AP Stat Trivia Review

Round One

Question 1 In one study on the effect of niacin on cholesterol level, 100 subjects who acknowledged being long-time niacin takers had their cholesterol levels compared with those of 100 people who had never taken niacin. In a second study, 50 subjects were randomly chosen to receive niacin and 50 were chosen to receive a placebo. A) The first study was a controlled experiment, while the second was an observational study. B) The first study was an observational study, while the second was a controlled experiment. C) Both studies were controlled experiments. D) Both studies were observational studies.

Question 2 Each of the 29 NBA teams has 12 players. A sample of 58 players is to be chosen as follows. Each team will be asked to place 12 cards with their players names into a hat and randomly draw out two names. The two names from each team will be combined to make up the sample. Will this method result in a SRS of the players? A) Yes, because each player has the same chance of being selected. B) Yes, because each team is equally represented. C) Yes, because this is an example of stratified sampling, which is a special case of SRS. D) No, because the teams are not chosen randomly. E) No, because not each group of players has the same chance of being selected.

Question 3 A consumer product agency tests miles per gallon for a sample of automobiles using each of four different octane of gasoline. Which of the following is true? A) There are four explanatory variables and one response variable. B) There is one explanatory variable with four response variables. C) Miles per gallon is the only explanatory variable, but there are four response variables. D) There are four levels of a single explanatory variable. E) Each explanatory level has an associated level of response.

Question 4 Your company has developed a new treatment for acne. You think men and women might react differently to the medication, so you separate them into two groups. Then the men are randomly assigned into two groups and the women are randomly assigned into two groups. One of the two groups is given the medicine, the other is given a placebo. The basic design of this study is: A) completely randomized B) randomized block, blocked by gender C) completely randomized, stratified by gender D) randomized block, blocked by gender and type of medication E) a matched pairs design

Question 5 A double-blind design is important in an experiment because: A) There is a natural tendency for subjects in an experiment to want to please the researcher. B) It helps control for the placebo effect. C) Evaluators of the responses in a study can influence the outcomes if they know which treatment the subject received. D) Subjects in a study might react different if they knew which treatment they were receiving. E) All of the above reasons are valid.

CHECK YOUR ANSWERS 1. B 2. E 3. D 4. B 5. E In the first study, the subjects were already niacin users. In the second study, the treatment of niacin was randomly assigned (imposed)to the subjects. 2. E Since two players were chosen from each of the 29 teams, this is a stratified sample, not a SRS. For this to be a simple random sample, all of the players would have been in one really big hat. Part of the definition of SRS means that all subgroups have the same chance to be selected. 3. D This experiment has one factor (explanatory variable) of gasoline, with four levels of octane. 4. B Since you think that men and women will react differently, you separated your subjects by gender first. This is an example of blocking. An experiment that uses blocking is called a randomized block design. 5. E Double-blinding is used in experiments so that neither the subject nor the evaluator will inadvertently affect the results of the study because they knew which treatment was received.

Round 2

Question 1 A school committee member is lobbying for an increase in the gasoline tax to support the county school system. The local newspaper conducted a survey of county residents to assess their support for such an increase. What is the population of interest here? A) All school aged children B) All county residents C) All county residents with school aged children D) All county residents with children in the school system E) All county school system teachers

Question 2 An experiment was designed to test the effect of 3 different types of paints on the durability of wooden toys. Since boys and girls tend to play differently with toys, a randomly selected group of children was divided into 2 groups by gender. Which of the following statements about this experiment is true? A) Type of paint is a blocking factor B) Gender is a blocking factor C) This is a completely randomized design D) This is a matched pairs design in which one boy and one girl are matched to form a pair.

Question 3 Which of the following is not a source of bias in a survey? A) non-response B) wording of the question C) voluntary response D) use of a telephone survey E) all are sources of bias

Question 4 Which of the following is not a valid sampling design? A) Number every member of the population and select 100 randomly chosen members B) Divide a population by gender and select 50 individuals randomly from each group C) Select every 20th person, starting at a random point D) select five homerooms at random from all the homerooms in a large high school E) All of these are valid

Question 5 Characteristics of a population are called ______________, while those of a sample are called _____________. Statistics; measures Parameters; statistics Statistics; variables Statistics; parameters None of these

Check your answers 1. B 2. B 3. E 4. E 5. B The population of interest is who you are interested in learning more about. In this case, “The local newspaper conducted a survey of county residents…”, so they are interested in learning more about the county residents. 2. B Since you think that boys and girls will play differently with the toys you first separate by gender. So gender is the blocking factor. 3. E Non-response is when someone that was chosen for our survey cannot be contacted or refuses to respond. Sometimes in a survey, a question will not be worded in a fair manner and will have a “leading statement” that affects the responses. Voluntary response surveys put out a general call and the people that choose to respond are then counted. This type of survey often over-represents people with strong opinions. The telephone issue is becoming more of a problem as the younger generations tend to use their cell phones more and more as their primary phone number. 4. E All of these use random sampling methods. 5. B This is the definition of parameters and statistics.

Round 3

Question 1 The control group in an experiment should be designed to receive: A) the opposite of the experiences afforded the experimental group. B) The experiences afforded the experimental group except for the treatment under experimentation. C) The experiences afforded the experimental group except for receiving the treatment at random. D) The experiences which constitute an absence of the experiences received by the experimental group.

Question 2 Which of the following is NOT true of simple random sampling? A) Whether or not a sample is random cannot be told from inspection of the sample. B) Characteristics of a random sample may differ widely from characteristics of its population. C) A sample must be reasonably large to be considered a random sample. D) Every element and every set of elements in the population must be given an equal chance for inclusion in the sample.

Question 3 Of A-D, which is not a critical part of designing a good experiment? A) Control of known sources of variability B) Random selection of subjects C) Random assignments of subjects to treatments D) Replication of the experiment on a sufficient number of subjects E) All of these are important

Question 4 A survey records many variables of interest to the researchers conducting the survey. Which of the following variables, from a survey conducted by the U.S. postal service, is categorical? A) county of residence B) number of people, both adults and children, living in the household C) total household income, before taxes, in 1993 D) age of respondent

Question 5 Hoping to get information that would allow them to negotiate new rates with their advertisers, Natural Health magazine phoned a random sample of 600 subscribers. 64% of those polled said they use nutritional supplements. Which is true? The population of interest is the people who read this magazine. “64%” is not a statistic; it’s the parameter of interest This sampling design should provide the company with a reasonably accurate estimate of the percentage of all subscribers who use supplements. A) I only B) I and II only C) I and III only D) II and III only E) I, II, and III

Check Your Answers 1. B 2. C 3. B 4. A 5. C The control group should be roughly the same as the experimental group EXCEPT for the treatment received. 2. C A random sample does not need to be large to be random. The randomness comes from the method used to select the subjects. 3. B When designing an experiment, we cannot randomly choose subjects to experiment on – that’s unethical! The randomization comes from assigning treatments to the people that volunteered to be in the study. 4. A The other options are quantitative variables – numerical values that you could measure and do math on. 5. C The magazine was interested in finding out information from their readers. The “64%” is a value that refers to the 600 people that were part of the sample and therefore the 64% is a statistic. The parameter would be the true (unknown) percent of all subscribers that use supplements. Since this sample was taken using random methods, it should be fairly reliable. There may be some minor issues with people not answering the phone, etc. Probably not enough to completely throw off the results.

Bonus round

Question 1 A researcher wants to compare the performance of three types of pain relievers in volunteers suffering from arthritis. Because people of different ages may react differently to medication, the subjects are split into two groups: under 60 and over 60. Subjects in each group are randomly assigned to take one of the medications. Twenty minutes later they rate their levels of pain. This experiment… A) is completely randomized. B) uses matched pairs. C) has two factors, medication and age. D) has one factor (medication) blocked by age. E) has one factor (age) blocked by type of medication.

Question 2 Male Female Democrat 300 600 Republican 500 Other 200 100 A review of voter registration records in a small town yielded the following table of the number of males and females registered as Democrat, Republican, or some other affiliation. The proportion of registered Democrats who are male is: A) 300 B) .33 C) .30 D) .15

Male Female Democrat 300 600 Republican 500 Other 200 100 Question 3 Using the same table, what is the marginal distribution of political party? A) Female: 33% Male: 67% B) Democrat: 45% Republican: 40% Other: 15% C) Democrat: 30% Republican: 50% Other: 20% D) Female: 50% Male: 50%

Check your answers 1. D This study split people by age because they thought age would make a difference. This is called blocking. The experiment was testing medication, which is the factor being studied. 2. B We are limiting ourselves to just the registered Democrats (900 total) and want to know the proportion of males in that group (300 out of 900). 3. B Marginal distributions look at the total percentages. We want the total percent of Democrats, Republicans, and Other.