Statistical Reasoning study cards

In a study, the data you collect is Number of traffic tickets. This data is: 1. Quantitative 2. Qualitative

1. Quantitative

_______________ sampling is like stratified sampling, but the idea is that entire groups are selected as opposed to individuals.

Cluster

Two statistics students at UCLA conducted an energy efficiency survey of graduate student apartments. There were seven university apartment buildings, and the students randomly selected three to be included in the study. In each building, they randomly chose 25 apartments. What is the largest group of students that the study results represent? 1. All UCLA graduate student apartments. 2. All UCLA graduate student apartments in this group of seven buildings. 3. All UCLA graduate student apartments in the three sampled buildings. 4. All UCLA graduate student apartments that were sampled in the three buildings.

2. All UCLA graduate student apartments in this group of seven buildings.

Determine whether the value 30% is a parameter or statistic: 30% of all vehicles sold are compact cars 1. Statistic 2. Parameter

2. Parameter

Determine if the quantity described below is a statistic or a parameter: The proportion of female students that attended BMCC last year. 1. statistic 2. parameter

2. parameter

A city council has requested a household survey be conducted in a suburban area of their city. The area is broken into many distinct and unique neighborhoods, some including large homes, some with only apartments, and others a diverse mixture of housing structures. Which approach would likely be the least effective? 1. Stratified sampling 2. Simple random sampling 3. Cluster sampling

3. cluster sampling

In a study, the sample is chosen by dividing the population by Gender, and choosing 30 people of each gender What is the sampling method? 1. Simple Random 2. Systematic 3. Stratified 4. Cluster 5. Convenience

3. Stratified

In a study, the sample is chosen by grouping the class by gender, then selecting 10 males and 10 females What is the sampling method? 1. Simple Random 2. Systematic 3. Stratified 4. Cluster 5. Convenience

3. Stratified

In a study, the sample is chosen by separating all cars by size, and selecting 10 of each size grouping What is the sampling method? 1. Simple Random 2. Systematic 3. Stratified 4. Cluster 5. Convenience

3. Stratified

For each stage in the multistage sampling plan of this study, identify the sampling technique that was used: The 2 companies' claims are classified (depending on their origin) according to 7 geographical regions, and within each region, the sampling continues. 1. cluster sampling 2. simple random sample 3. stratified sampling

3. stratified sampling *The claims are divided into groups/strata (regions), and then the sampling continues from within each such group.

For a ____________ sample, a random sample is taken from each group (or strata).

stratified

In a study, the sample is chosen by asking people on the street What is the sampling method? 1. Simple Random 2. Systematic 3. Stratified 4. Cluster 5. Convenience

5. Convenience

In order to obtain a sample of undergraduate students in the United States, a simple random sample of 10 states is selected. From each of the selected states, 10 colleges or universities are chosen at random. Finally, from each of these 100 colleges or universities, a simple random sample of 20 undergraduate students is selected. Thus, the final sample consists of 2,000 undergraduates. This is an example of: 1. simple random sampling. 2. multistage sampling. 3. convenience sampling. 4. stratified sampling 5. none of the above.

2. multistage sampling *This is an example of multistage sampling, because first a sample of a few states was selected, and then in each of those states another sample of a few universities was selected, and finally in each of those universities a sample of a few students was selected.

Ross Times, the student newspaper of Ross College, printed a "What do you think?" column feature asking: "Do you think that the college is doing enough to provide student parking?" Anyone could mail in a response or use the paper's Web site to respond. In all, 126 answers were received. This is an example of: 1. a voluntary response sample. 2. a multistage sample. 3. a simple random sample. 4. a convenience sample. 5. the placebo effect.

1. a voluntary response sample. *The response was voluntary, since the only responses that were recorded were from students who decided on their own to voice an opinion. This means the survey result could be biased , because it only represents the opinions of those students who, for whatever reason, bothered to write a response, rather than fairly reflecting the opinion of the whole college.

For each stage in the multistage sampling plan of this study, identify the sampling technique that was used: From each region, 5 representative counties are selected. (In total, all the claims originating from 35 counties are examined.) 1. cluster sampling 2. simple random sample 3. stratified sampling

1. cluster sampling *In this stage, whole groups of claims were selected. In particular, from each region, 5 groups of claims were selected (each group being all the claims originating from a certain county).

For each stage in the multistage sampling plan of this study, identify the sampling technique that was used: The research foundation identifies 5 large companies that represent a broad cross-section of patients, chooses 2 of the 5 at random, and gains access to the claims of all the companies' patients. 1. cluster sampling 2. simple random sample 3. stratified sampling

1. cluster sampling *two whole groups of patients (all the patients from two companies) were randomly selected.

Match the sample of students with the correct sampling method. Every third student on the class list. 1. random 2. systematic 3. convenience 4. cluster

2. systematic

When conducting a survey, it is important to use a random sample: 1. to get a significant result. 2. to avoid bias and to get a representative sample. 3. so that we can make causal conclusions. 4. to ensure truthful answers to the survey's questions. 5. none of the above.

2. to avoid bias and to get a representative sample. *Random selection ensures that the sample is unbiased on average, so that the results of the study can be generalized to the population.

For each stage in the multistage sampling plan of this study, identify the sampling technique that was used: Within each county (and for each company), claims of 25 male and 25 female patients are randomly selected. 1. cluster sampling 2. simple random sample 3. stratified sampling

3. stratified sampling *The claims are divided into groups/strata (by gender). Note that after the claims are divided into strata, 25 claims are chosen from each gender group using simple random sampling.

If we collect information on students' study practices and exam scores and find strong evidence of a positive association between not studying more than two hours and high grades, when can we generalize this finding to the general population? 1. The students participated in the study after seeing signs about the survey posted around campus. The signs were posted in every campus building, and so all students would see these signs and have the opportunity to participate. Therefore, all students are represented. 2. The student participants come from the student population. Additionally, the students in the study cannot have any misdemeanors, otherwise their answers could not be trusted. 3. There is at least one student from each year and ethnicity that is represented in the general student body. 4. A student list for the college was obtained and students were randomly selected from the list to participate.

4. A student list for the college was obtained and students were randomly selected from the list to participate.

Examine the following survey question for any sources of bias. Given that 18-year-olds are old enough to vote and to serve in the military, is it fair to set the drinking age at 21? Is the question biased? 1. Yes 2. No

1. Yes

Which of the following is an example of stratified sampling? 1. A sample of 351 people called a radio show to express their opinions about the verdict in the Michael Jackson trial. 2. In order to assess students' satisfaction with the food establishment on campus, the first 50 students that come out of the student center were interviewed. 3. A poll asked a random sample of 1,112 adults whether they believe that the use of marijuana for medical reasons should be legalized. 4. A health educator wanted to study the sleeping habits of the undergraduate students in her university. For her study, the researcher chose a simple random sample of size 150 from each of the classes (150 freshmen, 150 sophomores, 150 juniors, and 150 seniors), for a total of 600 sampled students. 5. The human resources department of a large bank wanted to assess the job satisfaction of the bank's workers. The department chose four of the bank's branches at random, and used all of the workers in those four branches as the subjects for the study.

4. A health educator wanted to study the sleeping habits of the undergraduate students in her university. For her study, the researcher chose a simple random sample of size 150 from each of the classes (150 freshmen, 150 sophomores, 150 juniors, and 150 seniors), for a total of 600 sampled students. *The researcher viewed the students as being divided into four separate †̃strata ′ (freshmen, sophomores, juniors, and seniors), and a few students from each stratum were selected.

As part of a statistics project, Charlie would like to collect data on household size in his city. To do so, he asks each person in his statistics class for the size of their household and reports the results of a simple random sample. However, this is not a simple random sample. Why? 1. Charlie did not use any randomization; he took a convenience sample. 2. Charlie did not use a random number table to randomize the order in which he collected the students' responses, so the sample cannot be random. 3. In this investigation of household size, each household represents a case. Charlie incorrectly sampled individuals instead of households. 4. Both (1) and (3) are correct. 5. Answers (1), (2), and (3) are all correct.

4. Both (1) and (3) are correct.

The school district is considering whether it will no longer allow students to park at school after two recent accidents where students were severely injured. As a first step, they survey parents of high school students by mail, asking them whether or not the parents would object to this policy change. Of 5,799 surveys that go out, 1,209 are returned. Of these 1,209 surveys that were completed, 926 agreed with the policy change and 283 disagreed. Which of the following statements are true? 1. It is possible that 80% of the parents of high school students disagree with the policy change. 2. The survey is unlikely to have any bias because all parents were mailed a survey. 3. The school district has strong support from parents to move forward with the policy approval. 4. Because many surveys have return rates of between 30% and 50%, it is likely that some of the mailings never reached the parents.

1. It is possible that 80% of the parents of high school students disagree with the policy change.

The faculty senate at a large university wanted to know what proportion of the students thought foreign language classes should be required for everyone. The statistics department offered to cooperate in conducting a survey, and a simple random sample of 500 students was selected from all the students enrolled in statistics classes. A survey form was sent by email to these 500 students. A) In this case, the population of interest is: 1. all the students at the university. 2. all the students enrolled in a statistics class. 3. the 500 students who got the email survey. 4. the students who responded to the email survey. 5. all the students who think that foreign language classes should be required for everyone. B) In this case, the sampling frame is: 1. all the students at the university. 2. all the students enrolled in a statistics class. 3. the 500 students who got the email survey. 4. the students who responded to the email survey. 5. all the students who think that foreign language classes should be required for everyone. C) Which of the following is true about this study? 1. Since the sample is random, it is representative of the population of interest. 2. Even though the sample is random, it is not representative of the population of interest.

A) 1. all the students at the university. * The faculty senate wanted to know what proportion "of the students" supported the proposal. The senate put no restriction on their group of interest, so they want to gauge the opinion of all students at the university. B) 2. all the students enrolled in a statistics class. *The sampling frame is the list of potential individuals from which the sample gets selected. In this case, that list is restricted to students enrolled in a statistics class. This is an example in which the sampling frame does not match the population that the faculty senate wants information about. C) 2. Even though the sample is random, it is not representative of the population of interest. *Although the 500 survey recipients were selected randomly from some larger sampling frame, the study isn′t representative of the intended population of all students at the university, because: (A) The sampling frame was only students in statistics (so the sampling frame didn′t match the population of interest), and (B) Returning the survey was voluntary (so the study results were potentially biased and thus not representative, even of just statistics students.