Vocab
A sample that consists of individuals from the population who are easy to reach.
Convenience Sample
Valid Statistical Question?
What proportion of New Jersey residents would choose vanilla as their favorite ice cream flavor?
Valid - whether they choose vanilla or a different flavor.
Give another name for a voluntary response sample.
Self Selected Sample
True/False: Undercoverage is caused by the individuals in the sample.
False. Undercoverage occurs when some members of the population are less likely to be chosen or cannot be chosen for the sample.
True/False: In an SRS, individuals are selected with replacement.
False. In an SRS, individuals are selected without replacement.
What are the four steps of the statistical problem solving process:
Ask questions, collect data, analyze data, interpret results
A large retailer prepares its customers' credit card bills using a machine that folds, stuffs them in envelopes, and seals them. Are the envelopes completely sealed? Inspectors choose 40 envelopes at random from the 1000 stuffed each hour for visual inspection. Identify the population and sample in this setting.
Population: 1000 stuffed envelopes
Sample: 40 that are inspected
State a benefit of using a random sample rather than a convenience or voluntary response sample.
Using a random sample helps to avoid bias.
List three factors that can lead to response bias.
Response bias can be a result of characteristics of the interviewer, wording of the question, and lack of anonymity, among other factors.
The management company of a local mall with 21 stores plans to survey 3 of the stores to determine the hours they would like to stay open during the holiday season. Describe how to select an SRS of 3 stores using slips of paper.
Give each store a distinct integer label from 1 to 21. Number 21 identically sized slips of paper from 1 to 21. Put these slips of paper into a hat and mix well. Select 3 slips of paper and survey the 3 stores that are labeled with the numbers selected
What is a census?
Is a data collection method for which data is collected from every individual in the population.
Aspirin prevents blood from clotting and so helps prevent strokes. A study asked if adding another drug named dipyridamole would help. Patients who had already had a stroke were randomly assigned to receive either aspirin only, dipyridamole only, both, or a placebo, and were followed for 2 years. Is this an observational study or an experiment?
Experiment. Treatments were imposed.
Many websites include customer reviews of products, restaurants, hotels, and so on. The manager of a hotel was upset to see that 26% of reviewers on a travel website gave the hotel a “1 star” rating—the lowest possible rating. Explain why this sampling method is biased. Is 26% likely greater than or less than the percentage of all the hotel’s customers who would give the hotel 1 star?
It is likely that the customers who chose to leave reviews feel strongly about the hotel, often due to a bad experience. Customers who had an average or good experience are less likely to leave a review. The sample is likely greater than the percentage of all customers.
The manager of a home improvement store wants to know the percent of residents in his town who mow their own lawns. To find out, he selects a random sample of 100 customers and asks each one if he or she mows the lawn. Explain how undercoverage might lead to bias in this study. Is the percent from the sample likely greater than or less than the percent for all town residents?
The residents in the town who are not customers of the home improvement store can’t be part of the sample. If residents are customers of the home improvement store, they are probably more “hands on” around their homes and are more likely to mow their own lawn than those residents who are not customers. Therefore, the percent from the sample is likely greater than the percent for all town residents.
The management company of a local mall with 21 stores plans to survey 3 of the stores to determine the hours they would like to stay open during the holiday season. Describe how to select an SRS of 3 stores using a random number generator.
Give each store a distinct integer label from 1 to 21. Using a random number generator, generate 3 integers from 1 to 21, ignoring repeated integers. Survey the 3 stores that are labeled with the generated integers.
_____________ is the fact that different ransom samples of the same size from the same population produce different estimates.
Sampling Variability
In an effort to reduce health care costs, General Motors sponsored a study to help employees stop smoking. In the study, 439 volunteer subjects were randomly assigned to receive up to $750 for quitting for a year, while the other 439 volunteer subjects were simply encouraged to use traditional methods to stop smoking. After one year, people who had the financial incentive were 3 times more likely to have quit smoking. What is the statistical question?
Will employees who are offered a financial incentive be more likely to quit smoking?
Newspaper readers sometimes write letters to the editor, hoping that their opinions will be published in the paper. The edi-torial staff at a local newspaper keeps track of the content of each letter that is submitted. After a controversial decision made by the mayor, 90% of the letters to the editor expressed opposition to the mayor’s action. Explain why this sampling method is biased. Is 90% likely greater than or less than the percentage of all city residents who oppose the mayor’s action?
It is likely that those newspaper readers who chose to write letters feel strongly about the mayor’s decision, often in opposition. Readers who don’t have a strong opinion are less likely to write a letter. It is likely greater than the percentage of all city residents who oppose.
Marcos asked a random sample of 50 mall shoppers for their weight. Twenty-five of the shoppers were asked directly and the other 25 were asked anonymously by means of a “secret ballot.” The mean reported weight was 13 pounds heavier for the anonymous group. Explain why the two means were so different.
The mall shoppers who were asked directly may be embarrassed or ashamed of their weight and then lie by giving a weight less than the true weight. Mall shoppers given an anonymous survey are more likely to be honest
A college administrator wants to estimate the mean distance that students at a large community college live from campus. To find out, she obtains a list of all students from the registrar’s database. Describe how you could select an SRS of 100 students.
Give each student a distinct integer label from 1 to the total number of students, N. Using a random number generator, generate 100 integers from 1 to N, ignoring repeated integers. Survey the 100 students who are labeled with the generated integers.
How does nonresponse differ from voluntary response?
Nonresponse occurs when an individual chosen for the sample cannot be contacted or refuses to participate. This differs from voluntary where the individual choose to be in the sample by responding to an invitation.
In an effort to reduce health care costs, General Motors sponsored a study to help employees stop smoking. In the study, 439 volunteer subjects were randomly assigned to receive up to $750 for quitting for a year, while the other 439 volunteer subjects were simply encouraged to use traditional methods to stop smoking. After one year, people who had the financial incentive were 3 times more likely to have quit smoking. What is the population, sample, and is it an experiment or not?
Population: All of the employees at General Motors who smoke. Sample: The 878 employees who volunteered. Experiment.
You have probably seen the mall interviewer, clipboard in hand, approaching people passing by. To estimate the mean amount of money that city residents plan to spend on holiday gifts, the interviewer surveys 100 mall shoppers. Explain how to avoid bias?
The interviewer could obtain a list of all city residents and randomly select a sample from this list to be surveyed.
A random sample of 1200 adult Americans is selected, and each person is asked the following question:
In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance?
Explain how the wording of the question could result in bias.
By making note of the huge national deficit, Americans might become more concerned about our government spending additional money on social programs. The percent from the sample who say yes is likely less than the true percent of adult Americans who favor spending money to establish a national system of health insurance.
A college administrator wants to estimate the mean distance that students at a large community college live from campus. To find out, she obtains a list of all students from the registrar’s database. Will your sample result be exactly the same as the true population mean? Explain your answer.
No; because different random samples will produce different means, it is unlikely that this sample provided a mean that is exactly correct.