﻿ Data Sampling: Representing Many by Sampling Some

# Data Sampling

Note: Since question 1 remains the same throughout the tool, the answer is provided once below. To access the answers to questions 2 and 3, which vary by survey, use the colored arrows further below to navigate the page.

Question 1: How do the results of the three samples you chose (in color) compare to the representative sample and the entire population (in black)? What conclusions can you draw about how to set up a representative sample?

In general, results from larger samples have a better chance of approaching the results from the entire population than do smaller samples. Similarly, results from representative samples have a better chance of approaching the results from the entire population than do samples that favor one segment of the population (examples include just men, just individuals older than 55, and so on).  It is possible to have results from a smaller sample that were closer to the population as a whole than a larger sample. Although you have a better chance of getting better results with a larger and/or representative sample, when it comes to chance, a higher likelihood doesn't mean that the outcome is certain. There's always some chance that the smaller sample will provide results that better reflect the population as a whole. Generally, though, when the stakes are high, it's worth the time and expense to make sure you have a representative sample that is large enough to give you confidence in the results.

#### SKATE PARK

A: Should the town use public funds to build a skate park?

Question 2: Should this survey be limited to individuals 18 and older? Brainstorm arguments for and against this matter.

Although individuals under 18 are unlikely to be taxpayers and thus have no obligation to fund the park, they will presumably be the park’s primary users, so their opinion might be considered.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

Students may have opinions on both sides of the issue. The skate park has the overwhelming support of the presumed users of the facility, those ages 11–17, and significant support among those ages 18–35. So the skate park would provide a valuable recreational opportunity for the younger citizens in the town. However, most registered voters do not favor using public funds to build the park, and going ahead with the plan might cause problems for the mayor in the next election.

B: If a skate park is built, should it charge a \$5 admission fee to cover maintenance costs?

Question 2: Hypothesize how the survey results might change if another amount were used for the proposed admission fee. Which citizens might be in favor of a higher amount or a lower amount, and why? What steps might you take next to determine a fair fee?

If the admission charge were set higher, presumably the age groups more likely to use the park would be less likely to accept the higher fee. Participants in older age bands might be in favor of a higher fee since it might reduce the park’s tax burden.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

Again, students may take positions on either side of the issue. Citizens in the two younger age categories support the construction of the park, but oppose a \$5 user fee. Citizens in the two older age categories oppose the construction of the park, but support the user fee. One possible recommendation to the mayor would be to support the construction of the park but insist on the user fee. That way, those who favor the park will see it built while those opposed to the park will be somewhat placated by the fact that a user fee will help cover costs.

C: If the park is built, should it also add a pro shop to sell skater gear to help subsidize the cost?

Question 2: Should this question be asked to all citizens of Statsboro or just potential users of the park?

Asking all citizens would be fair in that all taxpayers would pay for the construction of the pro shop. However, asking only potential users of the park would be preferable if the intent were to project a revenue stream from the shop.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

In this case, it may be better to look at the total number of people involved rather than percentages, considering the small size of the town. Less than half the people in the town favor the construction of the park. It is reasonable to assume that only some of the people who favor the park will actually use it and that only some of the people who use the park will want or need to purchase skateboard gear. Based on these numbers, it is unlikely that the shop would be successful, so the mayor should probably not support the shop.

D: Would you be willing to purchase warranty protection or a maintenance package for items bought from the pro shop?

Question 2: If the question were adjusted to ensure respondents knew the benefits of warranty protection, how might this affect the results?

It is possible that younger survey participants, those most likely to use the pro shop, have little or no experience with warranties and might not understand the meaning of the term. Their survey responses might not reflect their true opinion on the matter. Note: If appropriate for your class, this presents an opportunity to explore another practical use of statistics and probability, i.e., the expected value of the repair (average repair cost multiplied by the probability of needing a repair) versus the cost of a warranty.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

Since the shop does not appear to be economically viable, this is somewhat of a moot point. However, if the class favors the shop, it might want to recommend to the mayor that fairly priced warranty policies would benefit the town by providing extra revenue and provide protection to the shop’s customers.

#### PET INSURANCE

A: Should public funds be used to provide free pet insurance to people adopting pets to encourage more people to do so?

Question 2: What information might make this question more meaningful to the people being surveyed and more useful to the mayor?

It is not known whether or not offering free pet insurance would actually increase the number of adoptions.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

More than half of the town’s citizens favor the initiative and pet owners favor it by a wide margin. Pet owners probably care more about the initiative than those who don’t own pets, so the mayor would improve her standing with this important voter bloc by supporting this idea.

B: Should the shelter sell pet insurance at cost (meaning, with no profit and no loss) to individuals adopting pets?

Question 2: Do you hypothesize that more people will say yes to this question than the one about providing free pet insurance for those who adopt animals? Why or why not?

Presumably, people in favor of the first question would not be against this question. Some of the people opposed to the first question might be in favor of this one since there is no added tax burden.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

This idea appears to have the solid support of the public, so the mayor should support it.

C: Should the shelter offer to sell pet insurance at cost to any citizen, whether or not they adopted from the shelter?

Question 2: Do you hypothesize that certain population segments would feel more strongly about this question (pro or con) than others? Why or why not?

The first question is aimed at finding out whether or not the public would support an initiative that might increase the number of adoptions. This question is about an initiative that would benefit all pet owners, whether they were looking to adopt another pet or not. Presumably, pet owners would favor this while other segments of the population might be indifferent since there is no added cost to the town.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

The initiative has substantial support in the community so implementing the idea would be popular. However, the class should also consider that this function (i.e., selling pet insurance to the public) is not typical for town governments, so the mayor needs to carefully consider whether or not she wants to expand government operations into this area.

D: Should the pet insurance be sold for a profit (a financial gain) to help the shelter cover its operating costs?

Question 2: Should this question be asked of the general population or a segment of the population? Why or why not?

Asking potential users of the service would be more useful for projecting revenue streams.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

Although the number of potential customers is fairly small, there is no additional cost to the city and it is unlikely that anyone will vote against the mayor if she supports it. As noted in the answer to Question 2 for Survey C, this does represent a new function for the town government, so she should carefully consider whether or not this would be in the best interest of the people. Note: If appropriate for your class, this presents an opportunity to explore another practical use of statistics and probability, i.e., the expected value of the repair (average repair cost multiplied by the probability of needing a repair) versus the cost of insurance.

#### SUMMER CONCERT SERIES

A: Should the town hold a summer concert series?

Question 2: Do you think this question is specific enough to provide useful information to the mayor? If not, how could it be improved?

Some possible elaboration could include the number of concerts planned, the cost to the town, the types of music planned, etc.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

The idea appears to have wide support among different segments of the population. The mayor should move forward with the planning process

B: Would you be willing to pay a \$10 admission fee to attend a summer concert?

Question 2: What do you think the results would have been if the question had been "do you think a \$10 fee should be charged" rather than "would you be willing to pay a \$10 admission fee"? How are these questions different?

Asking “do you think a \$10 fee should be charged” is about how to fund the series. Asking “would you be willing to pay a \$10 admission fee” is more useful for projecting revenue.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

The idea seems to have the wide support of the public. The mayor should back this idea.

C: Would you support a law that would require the summer concerts to end no later than 9 p.m.?

Question 2: Do you think the results for this question would be different if the closing time were different? How might you break this survey question into two to collect more precise information?

Offering a range of end times might provide a better gauge of citizen sentiment. Some people might find 10 p.m. to be reasonable but 11 p.m. too late.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

Most groups seem to be opposed to a 9 p.m. cutoff for the concerts, although those aged 55+ seem to strongly support it. The mayor should seek additional information via a survey to see if a somewhat later cutoff time (say 10 p.m.) would be supported.

D: Should the town offer free parking to draw attendance?

Question 2: If you were asked this question, what additional information might you want to know before answering?

Participants might want to know if there is an existing problem with parking, if there would be an increased cost to construct and staff parking lots, and how many people would travel by car to the concerts.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

The citizens widely support this initiative and the mayor should be in favor of it, too.

#### PUBLIC COMPUTER CENTER

A: Should town funds be used to set up a computer center at the library to ensure that all residents have access to the Internet?

Question 2: Do you think that information about the total cost of the construction should be included with this question?

Without cost information, how can a respondent give an informed answer?

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

The majority of the town supports the idea although those of voting age are almost evenly divided. Before backing the idea, the mayor needs to determine what the costs of the project will be. If total costs are fairly low, it is unlikely that she will face voter backlash if she supports the idea.

B: Would you be willing to pay a yearly \$5 tax surcharge (an amount in addition to the town taxes you already pay) to cover the costs of building the computer center?

Question 2: Do you think that it’s fair to ask this question to all citizens whether they are current taxpayers or not?

Opinions will vary. On one side of the issue, taxpayers might not like having nontaxpayers be considered concerning an increase in their tax obligation. Others will argue that this should be a decision made by the entire community.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

This proposal is unpopular with all segments of the population. The mayor should avoid it!

C: Should there be a time limit associated with computer use at the library to ensure that everyone gets a turn on the Internet?

Question 2: Based on these survey results, what follow-up questions might you ask the residents of Statsboro to determine the best usage policy?

It might be useful to find out how many people intend to use the hotspot to see if there is an allocation issue.

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

This idea is widely supported by the citizens. The mayor should support this measure to ensure fairness for all.

D: Should the town offer to sell local business advertising that users of the computer center must view before connecting to the Internet?

Question 2: What are the potential issues the town might face if it sold advertising that users must view?

Does the advertising on the town’s site imply endorsement of the product? Should standards for appropriateness be established? Who will review the ads for appropriateness?

Question 3: Based on your analysis of the survey, what do you recommend the mayor do next?

This idea does not appear to be supported by the population, so the mayor should avoid it.