Math quiz 10-12
Some schools teach reading using phonics (the sounds made by letters) and others using whole language (word recognition). Suppose a school district wants to know which method works better. Suggest a design for an appropriate experiment.
(Randomly) assign half the reading teachers in the district to use each method. Students should be (randomly) assigned to teachers as well. Make sure to (block) both by school and grade (or control grade by using only one grade). Construct an appropriate reading test to be used at the end of the year, and compare (scores.)
For the following scenario, decide if the outcome is random. When playing a board game comma the number of spaces you move is decided by rolling a six dash sided die. Is the number of spaces you move random?
. Yes comma rolling a die results in random outcomes.
ver a 6-month period, among 32 people with a circulatory disorder, patients who were given a high dose (597 mg/day) of a certain dietary supplement improved more than those given a placebo. The researchers flipped a coin to determine if a patient would receive the supplement or a placebo, and then kept track of the dosages of supplements and placebos. What were the experimental units and how did the researchers randomize treatments? Part A)What were the experimental units? Part B)How did the researchers randomize treatments?
A) The experimental units are 32 people with a circulatory disorder. B)They flipped a coin.
In countries known to contain lower levels of vitamin Upper D, there were more reported cases of a particular type of rare disease. Some researchers hypothesized that a deficiency in vitamin Upper D would increase the risk of developing the disease. These researchers compared vitamin Upper D levels in blood samples from 180 exchange students who have developed the disease with blood samples of nearly 380 who have not. The samples were taken, on average, five years before the disease was diagnosed. Those with the highest blood vitamin Upper D levels had a 50% lower risk of developing the disease than those with the lowest levels. Complete parts a) through d). a) What kind of study was this? Select all that apply. b) Is that an appropriate choice for investigating this problem? Explain. c) Who were the subjects? d) What were the variables?
A) observational, retrospective B.)Yes, because the disease in the study is a rare disease, a retrospective study is appropriate. C) Exchange students D)The level of vitamin Upper D for the subject and whether or not the subject developed the disease
A pizza delivery driver, always trying to increase tips, runs an experiment on his next 40 deliveries. He flips a coin to decide whether or not to call a customer from his mobile phone when he is five minutes away, hoping this slight bump in customer service will lead to a slight bump in tips. After 40 deliveries, he will compare the average tip percentage between the customers he called and those he did not. Is this experiment blinded? Can it be double-blinded? Explain. Part A) Is this experiment blinded? Part B)Can this experiment be double-blinded?
A) Yes, because the customers are not aware of the differing treatments. B)Yes, because the customers are not aware of the differing treatments.
An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2-minute ride. Concerned about how patrons (who paid a large amount to enter the park and ride on the rides) feel about this, they survey every 10 th male as they exit the park comma starting from a randomly selected male. Complete parts a through d below. Part A)What kind of sample is this? Part B)What is the sampling frame? Part C)Is the sample likely to be representative of the population of interest? Part D)What members of the population of interest are omitted?
A)systematic sample B)all the male patrons C)No, the sample is not likely to representative of everyone in the park D)female patrons
A group of students in your intro stats class design an experiment to test whether popcorn stored in the freezer pops better (fewer kernels left un-popped) than room temperature popcorn. Two group members do the shopping separately and realize too late that they've bought two different brands. If they ignore this and randomly assign a mix of bags to each treatment group, what principle of experiment design have they ignored?
Blocking
The managers of a large company wished to know the percentage of employees who feel "extremely satisfied" to work there. The company has roughly 32 comma 000 employees. Three scenarios are given in parts a through c below. For each scenario, determine the sampling method used by the managers. Part A)The managers select a single branch at random and survey every employee of that branch. Part B)The managers use the company e-mail directory to contact every 60th employee on the list. Choose the correct sampling method below. Part C) The managers split the company into divisions, with each division containing employees that have similar jobs. Within each division, they select a SRS of employees to contact. Choose the correct sampling method below.
Part A) The managers used a cluster sample. Part B)The managers used a systematic sample. Part C)The managers used a stratified sample.
Administrators at a university were interested in estimating the percentage of students who are the first in their family to go to college. The university student body has about 40 comma 000 members. For each scenarios a through c, identify the kind of samples used by the university administrators. Part A)Select several dormitories at random and contact everyone living in the selected dorms. Choose the correct answer below. B)Using a computer-based list of registered students, contact 200 freshmen, 200 sophomores, 200 juniors, and 200 seniors selected at random from each class. Choose the correct answer below. C)Using a computer-based alphabetical list of registered students, select one of the first 20 names on the list at random, and then contact the student whose name is 40 names later, and then every 40th name after that. Choose the correct answer below.
Part A) cluster sample Part B)stratified sample Part C)systematic sample
Administrators at a university were interested in estimating the percentage of students who are the first in their family to go to college. The university student body has about 47 comma 000 members. The university administration is considering a variety of ways to sample students for a survey. For each of these proposed survey designs, identify the problem. Part A) Publish an advertisement inviting students to visit a website and answer questions. Part B) Set up a table in the student union and ask students to stop and answer a survey.
Part A)This would suffer from voluntary response bias. Part B)This would be a convenience sample.
Which matters more about a sample you draw from a population? Choose the condition below that is more important when choosing a sample from a population.
The size of the sample.
Many states run lotteries, giving away millions of dollars if your set of numbers matches the set of winning numbers. A machine pops up numbered balls to determine the winning set of numbers. Do you think this method guarantees randomness? Explain.
This method is random only if the balls generate numbers in equal frequencies.
If you create an online survey, individuals can choose on their own whether to participate in the sample. This causes a form of bias called __________.
Voluntary response
Some friends of yours in a political science class are angry about a new town ordinance restricting off-campus parties. They make an online survey asking students' opinions. This type of sampling might be classified as a __________ sample.
convenience
Subjects in an experiment for an herbal cold medicine either receive a tea made from the herb, or a placebo tea. Their doctor also doesn't know which tea was distributed to which subject. This experiment is ____________.
double blinded
A variable whose levels are controlled by the experimenter is called a ______________.
factor
A study based on data in which no one manipulates any experimental factors is called an _______________.
observational study
A "fake" treatment that looks just like the treatment being tested is called a _______.
placebo
You are doing a study for a non-profit group helping at-risk children in your city. Suppose you know that 14.2% of the children in your city live in poverty. This percentage is an example of a __________.
population parameter
When you sample so that every combination of individuals in your population has an equal chance of being chosen you are taking a __________.
simple random sample
ou are trying to study the amount of financial aid students at your University receive. You sample 50 students and find out the average size of their financial aid packages. The average of your sample is a __________.
simple statisitc
A friend of yours in your intro stats class obtains permission to randomly sample the University student body to conduct a satisfaction survey on some recent changes to the enrollment process. She randomly samples 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors. This is an example of a __________ sample
stratified
A company hoping to assess employee satisfaction surveys employees by assigning computer-generated random numbers to each employee on a list of all employees and then contacting all those whose assigned random number is divisible by 13. Is this a simple random sample?
Yes, this is a simple random sample. Each employee has an equal and independent chance of being selected.
