2110 Ch. 1 Homework
A simple random sample of n=300 full-time employees is selected from a company list containing the names of all N=5,000 full-time employees in order to evaluate job satisfaction. a. Give an example of possible coverage error.
Only employees in a specific division of the company were sampled.
Suppose you read a website that says that an agronomist found a more efficient way to grow mangoes.
Outcomes of a designed experiment
d. Give an example of possible measurement error.
Ambiguous wording in questions asked on the questionnaire.
Suppose that each of the N=3,800 registered students lived in one of the 20 campus dormitories. Each dormitory accommodates 190 students. It is college policy to fully integrate students by gender and class designation in each dormitory. If the registrar is able to compile a listing of all students by dormitory, what type of sample should you take?
A cluster sample
c. Why is the sampling in (a) not simple random sampling?
A simple random sample gives every sample of a fixed size the same chance of selection as every other sample of that size, which is not true with this sampling method.
For a study that consists of personal interviews with participants (rather than mail or phone surveys), explain why simple random sampling might be less practical than some other sampling methods.
A simple random sample would be less practical for personal interviews because of travel costs (unless the interviewees are paid to go to central interviewing location).
If the frame available from the registrar's files is a listing of the names of all N=3,800 registered students compiled from eight separate alphabetical lists, based on the gender and class designation breakdowns shown in the class designation table, what type of sample should you take?
A stratified sample
A bookstore wants to determine the best placement for comedy novels.
Conduct an observational study
Suppose you read a story that claims 2 in 10 adults in a certain country smoke.
Distributed by a organization
b. Explain how you would carry out the sampling according to the method stated in (a).
Divide the size of the sample needed by the total number of invoices to find the percentage of the total invoices that need to be in the sample. Then, multiply this percentage by the number of invoices in each stratum to find the number of invoices to take from each stratum.
b. Give an example of possible nonresponse error.
No attempt is made to contact nonrespondents to urge them to complete the evaluation of job satisfaction.
The registrar of a college with a population of N=3,800 students is asked by the president to conduct a survey to measure satisfaction with the quality of life on campus. The accompanying table contains a breakdown of the 3,800 registered students, by gender and class designation. The registrar intends to take a probability sample of n=200 students and project the results from the sample to the entire population of full-time students. Complete parts (a) through (d). A. Suppose the frame available from the registrar's files is an alphabetical listing of the names of all N=3,800 registered students. Note that a simple random sample, a systematic sample, a stratified sample, or a cluster sample could be taken. What is the advantage of selecting a simple random sample?
It is one of the simplest to select since the population frame is the file of 3,800 names.
B. If the frame is the same as in (a), what is the advantage of selecting a systematic sample?
It is the easiest to select by hand from the registrar's file of 3,800 names.
The table to the right shows data found at a government census website, under a "Did You Know" panel.
Results of a survey that was conducted
Suppose you have a data set about whether each tree in a forest is afflicted by a certain disease and the tree species. (5 sources of data)
Results of an observational study
Suppose that 5,000 sales invoices are separated into four strata. Stratum 1 contains 50 invoices, stratum 2 contains 500 invoices, stratum 3 contains 1,000 invoices, and stratum 4 contains 3,450 invoices. A sample of 500 sales invoices is needed. Complete parts (a) through (c) below. a. What type of sampling should you do? Why?
Take a simple random sample of people from each stratum.
A poll indicated that 60% of small businesses surveyed plan to spend as much or more in 2012 than they did in 2011 on online marketing. Three in four (75%) small businesses have websites, with nearly one-third (31%) having mobile websites that are designed to be viewed on smartphones. Preferences for various kinds of online marketing were found to vary by gender: Male small business owners are more likely than female owners to rely on their company website for marketing (65% vs. 58%), whereas female small business owners are more likely than their male counterparts to employ social media to market their business (48% vs. 34%). These results are based on an online survey, conducted in November 2011, of 1,232 small business owners and/or employees responsible for Information Technology (IT). Identify potential concerns with coverage, nonresponse, sampling, and measurement errors.
The sample is a self-selecting sample of people who responded online, so there is an undefined nonresponse error. Since this is not a random sample, sampling error cannot be determined. The survey does not cover anyone without a computer or internet access, so there is a coverage error. Measurement error is possible if a respondent incorrectly answers one of the survey questions.
c. Give an example of possible sampling error.
The sample statistics obtained from the sample will not be equal to the parameters of interest in the population.
You want to select a random sample of n=1 from a population of three items (which are called A, B, and C). The rule for selecting the sample is as follows: Flip a coin; if it is heads, pick item A; if it is tails, flip the coin again; this time, if it is heads, choose B; if it is tails, choose C. Explain why this is a probability sample but not a simple random sample.
This is a probability sample because the probability of each outcome is known, but it is not a simple random sample because there is a higher probability of picking item A than there is of picking item B or of picking item C.
A population has four members (called A, B, C, and D). You would like to select a random sample of n=2, which you decide to do in the following way: Flip a coin; if it is heads, the sample will be items A and B; if it is tails, the sample will be items C and D. Although this is a random sample, it is not a simple random sample. Explain why.
This is not a simple random sample because not every sample of n=2 has the same chance of selection as every other sample of that size.
A survey indicates that the vast majority of college students own their own personal computers. What information would you want to know before you accepted the results of this survey?
Were the questions clear, accurate, unbiased, and valid? What sampling design was used? What was the sample size? What questions were asked? Who funded the survey? What was the population from which the sample was selected?
A recent survey indicated that 29% of Americans spent more money in recent months than they used to. But the majority (58%) still said that they enjoy saving money more than spending it. What additional information would you want to know about the survey before you accepted the results of the study?
What was the sample size? What do they consider "recent months"? What sampling design was used? What was the population from which the sample was selected? Were the questions phrased in a way that led to more "enjoy saving" responses? Who funded the survey?
