Statistics Review
A hospital wants to survey religious participants in their city about what they seek from a hospital chaplain, so they randomly select 5 religious meetings in the city and survey every participant in those meetings. What type of sample is this?
cluster response sample
A professor wants to study the effectiveness of a new study tool for a course. There are 150 students registered for the course. The professor assigns each student a number from 1 to 150 and uses a random number generator to assign the first 75 students selected to use the new study tool. The remaining 75 subjects are assigned to use the previous study tool. What type of experiment design is this?
completely randomized
A professor wants to study the effectiveness of a new study tool for a course. There are 150 students registered for the course. Half of the freshmen are randomly assigned to use the new study tool, and the other half are assigned to use the previous study tool. The same method is used to randomly assign half of the sophomores, half of the juniors, and half of the seniors to each study tool. What type of experiment design is this?
randomized block
An insurance company wants to study whether offering incentives for preventative care reduces overall health care costs. They select a random sample of 200 of their customers. Half of the smokers are randomly assigned to be offered the incentive, and the other half are assigned to the control group. The same method is used to randomly assign half of the nonsmokers to the treatment group and half to the control group. What type of experiment design is this?
randomized block
Each law firm in one state registers its phone number with the state court system. An employee of the state court system uses a computer to select 500 random registered phone numbers, and the law firms associated with those numbers will be selected for an audit. What type of sample is this?
simple random sample
The lifespans of seals in a particular zoo are normally distributed. The average seal lives 13.8 years; the standard deviation is 3.2 years. Use the empirical rule (68 - 95 - 99.7\%) to estimate the probability of a seal living longer than 7.4 years.
97.5%
Private colleges tend to cost more than public colleges. Here are some summary statistics for the amount of college debt that undergraduate students graduate with from 4 year institutions in one region. Institution type Mean debt (thousands of dollars) Standard deviation (thousands of dollars) Private μ=$24 σ=$16 Public μ=$18 σ=$15 Niklas graduated from a private institution and Cem graduated from a public institution. Each had $35 thousand dollars of college debt. Relative to their institution type, who graduated with more debt?
Cem
The police set up checkpoints at randomly selected road locations, then inspected every driver at those locations. What type of sample is this?
Cluster random sample
what is the response variable?
change in blood pressure
A politician asks his neighbors their opinions about a controversial issue. What type of sample is this?
convenience sample
what is a response variable?
measures the result of a study
Rita teaches environmental biology. She has 2 forms of a midterm exam, and she wonders if either form is harder than the other. She teaches approximately 200 total students in 4 sections of the class. She randomly assigns half of the students in each section to each form of the exam. Rita will then see if the average scores are significantly different between each form. What type of experiment design is this?
A randomized block design where the 4 sections are the blocks
A concert venue offers tickets in 3 zones: orchestra, grand tier, and balcony. Tickets in the orchestra zone are most expensive, and tickets in the balcony zone are least expensive. Managers of the venue want to survey approximately 150 guests at an upcoming concert about their overall experience. They want to take a stratified random sample of guests based on the venue's zones. Which of these strategies will accomplish their intended design?
Randomly select 50 tickets from each zone and invite those guests to participate in the survey.
A teacher puts students' names in a hat and chooses without looking to get a sample of 3 students. What type of sample is this?
Simple Random Sample
Many investment decisions depend on a stock's performance relative to its own history. Here are some summary statistics about the closing prices of two stocks over the past year: Stock Mean Standard deviation Stock A μ=$4 mu σ=$0.50 Stock B μ=$32 mu σ=$5.75 Today, Eduardo bought shares at their closing prices in stock A for $4.75 sign while he bought shares in stock B for $28.50 For which stock did Eduardo pay less, relative to its previous prices?
Stock B
A support hotline asks callers to stay on the line after they have completed their call to respond to a short survey. What type of sample is this?
voluntary response sample
what is an experimental unit?
who or what we are assigning to a treatment
The grades on a history midterm at Almond are roughly symmetric with μ=81 σ=2.5 Luis scored 84 on the exam. Find the z-score for Luis's exam grade. Round to two decimal places.
1.20 standard deviation
An airline offers a certain flight once per day that usually contains about 250 passengers. The flight offers seats in first class (most expensive), business class, and economy class (least expensive). The airline wants to survey 500 passengers of this flight about their overall satisfaction. The passengers will be selected using a cluster random sample where each flight is a cluster. Why might the airline choose a cluster random sample instead of a simple random sample in this setting?
Contacting all of the passengers on a few flights will probably be more efficient than contacting passengers spread out across many flights. A simple random sample might result in a disproportionate number of passengers from one or more class, but a cluster sample is less likely to suffer this issue.
Students applying to a certain military academy must take a fitness test. One component of the test has applicants complete as many sit-ups as possible in fixed amount of time. Higher numbers of sit-ups are preferred, and the academy calculates the results separately for males and females. Here are some summary statistics for the sit-ups portion of the fitness test: Gender Mean Standard deviation Male μ=81 mu σ=4.7 Female μ=78 mu σ=5.7 Vitor (who is male) and Manuela (who is female) both completed 80 sit-ups on the fitness test. Relative to their gender, who completed more sit-ups?
Manuela
A principal orders t-shirts and wants to check some of them to make sure they were printed properly. She randomly selects 2 of the 10 boxes of shirts and checks every shirt in those 2 boxes. What type of sample is this?
cluster random sample
An insurance company wants to study whether offering incentives for preventative care reduces overall health care costs. They select a random sample of 200 of their customers. They use a random number generator to select 100 customer account numbers to offer the incentive. The remaining 100 customers are assigned to the control group. What type of experiment design is this?
completely randomized
A professor asks the first 5 students who arrive to class to participate in a research study about young adult sleep patterns. What type of sample is this?
convenience sample
A quality control worker at a factory selects the first 10 items she sees as her sample for the day. What type of sample is this?
convenience sample
What are the treatments?
kale based or kale free diet
A teacher puts students' names in a hat and chooses without looking to get a sample of 3 students. What type of sample is this?
simple random sample
Female barn owls tend to be larger than male barn owls. Here are some summary statistics for the masses of the barn owls sampled from one region. Gender Mean Standard deviation Male μ=15.75 oz σ=2.5 oz Female μ=17.5 oz σ=3 oz A male and a female barn owl, each with a mass of 14 oz, space, o, z, live on Aya's property. Relative to its gender, which owl has a smaller mass?
the female
The lifespans of lizards in a particular zoo are normally distributed. The average lizard lives 3.1 years; the standard deviation is 0.6 years. Use the empirical rule (68-95-99.7\%) to estimate the probability of a lizard living less than 2.5 years
16%
A pharmaceutical company is carrying out a trial for a new flea prevention medication that is designed to work for dogs or cats. They recruit pet owners and ask them what flea prevention they currently use. They randomly assign half of the dogs in the study to the new flea prevention medication, and the other half of the dogs in the study will receive their current prevention. A similar process is carried out with the cats in the study. What type of experiment design is this?
A randomized block design where the pet types (dogs and cats) are the blocks
Lilian's favorite magazine published 50 issues last year, and each issue contained approximately 250 pages. She wants to take a cluster random sample of about 1,000 total pages to estimate what proportion of all pages contained an advertisement. Which of these strategies will accomplish her intended design?
Randomly select 4 issues, and examine every page in those issues.
A concert venue offers tickets in 3 zones: orchestra, grand tier, and balcony. Tickets in the orchestra zone are most expensive, and tickets in the balcony zone are least expensive. Managers of the venue want to survey approximately 150 guests at an upcoming concert about their overall experience. They want to take a stratified random sample of guests based on the venue's zones. Which of these strategies will accomplish their intended design?
Randomly select 50 tickets from each zone and invite those guests to participate in the survey
A student council surveys 100 students by taking random samples of 25 freshmen, 25 sophomores, 25 juniors, and 25 seniors. What type of sample is this?
Stratified Random Sample
A store prints a request on each receipt asking customers to fill out a satisfaction survey online if they are willing.
Voluntary Response Sample
what is an explanatory variable?
explains changes in another variable
Karina wants to determine if kale consumption has an effect on blood pressure. She recruits 100100100 households and randomly assigns each household to either a kale-free diet plan or a kale-based diet. At the end of two months, she plans to record the original and final blood pressures for members of each household What is the explanatory variable?
kale consumption
An online retailer wants to study whether more lenient return policies increase purchasing behaviors. They select a random sample of 2000 customers who have made purchases in the past year. The company ranks the customers according to total cost of purchases made the previous year. For every 2 customers, in order, from the list, the online retailer randomly assigns one customer to the treatment group and the other to the control group. What type of experiment design is this?
matched pairs
A truck manufacturer selects 3 trucks at random from each of 6 models for safety testing. What type of sample is this?
stratified random sample
A large company surveys 100 employees by taking random samples of 10 managers and 90 non-managerial employees. What type of sample is this?
stratified sample random
What is the treatment?
the specific level of the explanatory variable given to individuals in an experiment. If there are multiple explanatory variables, a treatment is a combination of specific levels from each explanatory variable.
A restaurant leaves comment cards on all of its tables to learn about customer satisfaction. Each comment card is a brief survey that customers can fill out if they choose to. What type of sample is this?
voluntary response sample
Forest rangers at a national park want to take a sample of trees to estimate what proportion of trees in the park are infected with a certain disease. The population of trees in question is divided by a creek. East of the creek, most of the trees are oak. West of the creek, most trees are cedar, which are more likely to be infected. The rangers are considering taking a stratified random sample using each side of the creek as strata. They'll sample trees from each side proportionately based on the total number of trees on each side. Why might the rangers choose stratification instead of a simple random sample to estimate the proportion of infected trees?
In repeated sampling, estimates from this sort of stratified sample would likely vary less than estimates from simple random samples. A stratified random sample reduces the likelihood of getting disproportionate numbers of cedar or oak trees in the sample.
A group of researchers wants to study the effect of listening to music at different volumes on driving reaction times. They recruit 100 volunteers. While music plays in the car at one of two volume levels, each subject encounters a number of signs, some of which require braking, and their reaction times are recorded. The subjects repeat the experiment at the other volume level. The order of the conditions is randomly assigned for each subject. What type of experiment design is this?
matched pairs
A group of researchers wants to study the effect of listening to music at different volumes on driving reaction times. They recruit 100 volunteers. Half of the subjects with fewer than 10 years of driving experience are randomly assigned to take the test with one music volume, and the other half are assigned to take the test at the other music volume. The same method is used to randomly assign half of the drivers with at least 10 years of driving experience to each testing condition. What type of experiment design is this?
randomized block
who or what are the experimental units?
the households
A manager associated each employee's name with a number on one ball in a container, then drew balls without looking to select a sample of 5 employees. What type of sample is this?
simple random sample
Here are some summary statistics for the duration for which candles from a certain company burn. Candle type Mean duration Standard deviation Jar candle μ=25 σ=2.5 Pillar candle μ=95 σ=7.5 Andrei had cinnamon-scented jar candle that burned for 30 hours and a berry-scented pillar candle that burned for 88 hours. Relative to its type, which candle burned faster?
the berry scented pillar candle