Systematic sampling
Identify distributions, Part I. Four plots are presented below. The plot at the top is a distribution for a population. The mean is 10 and the standard deviation is 3. Also shown below is a distribution of (1) a single random sample of 100 values from this population, (2) a distribution of 100 sample means from random samples with size 5, and (3) a distribution of 100 sample means from random samples with size 25. Determine which plot (A, B, or C) is which and explain your reasoning.
Simple Random Sampling
MAT220_33_Statistics I_2020_21_TERM1
- Which sampling method does not require a frame? Choose the correct answer below.
A. Stratified
B. Simple random
C. Systematic
D. Cluster
E. All of the above sampling methods require a frame
- Determine whether the following statement is true or false. Explain. When obtaining a stratified sample, the number of individuals included within each stratum must be equal. Choose the correct answer below.
A. False. A stratified sample is constructed by successively selecting a stratum at random and then selecting a random individual from within that stratum. With this process, it is unlikely that all strata will be sampled from the same number of times. B. False. When taking a stratified sample, a simple random sample is drawn from one stratum at random. All other strata will not be included in the sample.
C. False. Within stratified samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population.
D. True. Sampling the same number of people from each stratum will result in a sample that is representative of the population at a lower cost than a simple random sample.
- To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at selects every th that comes off the assembly line starting with the until she obtains a sample of . General Electric 15 refrigerator seventh 30 refrigerators What type of sampling is used?
A. Systematic
B. Cluster
C. Simple random
D. Stratified
E. Convenience
- To determine customer opinion of their , randomly selects during a certain week and surveys all . safety features Toyota 120 dealerships customers visiting the dealerships What type of sampling is used?
A. Convenience
B. Cluster
C. Systematic
D. Stratified
E. Simple random
- IBM wants to administer a satisfaction survey to its current customers. Using their customer database, the company.
What type of sampling is used?
- Convenience
- Simple random
- Stratified
- Cluster
- Systematic
- A club wants to sponsor a panel discussion on an upcoming election. The club wants to have four of its members lead the panel discussion. To be fair, however, the panel should consist of two members of each party. Below is a list of members in each party. Obtain a stratified sample of two people from party 1 and two from party 2. Party 1 Party 2 Bolden Nolan Cooper Ochs Carter Pawlak Engler Rice Haydra Tate Keating Thomas Lukens Wright May Weber
Which of the following is a possible list of club members to lead the panel discussion?
A. Pawlak, Nolan, Wright, Cooper
B. Pawlak, Nolan, Wright, Carter
C. Cooper, Keating, May, Pawlak
D. Cooper, Keating, May, Rice
E. Pawlak, Nolan, Cooper, Keating
- The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all employees at the company and wants to conduct a systematic sample of size . 7707 70
(a) What is k? k =
(b) Determine the individuals who will be administered the survey. Randomly select a number from 1 to k. Suppose that we randomly select . Starting with the first individual selected, the individuals in the survey will be , , …, .
- For a poll of voters regarding a referendum calling for a national , design a sampling method to obtain the individuals in the sample. Be sure to support your choice. renewable energy incentive Which sampling method would most likely be used in a poll of voters regarding a referendum calling for a national renewable energy incentive?
A. Use stratified random sampling. Since this is a national issue, different geographical locations are likely to have similar views.
B. Use simple random sampling. Simple random sampling is always the best sampling method to choose regardless of the survey conducted.
C. Use convenience sampling. A large number of voters is needed to accurately reflect the nation’s voters; so, a quick way to collect information is needed.
D. Use cluster sampling. Each geographical region can be treated as a mini-population because voting results are independent of region.
E. Use systematic random sampling. By varying the k-value, a sampling of the whole nation can be selected to achieve the needed accuracy.
- What is a closed question? What is an open question? Discuss the advantages and disadvantages of each type of question. What is a closed question? What is an open question?
A. A closed question always has yes or no answers, whereas an open question is a free-response question.
B. A closed question has many correct answers, whereas an open question has only one correct answer.
C. A closed question has fixed choices for answers, whereas an open question is a free-response question.
D. A closed question is a free-response question, whereas an open question has fixed choices for answers. Discuss the advantages and disadvantages of each type of question.
A. Closed questions are harder to analyze, because they limit the responses. Open questions allow respondents to state exactly how they feel, but are easier to analyze due to the variety of answers.
B. Closed questions allow respondents to state exactly how they feel, but are harder to analyze due to the variety of answers and possible misinterpretation of answers. Open questions are easier to analyze, but limit the responses.
C. Closed questions are easier to analyze, but limit the responses. Open questions allow respondents to state exactly how they feel, but are harder to analyze due to the variety of answers and possible misinterpretation of answers.
D. Closed questions are easier to analyze, because they usually gather more accurate data. Open questions limit the responses, but are harder to analyze since not every viewpoint will be covered
- The following survey has bias.
(a) Determine the type of bias.
(b) Suggest a remedy. Suppose a survey regarding the sleeping habits of students is being conducted. From a list of registered students, a researcher obtains a simple random sample of 150 students. One survey question is “How much sleep do you get?”
(a) What is the type of bias? Nonresponse bias Response bias Sampling bias
(b) What is a possible remedy? Use systematic random sampling. Reword the question. Conduct face-to-face or telephone interviews
- A poll is being conducted to obtain a sample of the population of an entire country. What is the frame for this type of sampling? Who would be excluded from the survey and how might this affect the results of the survey? using random digit dialing, which means a computer randomly generates phone numbers of landlines What is the frame for this type of sampling?
A. The frame is people who like to talk on the phone.
B. The frame is anyone with a landline phone.
C. The frame is people who are home during the day.
D. The frame is the entire population of the country. Who would be excluded from the survey and how might this affect the results of the survey?
A. This could result in sampling bias due to under coverage. Any household without a landline phone, households on the do not call registry, and homeless individuals are excluded.
B. is excluded. This could result in sampling bias due to under coverage. Any person that does not like to talk on the phone
C. This could result in nonresponse bias due to people not participating in the poll. Any household without a landline phone, households on the do not call registry, and homeless individuals are excluded.
D. There is nobody that is being excluded from the survey.
- Why is it rare for frames to be completely accurate? Choose the correct answer below.
A. It is rare for frames to be accurate because individuals that were selected to be in the sample do not always respond to the survey, which can create nonresponse bias. B. It is rare for frames to be accurate because large sample sizes used in frames almost always result in data-entry errors.
C. It is rare for frames to be accurate because frames are obtained in a way that causes the sample to favor one part of the population over another.
D. It is rare for frames to be accurate because frames are obtained periodically, whereas populations are constantly changing.
- What are some solutions to nonresponse? Select all that apply.
A. reduce interview error
B. change wording of questions
C. use cluster sampling
D. reduce under coverage
E. use convenience sampling
F. use stratified sampling
G. offer rewards and incentives
H. attempt callbacks
- Define the following terms.
(a) Experimental unit
(d) Factor
(b) Treatment
(e) Placebo
(c) Response variable
(f) Confounding
(a) Define experimental unit. Choose the correct answer below.
A. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable
B. A person, object, or some other well-defined item upon which a treatment is applied
C. Any combination of the values of the factors (explanatory variables)
D. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication
(b) Define treatment. Choose the correct answer below.
A. The number of individuals in the experiment
B. Any combination of the values of the factors (explanatory variables)
C. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable
D. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable
(c) Define response variable. Choose the correct answer below.
A. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication
B. The effect of two factors (explanatory variables on the response variable) cannot be distinguished.
C. The variable whose effect on the response variable is to be assessed by the experimenter
D. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable
(d) Define factor. Choose the correct answer below.
A. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication
B. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable
C. Grouping together similar experimental units
D. A variable whose effect on the response variable is to be assessed by the experimenter
(e) Define placebo. Choose the correct answer below.
A. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication
B. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable
C. Grouping together similar experimental units
D. Using treatments on many experimental units
(f) Define confounding. Choose the correct answer below
A. Using treatments on many experimental units
B. The effect of two factors (explanatory variables on the response variable) cannot be distinguished.
C. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable
D. Grouping together similar experimental units
15. Explain the difference between a single-blind and a double-blind experiment. Choose the correct answer below.
A. In a single-blind experiment, there is a control group. In a double-blind experiment, there is both a control group and a placebo treatment is used.
B. In a single-blind experiment, the subject does not know which treatment is received. In a double-blind experiment, neither the subject nor the researcher in contact with the subject knows which treatment is received.
C. A single blind experiment is one in which each experimental unit is randomly assigned to a treatment. A double-blind experiment is one in which similar experimental units are grouped together and the experimental units within each block are randomly assigned to treatments.
D. In a single-blind experiment, the researcher does not know what the response variable is. In a double-blind experiment, neither the subject nor the researcher knows what the response variable is.