Sampling Plans
A large retail company wants to estimate customer satisfaction across its stores nationwide. The company creates a list of all customers who made a purchase in the past year, randomizes the list, and then surveys every 500th customer on the randomized list. Which sampling method is being used?
A) Simple random sample
B) Stratified random sample
C) Cluster random sample
D) Systematic random sample
D) Systematic random sample
A researcher wants to determine whether listening to music improves memory recall. Participants are randomly assigned to listen to music or sit in silence while studying the same list of words for the same amount of time. Each participant then receives the same amount of time to recall words. What is the explanatory variable?
A) Listening to music while studying
B) Whether the participant listens to music or studies in silence
C) The number of words recalled
D) The amount of study time, in minutes
B) Whether the participant listens to music or studies in silence
Which statement best describes the purpose of random assignment in an experiment?
A) To ensure that the sample represents the population
B) To eliminate all sources of bias
C) To create treatment groups that are similar with respect to extraneous variables
D) To ensure that participants do not know which treatment they receive
C) To create treatment groups that are similar with respect to extraneous variables
A city wants to estimate the proportion of households that use public transportation as their primary method of commuting. The city is divided into neighborhoods, each containing a mixture of household types and income levels. The city randomly selects 12 neighborhoods and surveys every household within each selected neighborhood. Why is this classified as a cluster random sample?
A) The neighborhoods were selected using a random mechanism.
B) The population was divided into non-overlapping groups.
C) All households within each selected neighborhood were included in the sample.
D) The households within each neighborhood are similar to one another.
C) All households within each selected neighborhood were included in the sample.
The organizers of a regional college fair want to estimate the average number of colleges that high school seniors attending the fair have applied to so far. During the fair, they randomly select 120 seniors from those in attendance and ask each selected student how many colleges they have applied to. All 120 students responded. Which statement correctly describes the sample and the population to which it would be most reasonable to generalize
the results?
A) The sample is all students attending the college fair, and the population is all high school seniors in the region.
B) The sample is the 120 selected seniors who responded, and the population is all high school seniors in the region.
C) The sample is the 120 selected seniors who responded, and the population is all students attending the college fair.
D) The sample is the average number of colleges applied to, and the population is all students attending the college fair.
C) The sample is the 120 selected seniors who responded, and the population is all students attending the college fair.
A company is testing three website layouts to determine which produces the longest average visit time. Users are randomly assigned to one of the three layouts, and time spent on the website is recorded. Which statement best describes the design?
A) A completely randomized design because users are randomly assigned to treatments
B) A matched-pairs design because each user sees one layout
C) A randomized block design because users are grouped by layout
D) An observational study because no control group is used
A) A completely randomized design because users are randomly assigned to treatments
A school district wants to estimate the average number of minutes students spend per day on social media. Students are divided into middle school and high school groups, and a simple random sample is selected from each group. What is the primary advantage of this method over one simple random sample of all students?
A) It eliminates response bias.
B) It can reduce variability by accounting for known differences between groups.
C) It ensures that every student has the same chance of being selected.
D) It allows cause-and-effect conclusions to be drawn.
B) It can reduce variability by accounting for known differences between groups.
The manager of a local gym wants to estimate the proportion of its members who plan to renew their membership next year. The manager posts a survey link on the gym's website and encourages members to complete the survey if they wish. After one week, 310 members have responded. Which is the most likely source of bias?
A) Members who responded may not be representative of all gym members.
B) The sample size is too large to produce an unbiased estimate.
C) The manager did not use random assignment.
D) The survey was posted for only one week.
A) Members who responded may not be representative of all gym members.
Researchers want to investigate whether two stretching routines affect sprint time in high school athletes. Because prior sprint-training experience may influence sprint time, athletes are first grouped by whether they participated in organized sprint training during the past year. Within each group, athletes are randomly assigned to one of the two routines.
Which design is used?
A) Completely randomized design
B) Randomized block design
C) Matched-pairs design
D) Observational study
B) Randomized block design
Which sampling plan is correctly paired with its defining characteristic?
A) Stratified random sample - all individuals within selected groups are surveyed.
B) Cluster random sample - individuals are selected at fixed intervals after a random start.
C) Systematic random sample - simple random samples are taken from each group.
D) Simple random sample - every possible sample of the same size has the same chance of being selected
D) Simple random sample - every possible sample of the same size has the same chance of being selected
Which scenario best illustrates nonresponse bias rather than another type of bias?
A) Individuals with strong opinions choose to participate in an online poll.
B) Survey responses differ from true responses because of leading question wording.
C) Selected individuals fail to respond, and those who respond differ in meaningful ways from those who do not.
D) A sampling method excludes a portion of the population entirely.
C) Selected individuals fail to respond, and those who respond differ in meaningful ways from those who do not.
A school district randomly selects 200 students from all middle school students in the district. The selected students are randomly assigned to use either a new online homework platform or the existing system for one grading period. The new-platform group shows a statistically significant increase in homework completion. Which conclusion is justified?
A) The platform caused increased completion rates for all middle school students.
B) The platform is associated with increased completion rates for all middle school students, but causation cannot be claimed.
C) The platform caused increased completion rates for the students in the study, and the result can be generalized to all middle school students in the district.
D) The platform caused increased completion rates for the students in the study, but the result cannot be generalized to all middle school students in the district.
C) The platform caused increased completion rates for the students in the study, and the result can be generalized to all middle school students in the district.
A school district recruits 120 student volunteers. Students are grouped by grade level and then randomly assigned to keep their phones either in a locked pouch or in their backpacks. After four weeks, the locked-pouch group has significantly higher quiz scores.
On your whiteboard: