Stats test 3

A sample produced a list of 5024 licensed drivers. The investigators then chose an SRS of 880 of these drivers to answer questions about their driving habits. (A) How would you assign labels to the 5024 drivers? (B) Use Table B, starting at line 119, to choose the first 55 drivers in the sample. Drag the token representing the label of the driver selected to the appropriate column. One question asked was, "Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?" Of the 880 respondents, 171 admitted that at least one light had been red. A practical problem with this survey is that people may not give truthful answers. (C) What is the likely direction of the bias: do you think more or fewer than 171 of the 880 respondents really ran a red light? (D) Why would there be such a bias?

(A) Assign labels 0001 through 5024 (B) Label of first driver selected - 1887 Label of second driver selected - 2099 Label of third driver selected - 4826 Label of fourth driver selected - 3547 Label of fifth driver selected - 4216 (C) More than 171 of the 880 respondents really ran a red light. (D) People may be concerned that they will get in trouble if they admit to running red lights.

All pharmacists in the Canadian province of Ontario are required to be members of the Ontario College of Pharmacists. Suppose the college is interested in obtaining members' views and understanding of the 2012 Expanded Scope of Practice Regulations, which authorizes pharmacists to provide additional services, including prescribing drug products for smoking cessation and administering the publicly funded influenza vaccine. To be sure that the opinions of all practice types are represented, you choose a stratified random sample of 10 pharmacists from each practice type. Explain how you will assign labels within each practice type, and then give the label numbers for the 10 pharmacists in each of community pharmacy and industry who will be part of your sample. Use Table B starting at line 125 for community pharmacies and at line 133 for industry. (A) How will you assign labels within each practice type? Drag the correct labels to the appropriate practice type columns. (B) Use Table B starting at line 1125 to select the 10 pharmacists from community pharmacies. The sample selected, with labels in order of selection, is: (C) Use Table B starting at line 133 to select the 10 pharmacists from industry. The sample selected, with labels in order of selection, is:

(A) Community pharmacy - 00001 to 10266 Hospital or other health care facility - 0001 to 2363 Academia or government - 001 to 307 Industry - 001 to 474 Corporate office, professional practice, or clinic - 001 to 130 (B) 06565, 00795, 08727, 09517, 06489, 05007, 04197, 08796, 07051, and 09547 (C) 457, 404, 180, 333, 020, 193, 181, 320, 161, and 337

As men age, their testosterone levels gradually decrease. This may cause a reduction in lean body mass, an increase in fat, and other undesirable changes. Do testosterone supplements reverse some of these effects? A study in the Netherlands assigned 237 men aged 60 to 80 with low or low‑normal testosterone levels to either a testosterone supplement or a placebo. The report in the Journal of the American Medical Association described the study as a "double‑blind, randomized, placebo‑controlled trial." How would you explain each of these terms to someone who knows no statistics? (A) Select the correct meaning of the term "double‑blind". (B) Select the correct meaning of the term "randomized experiment". (C) Select the correct meaning of the term "placebo‑controlled trial".

(A) Double‑blind means that the treatment—testosterone or placebo—assigned to a subject was unknown to both the subject and those responsible for assessing the effectiveness of that treatment. (B) Randomized experiment means that patients were randomly assigned to receive either the testosterone supplement or a placebo. (C) Placebo‑controlled means that some of the subjects were given placebos.

Researchers from the United Kingdom studied the effect of two breathing frequencies on both performance times and several physiological parameters in front crawl swimming. The breathing frequencies were one breath every second stroke (B2) and one breath every fourth stroke (B4). Subjects were 10 male collegiate swimmers. Each subject swam 200 meters, once with breathing frequency B2 and once on a different day with breathing frequency B4. (A) How would you describe the design of this matched pairs experiment, including the randomization required by this design? (B) Could this experiment be conducted using a completely randomized design? How would the design differ from the matched pairs experiment? (C) Suppose we allow each swimmer to choose his own breathing frequency and then swim 200 meters using his selected frequency. What would be a problem with then comparing the performance of the two breathing frequencies?

(A) Each swimmer swims one time using each breathing technique, B2 and B4. A coin is tossed to determine the order in which these techniques are used. (B)In a completely randomized design, the 10 male collegiate swimmers would be assigned randomly to the two treatments, 5 swimmers using technique B2 and the other 5 using technique B4. (C) If swimmers select their own technique, it would be an observational study.

On January 30, 2015, the Los Angeles Times ran an online poll on its website and asked readers the question, If the NFL comes to Los Angeles, which team would be the best fit? The St. Louis Rams, San Diego Chargers and Oakland Raiders are all on year‑to‑year leases, unhappy with their current venues, and mulling a possible relocation to L.A. Readers clicked on one of three buttons to vote: a picture of the Oakland Raiders logo, a picture of the San Diego Chargers logo, and a picture of the St. Louis Rams logo. In all, 12,212 (33%) selected the Oakland Raiders, 2038 (6%) selected the San Diego Chargers, and 22,721 (61%) selected the St. Louis Rams. (A) What is the sample size for this poll? (B) The sample size for this poll is much larger than is typical for polls such as the Gallup Poll. Why might the poll give unreliable information, even with such a large sample size?

(A) 36,971 (B) This poll may give unreliable information because it was a voluntary response poll.

Choose at random a person aged 20 to 39 years. Ask their age and marital status (never married, married, or widowed/divorced/separated). The table gives the probability model for 12 possible answers. (A) List the outcomes that make up the event A= {The person chosen is either 20-24 years old or is married}. (B) What is P(A)? (Enter your answer rounded to three decimal places.) (C) Explain carefully why P(A) ≠ P(B) + P(C), where B is the event that the person chosen is 20-24 years old and C is the event that the person chosen is married. Select the correct explanation from the choices.

(A) A consists of the outcomes in the first column together with the outcomes in the second row. (B) P(A) = .631 (C) The sum P(B) + P(C) counts the overlap (0.027) twice, so does not equal P(A).

Comment on each as a potential sample survey question. Is the question clear? Is it slanted toward a desired response? (A) "In light of skyrocketing gasoline prices, we should consider opening up a very small amount of Alaskan wilderness for oil exploration as a way of reducing our dependence on foreign oil. Do you agree or disagree?" (B) "Do you agree that a national system of health insurance should be favored because it would provide health insurance for everyone and would reduce administrative costs?" (C) "In view of the negative externalities in parent labor force participation and pediatric evidence associating increased group size with morbidity of children in day care, do you support government subsidies for day care programs?"

(A) The question is clear and slanted toward a desired response. (B) The question is clear and slanted toward a desired response. (C) The question is not clear but is slanted toward a desired response.

Blue Ribbon taxis offers shuttle service to the nearest airport. You look up the online reviews for Blue Ribbon taxis and find that there are 1717 reviews, six of which report that the taxi never showed up. (A) Is this a biased sampling method for obtaining customer opinion on the taxi service? (B) If this is a biased sampling method, what is the likely direction of the bias?

(A) This is a biased sampling method for obtaining customer opinions because those who take the time to write an online review are likely to do so because they are upset with the service they received. (B) The direction of the bias is likely to overestimate the proportion of customers who have a negative opinion on the service.

Students at University X must be in one of the following class ranks: freshman, sophomore, junior, or senior. At University X, 35% of the students are freshman and 30% are sophomores. If a student is selected at random, the probability that he or she is either a junior or a senior is:

35%

A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos. Imagine you stick your hand into the refrigerator and pull out a piece of fruit at random. What is the chance you don't get an apple?

38/44

Select the best definition of population and sample.

A population is the complete group under study. A sample is the sub-collection of members of the population from which data are actually collected.

The sampling examples below use either the stratified or the cluster method of sampling. Select the examples that use the stratified method.

A potato field is believed to be infected with a plant disease. The field is divided into 10 equal areas, and 25 potatoes are selected from each area to be tested for the disease. A questionnaire is created to gauge student opinion on a new university cafeteria. A sample of 40 freshmen, 50 sophomores, 60 juniors, and 50 seniors is selected to fill out the questionnaire.

A sociologist studying freshmen at a major university carried out a survey, asking, among other questions, how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist, who would like a simple random sample but finds it too time‑consuming to obtain such a sample, decides to use all students enrolled in his own class. This type of sample:

All of the answer options are correct. (likely results in undercoverage of certain types of freshmen. could lead to biased conclusions. is a convenience sample.)

Researchers must be cautious when designing web‑based surveys, because these surveys are particularly sensitive to:

All of the answer options are correct. (undercoverage. voluntary response bias. nonresponse.)

A sociologist studying freshmen at a major university carried out a survey, asking, among other questions, how often students went out per week, how many hours they studied per day, and how many hours they slept at night. Which strategy will provide a simple random sample?

Contacting the registrar and obtaining a list of all freshmen, from which a random sample will then be selected.

A student is chosen at random from a statistics class. Which of the following events are disjoint?

Event A is that the student is a junior. Event B is that the student is a senior.

T/F: A control group is always a placebo group.

False

T/F: Variables cannot be confounded in an experiment.

False

The probability of event A is P(A) = 0.5, and the probability of event B is P(B)=0.7. Are A and B disjoint?

No

One hundred volunteers who suffer from depression are available for a study involving a new drug that is thought to be effective in treating depression. Researchers want to compare the new drug with the drug currently in use. The researchers believe that men and women may respond differently to the drugs. Fifty of the volunteers are selected at random and are given the new drug, and the other 50 are given the drug currently in use. A psychiatrist evaluates the symptoms of all volunteers after four weeks to determine if there has been substantial improvement in the severity of the depression. Which of the following is correct?

This is an example of a completely randomized design.

A random variable X can take on the value 0, 1, 2, or 3. Select a legitimate discrete probability distribution for X.

X = 0 P(x) = 0.5 X = 1 P(x) = 0.3 X = 2 P(x) = 0.1 X = 3 P(x) = 0.1

A random variable X can take on the value 0, 1, 2, or 3. Which of the following is a possible probability model for X ?

X = 0 | P(x) = 0.5 X = 1 | P(x) = 0.3 X= 2 | P(x) = 0.1 X = 3 | P(x) = 0.1

Suppose there are three cards in a deck: one marked with a "1,"one marked with a "2,"and one marked with a "5." You draw two cards at random, without replacement from the deck of three cards. The sample space S = {(1,2), (2,1), (1,5), (5,1), (2,5), (5,2)} consists of these six equally likely outcomes. Let X be the total of the two cards drawn. Which of the following is the correct set of probabilities for X ?

X = 3 | P = 1/3 X = 6 | P = 1/3 X = 7 | P = 1/3

An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to study the students in a calculus class. After consultation with a statistician, the educator decides to randomly allocate students to either a group that will sleep for 8 hours the night before class or 6 hours. The educator does not know which group a student belongs to when she or he comes to class. This study is:

a single‑blinded randomized study, because the educator does not know the treatment groups students belong to but the students know.

In an experiment to determine if a new type of fertilizer is better than the current "standard" fertilizer for growing corn, 20 plots of land were randomly assigned one of the two types. At the end of the growing season, the corn yields for each plot were measured. It was found that plots located closer to the highway had smaller yields than other plots. The following year, the experiment was redone, but the plots were randomly assigned to either the new or old fertilizer according to the distance from the highway. The new experiment was:

blocked.

An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to study the students in a calculus class. Each student enrolled in the class is randomly assigned to either sleeping 6 or 8 hours the night before. Each student's eye movement is then tracked throughout the lecture. The amount of time is recorded whenever the student is not focused on either the instructor or taking notes. This study has:

one factor and two treatments.

Making an experiment double‑blind:

reduces bias.

A sociologist wants to study the attitudes of American male college students toward marriage and husband‑wife relationships. She gives a questionnaire to 25 of the men enrolled in Sociology 101 at her college. Twenty of the 25 men complete and return the questionnaire. The sample in this situation is:

the 20 men who completed and returned their questionnaire.

A political party sends a mail survey to 1500 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current president. Of the 1500 surveys sent out, 480 are returned, and of these, only 120 show that the respondent is satisfied with the president's job performance. The sample is:

the 480 voters who returned the surveys.

The probability distribution of a random variable is:

the possible values of the random variable and the frequency with which the variable takes each value.

Which of the following are reasons for performing experiments?

to determine if a particular treatment has a desired effect on the response variable to establish a cause-and-effect relationship between the treatment and the response

A sample of households in a community is selected at random from the telephone directory. In this community, 4%4% of households have no telephone, 10%10% have only cell phones, and another 25%25% have unlisted telephone numbers. The sample will certainly suffer from

undercoverage.

Although the rules of probability are just basic facts about percents or proportions, we need to be able to use the language of events and their probabilities. Choose an American adult aged 2020 years and over at random. Define two events: A= the person chosen is obese B= the person chosen is overweight, but not obese According to the National Center for Health Statistics, P(A)=0.38 and P(B)=0.33 . (A) Select the correct explanation describing why events A and B are disjoint. (B) Select the correct description stating what the event A or B is. (C) What is P(A or B)? (D) If C is the event that the person chosen has normal weight or less, what is P(C)?

(A) Event B rules out obese subjects. (B) A or B is the event that the person is overweight or obese. (C) P(A or B) = 0.71 (D) P(C) = 0.29

Classify each description as either an observational study or an experiment. (A) In a sleep study designed to test whether a new supplement helps individuals sleep longer, a computer randomly assigns each participant either to a group receiving the supplement or to a group receiving an inactive pill. (B) A poll is conducted in which 1000 registered voters are randomly selected from Florida. The voters are asked if they approve of the governor's stance on environmental issues. (C) Agricultural scientists seek to test the effects of a new pesticide on corn crops. Half of the participating farmers are assigned the new pesticide and the other half continue using an alternative pesticide. The crops are compared after two seasons. (D) Students from 10 schools are divided into groups by researchers, those that participate in musical activities and those that do not. Student grades are monitored for a year to determine if those who participate in musical activities achieve higher grades. (E) A cancer study began by surveying male patients between the ages of 35 and 55 at a local hospital about their exercise routine. The health of these men is tracked over 10 years to determine the effect of exercise on lowering the risk of cancer. (F) Researchers studying how exercise affects cholesterol sample 50 people who exercise regularly and 50 who do not. Blood was drawn from each person and serum cholesterol was measured.

(A) Experiment (B) Observational Study (C) Experiment (D) Observational Study (E) Observational Study (F) Observational Study

Textese is a sound‑based form of spelling to reduce the time of text messaging and the number of characters, using textisms such as "2day" for "today." Educators and parents have long been concerned about the effect of textese on spelling ability. A study of Australian children aged 10-12 considered the effect of text entry method on the spelling subtest of the Wide Range Achievement Test (WRAT). Multipress is the original entry method in which three or four letters are assigned a key and the key must be pressed one to four times to produce each letter. Predictive is a single key‑press per letter with suggested completion of the word. A total of 86 children took the WRAT and were classified according to text entry method usually used: multipress, 27 students; predictive, 45 students; or non‑texter, 12 students. (A) Identify the explanatory and response variables by placing each variable into the correct category. (B) Select an answer choice that correctly explains whether this is an observational study or an experiment. (C) The differences among the three texting methods were not statistically significant. Select the explanation that describes what "no significant difference" means in describing the outcome of this study.

(A) Explanatory - Text method used Response - WRAT score (B) This is an observational study because the researchers did not assign what text methods were used by the subjects. (C) "No significant difference" means that the observed differences could be due to chance. There was no systematic difference in spelling ability among the three groups.

In many settings, the "rules of probability" are just basic facts about percents. The Graduate Management Admission Test (GMAT) website provides information about the undergraduate majors of those who took the test in specific years. Suppose that in a certain year: 55% majored in business or commerce; 17% majored in engineering; 16% majored in the social sciences; 6% majored in the sciences; 4% majored in the humanities; and 2% listed some major other than the preceding. Assume there are no double majors. (A) What percent of those who took the test in this certain year majored in either engineering or the sciences? (Enter your answer as a percent and as a whole number.) (B) Select the probability rule you used to find the answer. (C) What percent of those who took the test in this certain year majored in something other than business or commerce? (Enter your answer as a percent and as a whole number.) (D) Select the probability rule you used to find the percentage of undergraduates who majored in something other than business or commerce.

(A) P = 23 (B) Rule 3. Two events A and B are disjoint if they have no outcomes in common and so can never occur together. If A and B are disjoint, P(A or B) = P(A) +P(B) (C) P = 45 (D) Rule 4. For any event A, P(A does not occur) = 1 - P(A).

The annual Atlantic Coast Conference men's basketball tournament has temporarily taken Joe's mind off of the Cleveland Indians. He says to himself, "I think that Notre Dame has probability 0.05 of winning. North Carolina's probability is twice Notre Dame's, and Duke's probability is four times Notre Dame's." (A) What is Joe's personal probability for North Carolina? (Enter your answer as a proportion rounded to one decimal place.) (B) What is Joe's personal probability for Duke? (Enter your answer as a proportion rounded to one decimal place.) (C) What is Joe's personal probability that 1 of the 12 teams other than Notre Dame, North Carolina, and Duke will win the tournament? (Enter your answer as a proportion rounded to two decimal places.)

(A) P(North Carolina wins) = .1 (B) P(Duke wins) = .2 (C) P = .65

Choose a student at random from a large statistics class. For each question, select the appropriate sample space S for the situation. (A) Does the student own a car or not? Select the appropriate sample space S for this situation. (B) What are the last three digits of the student's cell phone number? Select the appropriate sample space S for this situation. (C) What is the student's birth month? Select the appropriate sample space S for this situation.

(A) S = {owns a car, does not own a car} (B) S = {000, 001, 002, ..., 999} (C) S = {January, February, ..., December}

The Denver Police Department wants to know if Hispanic residents of Denver believe that the police use racial profiling when making traffic stops. A sociologist prepares several questions about the police. The police department chooses an SRS of 200 mailing addresses in predominantly Hispanic neighborhoods and sends a uniformed Hispanic police officer to each address to ask the questions of an adult living there. (A) What are the population and the sample? (B) Why are the results likely to be biased even though the sample is an SRS?

(A) The population is all Hispanic residents of Denver. The sample is the 200 adults who answered the questions at the selected mailing addresses. (B) This may suffer from response bias, since the officer doing the questioning was also Hispanic.

In 2010, the Physicians Foundation conducted a survey of physicians' attitudes about health care reform, calling the report "a survey of 100,000 physicians." The survey was sent to 100,000 randomly selected physicians practicing in the United States: 40,000 via post‑office mail and 60,000 via email. Assume that a total of 2437 completed surveys were received. (A) What population is sampled in this survey? (B) What is the sample size for this survey? (Enter your exact answer as a whole number.) (C) What is the rate of nonresponse for this survey? (Give your answer as a percent rounded to two decimal places.) (D) Why is it misleading to call the report "a survey of 100,000 physicians"?

(A) The population is all physicians practicing in the United States. (B) n = 2437 (C) nonresponse rate: 97.56 (D) It is misleading because only 24372437 responses were received.

What are the effects of low‑fat food labels on food consumption? Do people eat more of a snack food when the food is labeled as low‑fat? The answer may depend both on whether the snack food is labeled low‑fat and whether the label includes serving‑size information. An experiment investigated this question using university staff, graduate students, and undergraduate students at a large university as subjects. Subjects were asked to evaluate a pilot episode for an upcoming TV show in a theater on campus and were given a cold 24‑ounce bottle of water and a bag of granola from a respected campus restaurant called The Spice Box. They were told to enjoy as much or as little of the granola as they wanted. Depending on the condition randomly assigned to the subjects, the granola was labeled as either "Regular Rocky Mountain Granola" or "Low‑Fat Rocky Mountain Granola." Below this, the label indicated "Contains 1 Serving" or "Contains 2 Servings" or it provided no serving‑size information. Twenty subjects were assigned to each treatment, and their granola bags were weighed at the end of the session to determine how much granola was eaten. (A) How many factors and treatments are there? (B) How many subjects does the experiment require?

(A) There are two factors and six treatments. (B) 120 subjects.

Identify the type of sampling bias guaranteed to occur in each of the sampling schemes, based on the information provided. Some sampling schemes may incur multiple types of bias. (A) A political poll is conducted by contacting people on landline phones. The pollsters did not keep track of how many people they contacted who did not respond. (B) A political poll is administered by contacting people on landline phones. The pollsters contacted 10,000 households, and 2366 individuals agreed to speak with the caller. (C) A political poll is conducted by setting up a booth at a local shopping mall and inviting passersby to share their opinions. (D) A political poll asks the question, "If you found out that Candidate A was given a large sum of money by Special Interest Group B, would that change your opinion of how hypocritical Candidate A is?"

(A) Undercoverage (B) Undercoverage, nonresponse (C) self-selection, undercoverage (D) Response

Choose at random a person aged 20 to 39 years. Ask their age and marital status (never married, married, or widowed/divorced/separated). Offered is the probability model for 12 possible answers. (A) Is this a legitimate finite probability model? Select the correct description. (B) What is the probability that the person chosen is a 20‑ to 24‑ year‑old who is married? (Enter your answer rounded to three decimal places.) (C) What is the probability that the person chosen is 20-24 years old? (Enter your answer rounded to three decimal places.) (D) What is the probability that the person chosen is married? (Enter your answer rounded to three decimal places.)

(A) Yes. This is a legitimate finite probability model because each probability is between 0 and 1, and all sum to 1. (B) P⁡(20‑ to 24‑year‑old who is married) = .027 (C) P(20-24 year old) = .260 (D) P⁡(married) = .398

Choose an adult age 18 or over in the United States at random and ask, "How many cups of coffee do you drink on average per day?" Call the response X for short. Based on a large sample survey, a probability model for the answer you will get is given in the table. Number(N): 0 | Probability(P): 0.36 N: 1 | P: 0.26 N: 2 | P: 0.19 N: 3 | P: 0.08 N: 4 or more | P: 0.11 (A) Is this a valid finite probability model? (B) Describe the event X < 4 in words. (C) What is P⁡(X < 4)? (Enter your answer rounded to two decimal places.) (D) Express the event "have at least one cup of coffee on an average day" in terms of X. (E) What is the probability of this event? (Enter your answer rounded to two decimal places.)

(A) Yes. This is a valid finite probability model, because each probability is between 0 and 1 and all sum to 1. (B) The event X<4 is the event in which an individual drinks fewer than 4 cups of coffee on average per day. (C) P⁡(X < 4) = .89 (D) {X ≥ 1} (E) The probability of this event is .64

Do more creative store‑window displays affect shopper behavior? Six main‑street retailers selling everyday fashion items were used in the study. Pretests with shoppers showed the six stores to be comparable on brands and consumer perceptions of value for the money. Three of the retailers had more creative windows in terms of displaying items in a more innovative and artistic manner versus the less creative windows, which had a more concrete focus on the items on display. All display windows were of similar dimensions. Observers, in close proximity but out of sight of shoppers, watched their behavior as they passed the display windows, and for each shopper it was recorded whether they looked at the window or entered the store. A total of 863 shoppers passed the more creative windows and 971 passed the less creative windows. The study found that a higher percentage of shoppers looked at and entered the stores with the more creative windows, with the differences in shoppers' behavior between the more/less creative windows being statistically significant. In their paper, the authors of the study also reported the results of a second study to compare more/less creative window displays. In this second study, the authors used the same retailer and displayed the same merchandise in exactly the same way for both the more and less creative window displays. The differences between the window displays only involved the design surrounding the merchandise being more or less creative, not the content. Subjects, recruited from the retailer's customer database, were randomly assigned to view an image of one of the two window displays. After viewing the image, subjects answered questions about whether the products in the display made them want to enter the store. (A) Is this second study an observational study or an experiment? (B) What are the explanatory and response variables in the second study? Despite the results being statistically significant, the authors stated in their article about the first study: "The field study did not support an examination of why more creative store windows led consumers to enter the stores. ... The use of actual retailers' real store windows meant that the level of creativity was not the only variable that differed among the retailers and their windows." (C) How does the second study address some of those drawbacks? Does either study suffer from a lack of realism? Choose the best explanation.

(A) experiment (B) The explanatory variable is the window display (more or less creative), and the response variable is the desire to enter the store. (C) The drawbacks in the first study were that it was an observational study and that it did not control for confounding variables (such as variations in merchandise and potential customers). The second study addresses these drawbacks by using the same retailer and the same merchandise, and by only changing the creativity of the window display. Both studies suffer from a lack of realism, because the study design does not duplicate the conditions of all retailers. Rather, we can only appropriately draw conclusions for similar retailers within this same geographic region.

The list of individuals from which a sample is actually selected is called the sampling frame. Ideally, the frame should list every individual in the population, but in practice, this is often difficult. A frame that leaves out part of the population is a common source of undercoverage. Suppose that a sample of households in a community is selected at random from the telephone directory. (A) Which households are omitted from this frame? (B) What types of people do you think are likely to live in these households? These people will probably be underrepresented in the sample. Select all that apply. It is usual in telephone surveys to use random digit dialing equipment that selects the last four digits of a telephone number at random after being given the exchange (the first three digits). (C) Which of the households underrespresented in the sample will be included in the sampling frame by random digit dialing?

(A) households without telephones, those with only cell phones, and those with unlisted numbers (B) those who do not wish to have their phone numbers published those who choose not to have landline phones those who cannot afford a phone (C) Those with unlisted numbers will be included, in some percentage, while those people who do not have phones will not be included at all

Every year, the veterinary hospital at a major research university treats a number of horses that have stones called enteroliths in their guts. A sample of 20 years shows that on average about 2% of horses presenting at the veterinary hospital are treated for enteroliths. Some breeds of horses seem more prone to developing enteroliths than others. Below is a table with the distribution of enteroliths among the breeds. Breed(B): Arabian | Probability(P): 0.3 B: Thoroughbred | P: 0.2 B: Appaloosa | P: 0.15 B: Morgan | P: 0.10 B: Quarter Horse | P: ? The probability that a horse arriving at the veterinary hospital is not an Arabian or a quarter horse is:

0.45

An urn contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and count the number of red marbles in the 4 picks, the probabilities associated with this experiment are P(0) = 0.24, P(1) = 0.41, P(2) = 0.265, P(3) = 0.076, and P(4) = 0.009. The probability of less than 2 red marbles is:

0.65

You are using the table of random digits to choose a simple random sample of six students from a class of 30 students. You label the students 01 to 30 in alphabetical order, and then select a simple random sample. Which is a possible sample that could be obtained?

04, 18, 07, 13, 02, 05

Suppose we have a loaded die that gives the outcomes 1 through 6 according to the following probability distribution. Die Outcome(DO): 1 | Probability(P): 0.1 DO: 2 | P: 0.2 DO: 3 | P: 0.3 DO: 4 | P: 0.2 DO: 5 | P: ? DO: 6 | P: 0.1 What is the probability of rolling a 5?

1/10

In an experiment for a new drug, to determine the most effective dose and method of administration, patients were randomly assigned to a 5‑, 10‑, 15‑, or 20‑mg dose of the drug. In addition, the method of delivery of the drug (pill, skin patch, or nasal mist) was considered. In this experiment, how many treatments were there?

12

I want to take a survey of students currently enrolled in my statistics course. There are 250 of them, so I number them from 001 to 250 in alphabetical order. 69041/65817/87174/09514/8174/06423/93758/23612/17894 If I use the portion of the given random number table to select the first five students to be interviewed, which five numbers will be selected?

174, 095, 148, 064, 239

In an experiment for a new drug, patients were randomly assigned either to a placebo or to the active drug. In addition, the method of delivery of the drug (pill, skin patch, or nasal mist) was considered. In this experiment, how many factors were there?

2

Imagine that a traffic intersection has a stop light that repeatedly cycles through the normal sequence of traffic signals (green light, yellow light, and red light). In each cycle the stop light is green for 30 s, yellow for 3 s, and red for 50 s. Assume that cars arrive at the intersection uniformly, which means that in any one interval of time, approximately the same number of cars arrive at the intersection at any other time interval of equal length. Determine the probability that a car arrives at the intersection while the stop light is yellow. Give your answer as a percentage precise to two decimal places.

3.61 %

Select the studies below that use a matched pairs experimental design.

A study is designed to test which of two new methods is better at teaching children in first grade to read. Children in first grade are selected at random and are paired together based on reading ability. One student is taught with one method, and the other is taught with another method. A scientist seeks to compare the ability of a new hand sanitizer to eliminate bacteria against the hand sanitizer currently in use. Each subject uses the new hand sanitizer on one randomly chosen hand and the sanitizer currently in use on the other.

The local genealogical society in Coles County, Illinois, has compiled records on all 55,914 gravestones in cemeteries in the county for the years 1825 to 1985. Historians plan to use these records to learn about African Americans in Coles County's history. They first choose an SRS of 395 records to check their accuracy by visiting the actual gravestones. (A) Select the correct method to label the 55,914 records. (B) Use Table B, beginning at line 141, to choose the first six records for the SRS. Which of the choices would be the randomly sampled records?

A. Assign five‑digit labels to each record from 00001 to 55914. B. 35964,23822,50842,53372,50232,44575

A university's housing and residence office wants to know how much students pay per month for rent in off‑campus housing. The university does not have enough on‑campus housing for students, and this information will be used in a brochure about student housing. They obtain a list of the 12,304 students who live in off‑campus housing and have not yet graduated and mail a questionnaire to 200 students selected at random. Only 78 questionnaires are returned. (A) What is the population in this study? Be careful: about what group do they want information? (B) What is the sample? Be careful: from what group do they actually obtain information?

A. The population is all college students who live in off‑campus housing. B. The sample is the 7878 students who live in off‑campus housing and returned the questionnaire.

The figure displays several possible finite probability models for rolling a die. We can learn which model is actually accurate for a particular die only by rolling the die many times. However, some of the models are not valid. That is, they do not obey the rules. Which are valid and which are not? Select the best answer, with the correct explanation of what is wrong in the case of the invalid models.

Only Model 2 is valid. Models 1, 3, and 4 have probabilities that do not sum to 1. Model 4 has some probabilities that are greater than 1.

You read online that the probability of being dealt four‑of‑a‑kind in a five‑card poker hand is 1/4165. Explain carefully what this means. In particular, explain why it does not mean that if you are dealt 4165 five‑card poker hands, one will be four‑of‑a‑kind. Select the best explanation from the choices.

The probability is actually saying that in the long run, with a large number of five‑card poker hands, the fraction in which you will be dealt a four‑of‑a‑kind is 1/4165.

Select all of the statements that are axioms of probability.

The probability of the sample space is 1. The probability of any event is between 0 and 1 inclusively. If two events A and B are mutually exclusive (disjoint), then P(A or B) = P(A)+P(B).

Determine whether each of the random variables is continuous or discrete.

Continuous: The amount of time a randomly selected person can run before tiring, The average number of visits to a particular fast food restaurant in a given year by random sample of US adults Discrete: The value shown when a six-sided die is rolled, The number of tests taken in a given month by a randomly selected teenager, The number of visits to a website in a randomly selected hour of time

A firm wants to understand the attitudes of its minority managers toward its system for assessing management performance. The table consists of a list of all the firm's managers who are members of minority groups. Label the names alphabetically, as ordered in the table: top down and then from left to right. Use Table B at line 127 to choose three managers to be interviewed in detail about the performance appraisal system. Which three names are chosen?

Deis, Fernandez, Gemayel

Classify each described variable as discrete or continuous. Not every variable will be one or the other, but no variable can be both.

Discrete: Number of red marbles in a jar, Outcome of rolling a six-sided number cube Continuous: Temperature in Ohio, Volume of a cube Not used: Breed of a dog

A drug manufacturer conducted a study of a new antidepressant medication. The manufacturer sent an advertisement to all of the registered psychiatrists in a certain city seeking volunteers for the study from patients diagnosed with depression. Each participant completed a survey designed to measure depression, received the explanation that the new drug was intended to help alleviate the symptoms of depression, and was prescribed the drug for 12 weeks. At the end of the 12 weeks, the subjects were asked to complete the same survey. The researchers found a significant decrease in the subjects' signs of depression as measured by the survey. Which of the following is true about this study?

It may have suffered from the placebo effect.

Classify the experiments according to their experimental designs. Some designs may be used more than once. Exercise. A sample of 40 adults was separated into men and women. The members of each group were randomly assigned to two different exercise routines. The responses of each adult were recorded at the completion of the experiment. Vegetables. A sample of 50 vegetable plants was grouped into pairs of similar individuals based on type and size. Then, within these pairs, each vegetable plant was assigned to a different fertilizer. After three weeks, the responses of each pair were analyzed to compare the effects of the fertilizers. Track spikes. Twenty runners were assigned to run two laps, once with track spikes and once without track spikes. The order of treatments was randomized for each runner. The lap times of each runner were recorded to compare the effects of the two different treatments. Lakes and birds. A random sample of 100 lakes was selected in a particular state. To compare the diversity of birds among the lakes, the count and species identity of all birds were recorded for each lake over a 24-hour period. Medical treatments. Eighteen volunteers were randomly assigned to three different medical treatments. At the conclusion of each treatment, the response of each volunteer was measured.

Exercise - block design (not matched pairs) Vegetables - matched pairs design Track Spikes - matched pairs design Lakes and Birds - observational study Medical Treatments - completely randomized design

The probability of event A is P(A) = 0.3, and the probability of event B is P(B) = 0.25. Are A and B disjoint?

It is impossible to determine from the information given.

Every time that a student attended office hours one semester, a statistics professor asked if the student was satisfied with his teaching. Over 90% of the students said that they were satisfied with his teaching. Does this provide convincing evidence that the majority of the students in the professor's class are satisfied with his teaching?

No, this is an example of response bias.

Consider the probability distribution for a random variable X. X = 3 P(x) = 0.15 X = 4 P(x) = 0.10 X = 5 P(x) = 0.20 X = 6 P(x) = 0.25 X = 7 P(x) = 0.30 Find the probability P(X ≤ 5.5). Use decimal notation. Give your answer to two decimal places.

P (X ≤ 5.5) = .45

Suppose that in a ring toss game at a carnival, players are given 5 attempts to throw the rings over the necks of a group of bottles. The table shows the number of successful attempts for each of the players over a weekend of games. Complete the probability distribution for the number of successful attempts, X. Please give your answers as decimals, precise to two decimal places. Successes | # of players 0 | 31 1 | 68 2 | 26 3 | 16 4 | 6 5 | 2

P(X = 0) = .21 P(X = 1) = .46 P(X = 2) = .17 P(X = 3) = .11 P(X = 4) = .04 P(X = 5) = .01

Students at a particular university must be in exactly one of the class ranks: freshman, sophomore, junior, or senior. At this university, 35% of students are freshmen and 30% are sophomores. If a student is selected at random, what is the probability that the student is either a junior or a senior?

P(junior or senior) = 35

Two antigens, antigen A and antigen B, determine the four major human blood groups: A, B, AB, and O. The table below shows the percentage distribution of blood groups for the Caucasian population in the United States. Blood Group(BG): A | Antigen(A): A | Distribution(D): 40% BG: B | A: B | D: 11% BG: AB | A: A,B | D: 4% BG: O | A: None | D: 45% Calculate the probability of randomly picking a blood sample that does not contain antigen A, that is, a blood sample that belongs to either blood group B or blood group O. Give your answer as a whole number percentage.

Probability = 56

I select two cards from a standard deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the following is an appropriate sample space S for the possible outcomes?

S = {(red, red), (red, black), (black, red), (black, black)}

A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos. Imagine you stick your hand into the refrigerator and pull out a piece of fruit at random. What is the sample space for your action?

S = {apple, orange, banana, pear, peach, plum, mango}

On a recent visit to New York City, Sam made a list of 200 museums, cultural institutions, and historic sites that he would like to visit on a single sheet of paper. He only had time to visit four of these places, and decided to use the method of systematic random sampling to select the four places to visit. Determine which method best describes a systematic random sample.

Sam assigns a number from 1 to 200 to each place. Next, he uses a random number generator to choose a number between 1 and 50. He chooses that place and every fiftieth place after that until he has chosen a total of four.

Price promotions are commonly used by retailers to motivate consumers to make a purchase. Both the amount off and percentage off are in widespread use, and research on when to use each method has been mixed. The current study evaluated intent to purchase a lower‑priced item and a higher‑priced item using either a fixed amount or a percentage off. For the lower‑priced item, participants saw a promotion for balloons regularly selling for 48 pesos, but on sale with either a 12-peso or a 25% discount. The higher‑priced item was a 480-peso sweater on sale with either a 120-peso discount or a 25% discount. One hundred and fifty‑one students were randomly assigned to the treatments and responded to two questions measuring value perceptions: "I would be saving a lot of money if I made my purchase at this store," and "This store is selling the advertised product at a considerable discount." Participants answered each question on the scale of 1 ("strongly disagree") to 5 ("strongly agree"). Identify the subjects, the factors, the treatments, and the response variables for this experiment. Sort the information into their respective categories by dragging each token to the correct column.

Subject(s) - Students Factor(s) - Price of item, Type of discount Treatment(s) - The combinations of low and high prices and the amount off or percentage off discount Response variable(s) - The ratings on each of the two questions

Select the experiments that use a completely randomized design.

To test an epidermal treatment on fish in polluted stream water, 50 fish with epidermal abrasions from the same stream are randomly placed into two aquariums. One aquarium receives the epidermal treatment, and the other receives no treatment. In a hematology study designed to test whether a new supplement helps individuals increase hemoglobin levels, a computer randomly assigns participants into a group receiving the supplement and a group receiving an inactive pill.

One hundred sixty people who suffer from painful diabetic neuropathy have volunteered to participate in a study. Eighty are selected at random and are given the drug gabapentin, which, although originally intended to prevent epileptic seizures, has properties that may make it useful to alleviate neuropathy. The remaining participants are given a placebo. A neurologist evaluates the symptoms of all volunteers after two months to determine if there has been substantial improvement in the severity of the symptoms. Suppose the volunteers were first divided into men and women, and then half of the men were randomly assigned to the new drug and half of the women were assigned to the new drug. The remaining volunteers received the placebo. This would be an example of:

a block design.

An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to study the students in a calculus class. The educator has contacted a statistician to help plan a proper study for the assessment of cause and effect. The type of study required is called:

a completely randomized design.

A market researcher wants a large sample size for her survey, so she decides to stand in the food court of a mall during Christmas shopping season. Within the first three hours, she asks 150 shoppers about their automobile preferences. This is an example of:

a convenience sample.

A sociologist studying freshmen at a major university carried out a survey, asking, among other questions, how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist used an introductory sociology class to carry out the survey and asked only the freshmen to answer the questions. The sample is called:

a convenience sample.

In an experiment to determine if a new type of fertilizer is better than the current "standard" fertilizer for growing corn, 20 plots of land were randomly assigned one of the two types. At the end of the growing season, the corn yields for each plot were measured. It was found that plots located closer to the highway had smaller yields than other plots. In this experiment, distance from the highway is:

a lurking variable.

To compare the effectiveness of two detergents at removing common stains (such as mustard, grass, and blood), researchers prepared stained clothing samples. Each sample was cut in half and each of the two pieces was assigned, using a random mechanism, to one of the two detergents. After washing, the two halves were compared with each other. Which term best describes the experimental design used in this study?

a matched pairs experiment

A researcher is interested in the cholesterol levels of adults in the city in which she lives. A cholesterol screening program is set up in the downtown area during lunch hour. Individuals can walk in and have their cholesterol determined for free. A total of 173 people use the service, and their average cholesterol level is 217.8. The sample obtained is an example of:

a sample probably containing bias and undercoverage.

Select the best definition of multistage sampling. Multistage sampling is

a sampling procedure that either employs multiple sampling methods to select a sample, or which uses one sampling method multiple times to select a sample

Which choice best describes a simple random sample?

a selection of members from a population in such a way that every possible sample of the same size has an equal chance of being chosen

Jean is planning to take a foreign language class. To research how satisfied other students are with their foreign language classes, she decides to take a sample of 50 such students. The university offers classes in five languages: Spanish, German, Russian, French, and Japanese. She will select a random sample of 10 students from each language class. Which term best describes the sampling technique Jean is using?

a stratified random sample

For a large lecture class, a professor decides to make his class notes available on the Internet. During one of his lectures, he mentions that he would like some feedback on the usefulness of these notes on the Internet and asks students to leave written comments in his mailbox. He gets comments from 23 students and most indicate that having the notes readily available helped them in the course. This is an example of:

a voluntary response sample.

Researchers collected seeds from a certain wild plant and planted them in groups of kin (seeds of the same mother plant) or non‑kin (seeds from different plants). Each group of four seeds was planted either together in one pot or in a cluster of four pots that contained the same volume of soil. After eight weeks, the researchers measured the amount of roots each plant had produced. They found that related plants grown together in one pot produced smaller root systems so as not to compete with one another. Plants grown in separate containers and non‑kin plants grown in a single container had 15% more roots. Was this a sample survey, an observational study, or an experiment?

an experiment

Researchers investigated reasons why different species of birds begin to sing at different times of the morning. They captured and examined birds of 57 species at different sites around England. They reported that there is a strong relationship between the diameter of a bird's eye and the time it starts singing in the morning: birds with larger eyes tend to start singing earlier. This is an example of:

an observational study, not an experiment.

Researchers have noted that children who learn to play a musical instrument through taking lessons have higher average SAT scores, higher average GPAs, and higher average class ranks. This is an example of:

an observational study.

To determine if living next to high‑voltage power lines increases the chance of getting cancer, researchers selected several homes at random, and then determined whether each home was within 50 yards of a high‑voltage power line and whether anyone in the home had cancer. They compared the proportion of cancer cases in homes within 50 yards of a high‑voltage power line with the proportion of cancer cases in homes more than 50 yards from a high‑voltage power line. This is:

an observational study.

I choose a card at random from a well-shuffled deck of 52 cards. There is a 1/4 probability that the card chosen is a spade, a 1/4 probability that the card is a heart, a 1/4 probability that the card is a diamond, and a 1/4 probability that the card is a club. Both spades and clubs are black cards, whereas hearts and diamonds are red. The events card is a heart and card is a club are:

disjoint events.

Choose the correct meaning of a double-blind, placebo-controlled experiment. In a double-blind, placebo-controlled experiment,

neither the subjects nor the people administering the treatments know who received a treatment and who received an inactive substance.

A sociologist studying freshmen at a major university carried out a survey, asking, among other questions, how often students went out per week, how many hours they studied per day, and how many hours they slept at night. Students will often overstate the number of hours studied, because they do not want to admit to not studying enough. This type of distortion is called:

response bias.

Researchers have noted that children who learn to play a musical instrument through taking lessons have higher average SAT scores, higher average GPAs, and higher average class ranks. The various measures of academic success described are examples of:

response variables.

We need to survey a sample of the 300 passengers on a full flight from Cincinnati to London. We randomly generate 30 seat numbers and survey the passengers who sit there. What best describes the sampling technique being used?

simple random sample

Researchers collected seeds from a certain wild plant and planted them in groups of kin (seeds of the same mother plant) or non‑kin (seeds from different plants). Each group of four seeds was planted either together in one pot or in a cluster of four pots that contained the same volume of soil. After eight weeks, the researchers measured the amount of roots each plant had produced. They found that related plants grown together in one pot produced smaller root systems so as not to compete with one another. Plants grown in separate containers and non‑kin plants grown in a single container had 15% more roots. What is the response variable?

the amount of roots the plant produced

In a study of human development, investigators showed two different types of movies to groups of children. Crackers were available in a bowl, and the investigators compared the number of crackers eaten by children watching both movies. One type of movie was shown at 8 a.m., right after the children had breakfast and the other type of movie was shown at 11 a.m., right before the children were to have lunch. It was found that more crackers were eaten during the movie shown at 11 a.m. than during the movie shown at 8 a.m. The investigators concluded that the different types of movies had different effects on appetite. The treatment in this experiment is:

the different kinds of movies.

A university financial aid office wants to estimate how much their students typically spend on textbooks each term. It sends an email survey to 350 randomly selected students asking them to report the amount they spent on textbooks this term. What is the population of interest in this study?

the entire student body of the university

A sociologist studying freshmen at a major university carried out a survey, asking, among other questions, how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist used an introductory sociology class to carry out the survey, instructing the students to participate only if they were freshmen. The sample consists of:

the freshmen in the class who answered the survey questions.