6.1 Exercises
1) Explain the difference between a parameter and a statistic.
2) Suppose you are trying to gather information about the ethnic background of students at an elementary school. Assume the school has 500 students and you are trying to minimize sampling error. Give examples of each of the following. In doing so, state the size of your sample and be clear about exactly how your sample is selected
a) A simple random sample
b) A cluster sample
c) A systematic sample
3) The Leominster City Council wants to know whether the 43,613 citizens of the city approved of a proposal to spend $1,000,000 to revitalize the downtown. The following study was conducted for this purpose. A survey was mailed to every 10th person on the list of registered voters in the city (it was mailed to 3000 people) asking about the proposal. Citizens were asked to complete the survey and return it to the Council by mail in a self-addressed, stamped envelope. 2700 people responded; of these, 75% supported the expenditure and 25% did not.
- The population for this study is
- all registered voters in the city
- all citizens of the city of Leominster
- the 3500 people who were sent a survey
- the 3100 people who returned a survey
- none of the above
- The “75%” reported above is a
- parameter
- population
- sample
- statistic
- none of the above
c) What is the sampling rate for this survey?
d) What is the response rate for this survey?
e) True or False? The results of this survey may be unreliable because registered voters may not be representative of all the citizens. Explain your answer.
f) True or False? The method of sampling in this survey could best be described as simple random sampling. Explain your answer.
g) What type of bias(es) may be present in this study. You may list more than one. Explain each choice.
4) A researcher wants to predict the outcome of the Frostbite Falls mayoral election. In order to do this, she mailed a survey to every tenth person on a list of all 40,980 registered voters in the city. One thousand fifty-six people returned the survey. 34% of respondents said they supported Snidely Whiplash; 48% said they supported Dudley DoRight; the remaining 18% were undecided.
- The population for this study is
- all mayoral-race voters in the city of Frostbite Falls
- all citizens of the city of Frostbite Falls
- the people who were sent a survey
- the people who returned a survey
- none of the above
b. What is the response rate?
c. What is the sampling rate?
- The “48%” reported above is a
- parameter
- population
- sample
- statistic
- none of the above
- This survey suffers primarily from
5) Sometimes a website or publication will advertise a poll asking its viewers to ‘call in’ or ‘click to respond’ to questions on a topic. In this case, we say that the sample is self-selected. What types of sample biases are likely in this type of survey? Explain.
6) A middle school is planning a long weekend class trip for their 8th graders and asked a few trusted students to help decide what location they should go to out of the following: New York City, Quebec or Washington DC. Each of the three students (Neave, Mario and Anya) decided to collect corresponding data from the 350 members of their 8th grade class and their responses were follows:
Neave: We should go to New York City. A couple of days last week, I checked the cafeteria during lunch and walked the halls during passing time, looking for 8th graders. To be fair, I found 30 boys and 30 girls, each from a variety of races/ethnicities. Of them, 25 preferred New York City, 15 preferred Quebec, 19 preferred Washington DC, and 1 didn’t care either way.
Mario: No, we should go to Quebec. I figured this out by taking a list of all 350 8th graders and rolled a standard die for each one; I decided to ask all those for whom I rolled a 6. In the end, 20 preferred Quebec, 10 preferred New York City, 7 preferred Washington DC, 1 didn’t care either way, and 2 people couldn’t be reached. So most want the Quebec trip.
Anya: Actually, most people want to go to Washington DC. I emailed everyone in the 8th grade class to find out what they wanted. Of those that responded, 25 wanted to go to Washington DC, 11 wanted to go to New York City, 11 wanted to go to Quebec, and 3 said they had no preference.
Based only on their arguments, where would you (as their advisor) recommend that the 8th grade trip take place, New York City, Quebec or Washington DC? Give your best argument to justify your decision.
A value calculated using all the data from the population.
A value calculated using data from a sample.
A subset of the population from which data are collected.
Selecting data points randomly from a population, like picking names out of a hat.
A method of selecting samples that breaks up the population into groups/clusters and randomly select a certain number from each group.
A method of selecting samples in which researchers choose members of the population at regular intervals.
The entire group that the collected data are intended to describe.
Sampling rate equals
(size of the sample) ÷ (size of the population).
This number is often multiplied by 100 to get a percent.
The number of responses divided by the number in the sample (multiply by 100 to get it as a percent).
A sample is biased if members of the population do not have equal likelihood of being in the sample.
Types of bias include:
Sampling bias: when the sample is not representative of the population
Voluntary response bias: the sampling bias that often occurs when the sample is volunteers
Self-interest bias: bias that can occur when the researchers and/or participants have an interest in the outcome
Response bias: when the responder gives inaccurate responses for any reason
Perceived lack of anonymity: when the responder fears giving an honest answer might negatively affect them
Loaded question bias: when the question wording influences the responses
Non-response bias: when people refusing to participate in the study can influence the validity of the outcome
