Workshop Statistics: Discovery with Data and Fathom

Topic 12: Sampling

Activity 12-1: States and SATs

(a) yes
(b) No, we didn't collect data from all students at the school. To decide if you have a reasonable estimate, you have to decide if you think the travel behavior of your class is representative of that of the rest of the school.
 

Activity 12-2: Elvis Presley and Alf Landon

(a) (b) No, it is probably not an accurate reflection of beliefs of all Americans.  People who choose to call in (take the time, spend the money) probably feel differently about the issue than other Americans. Was also only a Dallas radio station, may not be broadcast nationwide, and opinion of southerns may differ since Elvis was from the south..

(c)

(d) Their prediction was in error because their sampling technique was biased.  By sampling people who owned vehicles, they were looking at people with some money. In 1936, people with money tended to vote Republican (conservative).  Those without money tended to vote Democratic (social change). Thus, the pollsters heard mostly from Republicans, but then lots of Democrats turned out on election day.
 

Activity 12-3: Sampling Senators

(a) (b) Answers will vary from student to student.
(c) sample
(d)-(h) Answers will vary from student to student.
(i) Answers will vary from class to class.
(j) This sampling method is biased because people will tend to choose senators from their own state, as well as senators who have served for many years. The latter has a direct impact on our measurement of "years of service."
(k) No, this would not be likely to produce more representative samples.  Taking more data doesn't make up for the fact that the sampling is biased.
 

Activity 12-4: Sampling Senators (cont.)

Students' answers to (a)-(h) may differ since the data is chosen randomly.  These are meant to be sample answers using row 1 of the random number table.
(a)
ID #
Name
Party
Years
Your state?
17
Byrd
Dem
40
no
13
Brownback
Rep
2
no
92
Stevens
Rep
31
no
78
Reid
Dem
12
no
38
Frist
Rep
4
no
(b) no
(c)
Years of service
Sample Mean
Min
Max
17.8
2
40

(d) The proportional breakdown is Democrats - .4, Republicans - .6.  This is not equal to the proporitonal breakdown of the entire population of Senators, though it is close.  The mean years of service of the sample is higher than that of the population.
(e) This does not mean that this sampling is biased, we may have just gotten unlucky.
(f)-(h) Answers will vary from class to class.
(i)

Activity 12-5: Sampling Senators (cont.)

(a)-(f) Answers will vary from student to student.
(g) The distribution using a sample size of 20 should have less variability.
(h) A sample size of 20 is more likely to have a mean closer to the true mean of the population.

Activity 12-6: Sampling Senators (cont.)

Students' answers may differ since the data is chosen randomly.  These are meant to be sample answers.
(e)

        The distribution is roughly symmetric, with a center of spread around .45.  There is a high level of granularity.

(f)

(g) Yes, both distributions seem to be centered at the population value of .45.  The mean of the first distribution is .43 and the mean of the second distribution is .46.  Both of these are pretty close to .45, so the sample proportion is unbiased.
(h) Yes, these distributions seem to have similar variability.
(i) Nothing significant changed when we sampled from the larger population.