Identify Sampling Method.
Identify the sampling method used in each situation (SRS, stratified, cluster, or systematic).
A veterinarian numbers her 340 patient files from 1 to 340 and uses a random number generator to select 30 unique files.
Simple random sample.
A radio station receives 6,000 contest entries and will draw 3 winners, each receiving the same prize.
Describe how the station would draw the winners without replacement.
Place all 6,000 entries in a container, mix well, and draw one entry at a time. Set each winning entry aside (do not return it) before the next draw, so no entry can be drawn twice.
Sitbit has 18,000 users in three subscription tiers (Free, Plus, Premium Recliner). Users are also organized into 600 workplace teams of 30 users each; each team includes a mix of all three tiers.
Describe a cluster random sample of 300 users using workplace teams.
Number the 600 teams 1 to 600 and use a random number generator to select 10 teams (ignore repeats).
Survey ALL 30 users on each of the 10 selected teams: 10 × 30 = 300 users.
. Ree-bawk wants to survey the 5,400 farms that purchased its chicken sneakers last year. The farms are grouped into 180 delivery zones, each containing 30 farms of varied sizes and types. Ree-bawk randomly selects 6 delivery zones and surveys every farm in those zones. Which sampling method is this? (A) Cluster random sample
(B) Stratified random sample
(C) Simple random sample
(D) Sampling with replacement
(A) Cluster random sample. He takes ALL from SOME groups (entire randomly chosen zones).
Port Verde has 60,000 households in 15 neighborhoods; neighborhoods vary widely in average commute distance. The city hopes to survey 500 households.
Describe a stratified plan using the 15 neighborhoods as strata, and one statistical advantage over an SRS.
Use the 15 neighborhoods as strata and select a separate SRS of households within every neighborhood (about 500/15 ≈ 33 each, or proportional to neighborhood size), totaling 500. Advantage: since commute distance varies widely between neighborhoods, stratifying guarantees every neighborhood is represented, which reduces variability and gives a more precise estimate than an SRS.
Identify the sampling method used in each situation (SRS, stratified, cluster, or systematic).
A Toy-yoda inspector randomly selects one of the first 25 toys off the line, then tests every 25th toy after that.
Systematic random sample.
A radio station receives 6,000 contest entries and will draw 3 winners, each receiving the same prize.
If the station instead drew with replacement, what could happen that cannot happen without replacement?
The same entry could be drawn more than once, so one person could win two or even all three prizes.
Sitbit has 18,000 users in three subscription tiers (Free, Plus, Premium Recliner). Users are also organized into 600 workplace teams of 30 users each; each team includes a mix of all three tiers.
Satisfaction is expected to differ across tiers. Which method is more appropriate? Justify.
Stratified. When groups are expected to differ on the variable of interest, stratifying guarantees all three tiers are represented and produces a more precise estimate of overall satisfaction.
Mr. Sullivan randomly selects one of the first 12 exams in a stack of 240, then checks every 12th exam after that. Which method?
(A) Simple random sample
(B) Cluster random sample
(C) Stratified random sample
(D) Systematic random sample
(D) Systematic random sample: a random starting point and a fixed, periodic interval.
Port Verde has 60,000 households in 15 neighborhoods; neighborhoods vary widely in average commute distance. The city hopes to survey 500 households.
A council member proposes randomly selecting 3 neighborhoods and surveying every household in them. Name this method and give one reason to prefer the plan in (b).
Cluster random sampling. Because neighborhoods differ widely in commute distance, the 3 selected neighborhoods may not represent the whole city; the stratified plan includes households from all 15 neighborhoods, so it avoids that risk.
Identify the sampling method used in each situation (SRS, stratified, cluster, or systematic).
Gramma-zon divides customers into four shipping regions and selects an SRS of 50 customers from each region.
Stratified random sample.
A radio station receives 6,000 contest entries and will draw 3 winners, each receiving the same prize.
Which strategy is more appropriate for this contest? Explain.
Without replacement. The prizes are identical, so there is no reason to allow repeat winners; drawing without replacement spreads the 3 prizes among 3 different winners.
A warehouse must inspect 100 of 10,000 packages moving along a conveyor belt. Explain why a systematic random sample might be more convenient than an SRS.
The packages are already in a sequence on the belt. An SRS would require numbering all 10,000 packages and pulling scattered packages. Instead, randomly select one of the first 100 packages, then inspect every 100th package after that, which is easy to do as they pass.
A battery tester selects a battery from a large bin, records its voltage, and returns it to the bin before the next selection. Which of the following statements is true?
(A) This is sampling without replacement, so no battery can be tested twice.
(B) This is sampling with replacement, so the same battery could be tested more than once.
(C) This is sampling with replacement, so every battery will be tested exactly once.
(D) This is sampling without replacement, so the sample must include every battery in the bin.
(B) This is sampling with replacement, so the same battery could be tested more than once.
A city recreation department has 5,000 registered pool members organized into 25 swim sessions of 200 members each. Each session includes a similar mix of ages and skill levels. The department randomly selects 3 sessions and surveys every member in the selected sessions. Which sampling method is the department using?
(A) Stratified random sample
(B) Cluster random sample
(C) Simple random sample
(D) Systematic random sample
(B) Cluster random sample
Identify the sampling method used in each situation (SRS, stratified, cluster, or systematic).
Best Wrestern randomly selects 8 of its 94 locations and surveys every guest who checks out of those 8 hotels.
Cluster random sample.
An environmental scientist wants to test 40 of the 900 storm drains in a city. Describe how to select an SRS of 40 drains using a random number generator
Number the drains 1 to 900. Use a random number generator to generate integers from 1 to 900, ignoring repeats, until 40 unique numbers are obtained. Test the 40 drains whose numbers were selected.
Which of the following best describes a simple random sample ofsize n?
(A) Every individual in the population has an equal chance of being selected.
(B) Every possible sample ofsize n has an equal chance of being selected.
(C) The population is divided into groups and an equal number of individualsis selected from each group.
(D) Individuals are selected at regular intervals from an ordered list.
(B) Every possible sample of size n has an equal chance of being selected. “Every individual has an equal chance” (choice A) is not enough to make an SRS.
A state agency wants to estimate support for a new highway project. Opinions are expected to differsharply between urban and rural residents. Which sampling plan is most appropriate, and why? (A) A clustersample of towns, because surveying entire towns is more convenient
(B) A systematic sample from a statewide phone list, because it is easy to carry out
(C) A simple random sample, because every resident has an equal chance of selection
(D) A stratified random sample using urban and rural residents as strata, because it guarantees both groups are represented
(D) A stratified random sample using urban and rural residents as strata, because it guarantees both groups are represented.
A seed company wants to estimate the germination rate of the 2,000 seed packets in its warehouse. The packets come from four crop types, and germination rates are expected to differ by crop type. Why would a stratified random sample using crop type as strata be an appropriate choice?
(A) It gives every packet an equal chance of selection, which makes it a simple random sample (B) It saves time because only one crop type needs to be tested
(C) It is the only sampling method that uses random selection
(D) It guarantees that each crop type is represented in the sample
(D) It guarantees that each crop type is represented in the sample
A biologist catches a fish, records its length, and releases it before catching the next fish. Some fish may be measured more than once. With or without replacement?
With replacement. Each fish is returned to the lake before the next selection, so the same fish can be selected again.
Sitbit has 18,000 users in three subscription tiers (Free, Plus, Premium Recliner). Users are also organized into 600 workplace teams of 30 users each; each team includes a mix of all three tiers.
Describe a stratified random sample of 300 users using subscription tier.
Separate all 18,000 users into three strata by tier: Free, Plus, and Premium Recliner.
Select an SRS of 100 users from each tier (numbering users within each tier and using a random number generator, ignoring repeats), for 300 total.
Mr. Bean wants to sample 10 students from his statistics class to taste test his famous chili. He divides the class into juniors and seniors, then randomly selects 5 students from each group. Which sampling method did Mr. Bean use?
(A) Simple random sample
(B) Systematic random sample
(C) Stratified random sample
(D) Cluster random sample
(C) Stratified random sample. He takes SOME (an SRS) from ALL groups.
The city of Port Verde is considering a bike share program. The city has 60,000 households spread across 15 neighborhoods, and the neighborhoods vary widely in average commute distance. The city hopes to survey 500 households.
Describe how the city could select a simple random sample of 500 households.
Obtain a list of all 60,000 households and number them 1 to 60,000. Use a random number generator to generate integers from 1 to 60,000, ignoring repeats, until 500 unique numbers are obtained. Survey those 500 households.
3. Toes R Us, a sock subscription service, numbers its 8,400 subscribers from 1 to 8,400 and uses a random number generator to select 150 unique numbers, ignoring any repeats. Which of the following statements is true?
(A) The service is sampling without replacement, and every possible sample of 150 subscribers is equally likely
(B) The service is sampling with replacement because the numbers are generated at random
(C) The sample is a systematic random sample because the subscribers are numbered in order
(D) The sample is a stratified random sample because the subscribers are divided into groups
(A) The service is sampling without replacement, and every possible sample of 150 subscribers is equally likely