INVESTIGATING STATISTICAL CONCEPTS, APPLICATIONS, AND METHODS

BRIEF SOLUTIONS TO INVESTIGATIONS FOR SECTION 1.4

Investigation 1.4.1: Foreign Language and SAT Scores

(a) EV = foreign language study (categorical); RV = SAT verbal (quantitative)

(b) Possibilities include ambition, overall academic achievement, verbal ability.  For example, maybe those who take a foreign language are more likely to be interested in attending college and therefore study harder for the SAT.

(c) Randomly assign students to take a foreign language or not

(d) Want the two groups to be as similar as possible.

(e) The power of suggestion could be enough to help improve their performance.

 

Investigation 1.4.2: Have a Nice Trip

(a) This would be a problem as gender would be confounded with the recovery strategy employed.  If one group did better you wouldn’t be able to decide whether it was the strategy used or their gender.

(b) Want everything about the two groups to be as similar as possible.

(c)-(d) Results will vary

(e) Difference won’t always be zero but distribution should be centered around zero and should be equally likely to be positive as negative.

(f)-(g) Results will vary but the two outcomes will probably not be identical.

(h) Distribution should center symmetrically around zero.

(i) Center: 0, Largest: around .67, smallest: around -.67

(j) No, but most randomizations produce a difference that is close to zero

(k) Yes, as seen by the distribution being centered around zero

(l) Yes, as seen by the distribution being centered around zero

(m) Yes, as seen by the distribution being centered around zero

 

Investigation 1.4.3: Have a Nice Trip (cont.)

(a) Make sure you have the same number of men and women in the two groups

(b) Equal

(c) The difference in proportions will always be zero, by your design.

(d) Should be less variation than when didn’t block on gender

(e) Since height is related to gender, by making the groups more similar with respect to gender, will also be more similar with respect to height.

(f) This time, the distributions look pretty similar. Presumably gender is not related to either of these two variables.