Stat 217 - HW 2 Solutions

1) (2 pts) Take the “Learning Styles Survey”

2) For each research question below

(i) Identify the observational units and variable of interest

(ii) Identify the population of interest

(iii) Describe in words the parameter of interest

(iv) Specify a sampling frame (p. 34) you could use (e.g., list of all registered students at Cal Poly) to select a random sample from the population and briefly outline your sampling process.

(a) Estimate the average number of words on a page of a history textbook.

(i) observational units = pages, variable = number of words

(ii) population = all pages in history textbook

(iii) parameter = average number of words per page in the book

(iv) sampling frame = list of page numbers with words

(b) Do a majority of Cal Poly professors classify themselves as liberals?

(i) observational units = people, variable = political self-classification

(ii) population = Cal Poly professors

(iii) parameter = proportion of all Cal Poly professors that are liberal

(iv) sampling frame = staff roster with all faculty members lists

(i) observational units = Cal Poly study, variable = amount paid for books this quarter

(ii) population = all Cal Poly students

(iii) average price paid by all CP students this quarter

(iv) registration list this quarter

(d) Do college freshmen really tend to gain an average of 15 pounds during their first term at college?

(i) observational units = college freshmen, variable = amount of weight gained

(ii) population = all college freshmen

(iii) parameter = average amount of weight gained during their first term by all college freshmen

(iv) sampling frame = a list of all college freshmen from registration records

3) Activity 5-14 (p. 86) – 10 pts

a. Parts a and b only have one variable so you cannot distinguish between explanatory and response variables in these cases (you could consider the one variable a response variable in each case).

For part c, the explanatory variable is whether their version of the exam asks them to indicate race; the response variable is score on SAT-like exam.

For part d, the explanatory variables are gender and race of “customer”; the response variable is price negotiated for the car.

b. The observational studies are part a (height of American CEOs) and part b (marriage counselors). The experiments are part c (SAT-like exam given to African American students) and part d (best prices at car dealerships).

c. Because parts a and b are observational studies, you cannot draw any cause-and effect

conclusions from either of them. In part a, because the economist took a random sample of American CEOs, you are probably safe in generalizing the results to the population of American CEOs.

In part b, you are not told that the psychologist interviewed a random sample of marriage counselors, so you might hesitate to generalize these results to any larger population of counselors.

In part c, you should be able to draw a cause-and-effect conclusion if an effect is found, because a randomized, controlled experiment was performed. You should be cautious in generalizing your results to African American college students at similar colleges, however, because you were not told how the 200 students were selected for the study.

In part d, if a significant difference is found in average price among the four types of customers, you should be able to attribute the difference to race, gender, or both because you used a comparative, randomized experiment. You should be cautious about generalizing these results because you are not told how the 10 dealerships were selected, and they were all apparently in the same city.

4) (Topics 4 and 5, 7 pts)

(a) The observational units are pedestrians downtown

Response variable is whether or not the person agreed to hold her hand (categorical and binary)

(b) Answers will vary but one example is whether she approached from the left or the right. The researcher could flip a coin to decide before approaching the pedestrian.

(c) Random sampling would be involved if she got a list of all pedestrians, assigned them numbers, randomly selected a set of numbers, and then only approached those individuals. So random sampling would deal with how those in the study were selected from the population.

Random assignment would be involved if she randomly assigned them to different treatment conditions as in (b).

(d) Answers will vary. One possibility is people crossing the street in the daytime in downtown SLO? Probably not willing to say all Californians or even all SLO residents but can probably say something beyond just the people interviewed or even people there that evening.

5) (Topic 6, 6 pts)

(a) conjecture

(b)

	Positive test	Negative test	Total
Carries AIDS virus	(2) 4885	(2) 115	(1) 5000
Does not carry AIDS	(3)73630	(3) 921370	(1) 995,000
Total	(4) 78515	(4) 921485	1,000,000

Now calculate from the table the proportion of people with positive tests that actually carry the aids virus.

4885/78515 = .062

(d) .062 / (115/921485) = 496.8

You are almost 500 times more likely to have AIDS if you have a positive test than if you test negative. Of course 500 times a very small number is still pretty small.