1. (10 points total)
The magazine BusinessWeek ran an online poll on their website and asked the readers the
following question: “Do you think Google is too powerful?” Poll participants were offered three buttons as response: “yes”, “no”, or “not sure”.
In all 1336 (35.9%) said “yes”, 2051 (55.1%) said “no” and 335 (9.0%) said “not sure”
1a. (5 points)
What is the sample size for this poll? Answer: 3722
Sample size = 1336 + 2051 + 335 = 3722
1b. (2 points).
The magazine BusinessWeek was careful to note that: “These are surveys, not scientific polls”. In 1-2 sentences, explain what is meant by this statement.
Answer:
A scientific poll would have involved the selection of study participants by some mechanism of chance. Most likely, BusinessWeek did not use a probability sampling plan to obtain its sample. The use of a probability sampling plan means that the selection of an individual for inclusion (or exclusion) is out of the hands of the investigator and is instead determined by chance.
1c. (3 points).
Do you think this poll might have given unreliable information? In 1-2 sentences, explain your reasoning.
2. (10 points total)
Some highway planners decided to change a two-way main street in West Lafayette, Indiana into a one-way street. The Lafayette Journal and Courier took a one-day poll by inviting readers to call a telephone number and record their comments. The next day, the paper reported the following:
Journal and Courier readers overwhelmingly prefer two-way traffic flow in West Lafayette’s Village area to one-way streets. By nearly a 7-1 margin, callers to the newspaper’s Express Yourself opinion line on Wednesday complained about the one-way streets that have been in place since May. Of the 98 comments received, all but 14 said “no” to one-way.
2a. (5 points)
What population do you think the newspaper wants information about? Answer:
It is likely that the population of interest to the newspaper is: persons who drive through, or live near, or who frequent the area of West Lafayette Village.
2b. (5 points).
In your opinion, is the proportion of this population who favor one-way streets almost certainly larger or smaller than the proportion 14/98 in the sample? In 1-2 sentences, explain your reasoning.
Answer:
In my opinion, the proportion of this population who actually favor one-way streets is likely to be larger than 14/98 for the following reason. People are more likely to speak up in complaint (“I don’t like the change to a one way street”) than to speak up in acquiescence.
3. (10 points total)
The University of Massachusetts/Amherst wants to gather student opinions about parking for students on campus. It isn’t possible to contact all the students. A sampling must be done instead.
3a. (5 points)
Design your own bad sample. Give an example of a way to choose a sample of students that is poor practice because it depends on voluntary response. In 1-2 sentences, explain why you believe this is poor practice.
Answer:
Obtain study participants by invitation offered to students waiting in line to obtain their first parking permit.
This would be a poor approach because, often, it is difficult to obtain a first parking permit at a University because the availability is limited. Sampling individuals who do not yet have their first permit is likely to be an oversampling of individuals who are unhappy with the campus’s policy on parking for students.
3b. (5 points)
Design your own bad sample. Give an example of a bad way to choose a sample of students that does NOT use voluntary response. In 1-2 sentences, explain why you believe this is also poor practice.
Answer:
Obtain study participants by making study participation a requirement for graduation. This might also be a poor approach for a variety of reasons. One is that it might oversample
4. (10 points total)
The San Francisco Bay Times reported on a poll in New Zealand that found that New Zealanders opposed the nation’s new gay-inclusive civil-unions law by a 3-1 ratio. This poll was a call-in poll that cost $1 to participate in. The San Francisco Bay Times article also reported that a scientific polling organization found that New Zealanders favor the law by a margin of 56.4% to 39.3%.
In 1-3 sentences, explain why the two polls can give such widely differing results and which poll is likely to be more reliable.
Answer:
Two polls that survey responses to the same question will give different answers if the subjects selected for participation differ and if the nature of this difference is related to the responses. Important Reminder – It is not enough that there is an oversampling of some sub-population. The oversampling will only bias the study outcome if the nature of the oversampling is related to the survey responses.
The scientific poll is likely to have been more reliable as, presumably, there was less potential for selection bias in its conduct.
The scientific poll is likely to be more reliable if the “call-in poll”, with its $1 participation cost, oversamples individuals with sufficiently strong negative views of gay-inclusive civil unions that they choose to spend $1 to have their voice known.
5. (10 points total)
Suppose the University of Massachusetts/Amherst has 30,000 undergraduate students and 10,000 graduate students. A survey of student opinion concerning health care benefits for domestic partners of students selects 300 of the 30,000 undergraduate students at random and then separately selects 100 of the10,000 graduate students at random. The 400 students chosen comprise the study sample.
5a. (5 points)
Does this sampling method give each student an equal chance of being selected? In 1-2 sentences, explain your reasoning.
Answer: Yes.
Yes, because 30,000/300 = 100 and 10,000/100=100. That is, every undergraduate student has a 1 in 100 chance of being selected and every graduate student has a 1 in 100 chance of being selected.
5b. (5 points)
In 1-2 sentences, explain why this sampling method is not simple random sampling. Answer:
This sampling method is not simple random sampling because it is stratified random sampling. In simple random sampling, the two groups of students, undergraduates and graduates, would not have been sampled separately. Instead, the sampling method used here was separate random sampling of the two groups of students.
6. (10 points total) 6a. (2 points)
TRUE or FALSE - TRUE.
In a table of random digits, each pair of digits has a 1 in 100 chance of being the pair 33.
6b. (2 points)
TRUE or FALSE - FALSE.
In a table of random digits, there are exactly four 4’s in each row of 40 digits.
6c. (2 points)
TRUE or FALSE - FALSE.
In a table of random digits, the digits 99999 can never appear as a group because this pattern is not random.
6d. (2 points)
Voter registration records show that 15.4% of all voters in Philadelphia are registered as Republicans. However, a radio talk show host in Philadelphia found that of 20 local residents who called the show recently, 60% were registered Republicans.
Choose ONE: Complete the sentence with either “parameter” or “statistic”
The bold face number 15.4% is a __parameter____________.
Choose ONE: Complete the sentence with either “parameter” or “statistic”
The bold face number 60% is a __statistic____________.
6e. (2 points)
A national polling organization uses a random digit dialing device to dial residential landline phone numbers in the United States. Of the first 100 numbers dialed, 32 are unlisted numbers. This is not surprising, because 34% of all residential phones in the United States, including cell-phone-only and many unlisted landline phone households, are not covered by current landline phone number sampling methods.
Choose ONE: Complete the sentence with either “parameter” or “statistic”.
The bold face number 32 is a __statistic_____________.
7. (10 points total)
The Denver Police Department wants to know if Hispanic residents of Denver believe that the police use racial profiling when making traffic stops. A sociologist prepares several questions about predominantly Hispanic neighborhoods and sends a uniformed Hispanic police officer to each address to ask the questions of an adult living there.
7a. (2 points)
What is the population?
Answer:
The population is comprised of all Hispanic residents of Denver.
7b. (3 points)
What is the sample? Answer:
The sample is comprised of the adults who actually provided answers to the police officer.
7c. (5 points)
In 1-2 sentences, explain why the results are likely to be biased even thought the sample is a simple random sample.
Answer:
The responses could be biased if the survey responses are an oversampling of any of the following, at least: (1) non-English speaking Hispanics if, compared to English speaking
8. (10 points total)
8a. (2 points) Fill in the blank. Choose the ONE BEST answer.
A simple random sample is a sample chosen in such a way that every unit in the population has a(n) ________ chance of being selected into the sample.
__A. equal __B. unequal __C. known
8b. (2 points) Multiple Choice. Choose ONE.
In a random digit table, approximately what percent of the digits are 9 or 2?
__A. 20% __B. 10% __C. unknown
8c. (2 points). TRUE or FALSE.
Sampling with replacement from a very large population gives virtually the same result as sampling without replacement. TRUE
8d. (2 points) Complete the sentence by choosing the ONE BEST last word
In a stratified random sample, the selection probability for each element within a stratum is __. __A. equal
__B. unequal __C. known
8e. (2 points) Fill in the blank. Choose the ONE BEST answer.
A probability sample is a sample chosen in such a way that each possible sample has a (n) _____ chance of being selected.
__A. equal __B. unequal __C. known __D. unknown
9. (10 points total)
An epidemiologist wishes to estimate the average length of hospitalization for cancer patients discharged from the hospitals in her region of the country. There are 500 hospitals with the number of beds ranging from 30 to 1200 in the region.
9a. (5 points).
In 1-2 sentences, discuss what difficulties the researcher might encounter in drawing a simple random sample.
Answer:
There are lots of challenges here! These might include, but are not limited to: (1) Each hospital might have its own human subjects protection protocol and procedures that have to be followed before a sample can be drawn. This would make the project perhaps
unreasonably time consuming; (2) There may be differences in the type of hospital that are related to both the likelihood of participation in sampling and in the length of stay
outcomes. For example, some hospitals might be urban, others rural. Some might be teaching, others non-teaching. If these selection differences occur, then the study findings might be biased.
9b. (5 points).
In 1-2 sentences, offer suggestions for obtaining a representative sample. Answer:
One approach might be the following. Step 1 – Partition all the hospitals into groups (“bins”) of “like” hospitals, where the groups are defined by the characteristics thought to be related to length of stay (rural/urban, teaching/non-teaching); e.g. – one bin might contain the 15 hospitals that are rural and with 100 beds or less. Step 2 – Request consent from every hospital. Step 3 – Create a sampling frame that is a listing of the consenting hospitals only. Step 4 – From each “bin” of consenting hospitals, query the hospital billing data base (billing data bases, not surprisingly, tend to be of high quality). In this query,
10. (10 points total)
A city planner is interested in estimating the proportion of passenger cars that have only one occupant during rush hours.
10a. (2 points).
What is the population of interest? Answer:
The population is comprised of all passenger cars on the city’s road during rush hours.
10b. (2 points).
Suggest a sampling frame that the city planner might use to obtain a sample.
Answer:
Oh my goodness, this is a challenge! A possible sampling frame could be constructed from
10c. (3 points).
In 1-2 sentences, advise the city planner on how to actually use the sampling frame to obtain a sample?
Answer:
10d. (3 points).
In your opinion, is the sampling frame you suggested in #10b representative of the population you identified in #10a? In 1-2 sentences, explain your reasoning.
