Practice Assignment (to be randomly discussed Wednesday, March 31)

1) Suppose that a commuter Alex wants to determine which of two possible routes gets him to work more quickly. Suppose that he drives route 1 for 10 days and route 2 for 10 days, recording the commuting times (in minutes) as follows (Jan-Mar):

Alex 1 19.3 20.5 23.0 25.8 28.0 28.8 30.6 32.1 33.5 38.4 =28, s=6

Alex 2 23.7 24.5 27.7 30.0 31.9 32.5 32.6 35.5 38.7 42.9 =32, s=6

(a) Construct side by side boxplots for the 2 routes (use 10-50 as your horizontal scale).

(b) Find the p-value to decide if these sample commuting times provide evidence that the mean commuting times with these two routes differ.

2) Here are sorted commuting times on two routes for Barbara (Apr-Jun).

Barb 1 16.4 17.6 20.2 21.0 23.8 26.4 30.4 30.6 31.6 32.0 =25 s=6

Barb 2 24.4 27.1 32.0 34.0 35.1 36.1 37.8 38.3 41.3 43.9 =35 s=6

- Do steps (a) and (b) as above.

3) Here are sorted commuting times on two routes for Carl (Jul-Sept)

Carl 1 23.7 24.3 25.5 26.8 28.0 28.4 29.3 30.1 30.6 33.3 =28, s=3

Carl 2 27.7 28.5 29.1 30.2 32.1 32.4 34.0 34.6 35.3 36.1 =32, s=3

- Do steps (a) and (b) as above.

4) Here are sorted commuting times on two routes for Donna (Oct-Dec)

Donna 1

10.1 13.5 20.9 21.7 23.7 22.8 23.0 23.5 24.0 24.8 24.9

25.0 25.8 26.0 26.1 26.5 26.6 26.7 27.1 28.0 28.4 28.5

28.9 29.0 29.3 29.8 30.1 30.0 30.2 33.2 32.4 33.3 33.4

33.8 33.8 34.0 35.3 36.6 39.5 39.9 =28, s=6

Donna 2

20.4 22.4 24.2 24.4 24.4 25.0 25.4 25.6 26.2 27.2 27.7

28.6 28.9 28.9 29.4 29.5 30.4 30.4 31.0 31.2 32.4 32.5

33.8 33.9 34.0 34.9 35.4 35.5 35.5 36.1 36.4 36.6 37.2

37.3 37.5 38.0 39.7 41.5 44.4 46.2 =32, s=6

- Do steps (a) and (b) as above.

Homework Assignment (due Friday, April 2)

1) For the four drivers discussed in the Practice Assignment problem, discuss what was different in each situation that contributed to the different p-value.

2) Recently, the class filled out the following survey question. Some of you asked if they were surprised that research showed "Absence makes the heart grow fonder". The rest of you were asked if it was surprising that research shows "Out of sight, out of mind".

(a) Conduct a test of significance to determine if the difference in responses is statistically significant. Comment on the validity of the procedure.

(b) This problem has the moral "Always state your hypotheses before you see the data, since once you see the data/hear the result, it's easy to say you knew what direction the result would be in". Do these data support that statement? (This is advice in general when deciding one-sided vs. two-sided alternatives, not just for this particular example.)

3) (p. 556) 7.62, 7.64 (p. 6.13) 8.42 and check technical assumptions

4) In an experiment, two individuals of different races and sexes visited car dealerships to request the best possible deal on a certain car. Both people visited each dealership and asked about the same car. Below are the agreed upon prices in dollars.

(a) Explain how you would use randomization to carry out the experiment?

(b) To see if there is a difference in price offered by the dealership to the two visitors, which test procedure (one sample means, two sample means, one sample proportion, two sample proportion) would you use? Explain.