Homework 4 Solution

Chapter 12, #12:
For each, indicate what kind of sampling strategy is involved and what (if any) biased might result.
a) Run  a poll on the local TV news, asking people to dial one of two phone numbers to indicate whether they favor or oppose the plan.

People with strong opinions for or against are more likely to call-in, which would lead to a biased sample.  (The responders are different from the population.)

b) Hold a PTA meeting at each of the 20 elementary schools and tally the opinions expressed by those who attend the meetings.

Once again, there's no guarantee that people who attend the meetings are representative of the population as a  whole. People who attend meetings are probably, again, people who hold strong opinions but also people who have the time and money to get to the meeting.  Parents who work in the evening, for example, will be excluded from this survey.

c) This uses a random sampling scheme.  This is a stratified random sample:  each school represents a stratum, and  a random sample of size 1 is taken from each stratum. This should be unbiased, if done well.

d) This is a systematic sample, and should have no bias as long as there is no relationship between the order in the district's enrollment records and  the variables of interest.  If the list were organized, for example, in terms of the students' grades, this might cause a bias.

Chapter 12, #18
.....Overall it appears my car gets 28.8 miles per gallon.
a) What statistic have I calculated?
This is the average mileage of the  last six fill-ups.
b) What is the parameter I'm trying to estimate?
Mean mileage of ALL fill-ups.
c) How might my results be biased?
This is not a random sampel of all fill-ups. If the author had just driven across country, the last 6 fill-ups would have been all highway mileage, for example, and might be higher numbers than if it included "city" driving.
d) When the EPA predicts fuel economy, what parameter is it trying to estimate?
A more complicated one:  the mean mileage of all cars of a particular type, over the lifetime (?) of the car.