the 90th percentile? Or are those differences about the same? Explain briefly.

V. A) (10) Find the equation of the line passing through the points P = (1, −2) and Q =

(4, 3) in the plane. B) (10) Find the equation of the line parallel to the line in part A and passing through

the point R = (1, 2).