STA2023 - Exam 1 Review

(Module 3) Find the sample standard deviation of the following data set, using the statistical functions on your calculator. 0.2315 0.4725 0.87650.4865 0.5326 0.7976 a. 0.2358 b. 0.2153 c. 0.5662 d. 0.1895

a. 0.2358

(Module 14) Scores on an exam follow an approximately Normal distribution with a mean of 74.3 and a standard deviation of 7.4 points. What percent of students scored below 70 points? a. 0.2810 b. 0.719 c. 0.58 d. 0.42 e. 0.2483 f. 0.7517

a. 0.2810

(Module 6) A least squares regression line was created to predict the Exam 3 score of STA 2023 students based on their Exam 1 score. The study found that the value of R-squared was 28.8% and the least squares regression line was yhat=50.57+0.4845x. What is the correlation coefficient, r? a. 0.54 b. -0.54 c. 5.37 d. -5.37 e. 0.08 f. -0.08

a. 0.54

(Module 8) Suppose that we were going to conduct a study to determine if there is an increased risk of getting lung cancer based on whether a person smokes or not. In the group of smokers(1) , we find that 10 out of 100 get lung cancer. In the non-smokers group(2), we find that 5 out of 200 get lung cancer. What is the sample relative risk? a. 4 b. 0.1 c. 0.05 d. 0.4

a. 4

(Module 16) Scores on an exam follow an approximately Normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. What percent of students scored above 60 points? a. 99.64% b. 0.0036 c. 2.69% d. 1.69% e. 98.31%

a. 99.64%

(Module 12) Given the following: P(A) =0.3 P(B) = 0.2 P(A and B) = 0.4 Which of the following is true? a. A and B are neither disjoint nor independent. b. A and B are independent. c. A and B are disjoint. d. A and B are independent and disjoint.

a. A and B are neither disjoint nor independent.

(Module 3) Scores on an exam follow an approximately bell shaped distribution with a mean of 76.4 and a standard deviation of 6.1 points. Approximately, what percentage of the data is between 64.2 points and 88.6 points? a. 68% b. 95% c. 99.7% d. 50%

b. 95%

(Module 5) Mark the following statement as true or false. "if you change the units of one of the variables, the value of correlation will increase or decrease. " a. True b. False

b. False

(Module 5) A sociologist is interested in seeing if people's satisfaction with their married life (very satisfied, somewhat satisfied, fairly satisfied, not satisfied) is associated with their parent's marital status (divorced, widowed, still married). Which is more naturally the explanatory variable? a. Satisfaction with married life b. Parent's marital status

b. Parent's marital status

(Module 15) A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independent and that she throws 5 shots. Let X = the number of shots that he makes. What is the sample space for X? a. S: {makes it, not} b. S: {0, 1, 2, 3, 4, 5} c. S: (0, 5) d. S: [0, 5]

b. S: {0, 1, 2, 3, 4, 5}

(Module 3) If the mean is equal to the median, which of the following is true? a. There is a mistake. The mean can not equal the median. b. The data is probably symmetric. c. The data is probably skewed. d. The data has to be bell shaped distributed

b. The data is probably symmetric.

(Module 15) What are the four conditions necessary for X to have a Binomial Distribution? Mark all that apply. a. X counts the number of trials until you get a success. b. The probability of success, p, is constant from trial to trial. c. You must have at least 10 successes and 10 failures. d. There can only be two outcomes, success and failure e. X can take on any value in an interval. f. The trials must be independent. g. There are n set trials.

b. The probability of success, p, is constant from trial to trial. d. There can only be two outcomes, success and failure f. The trials must be independent. g. There are n set trials.

(Module 9) A study was interested in determining if walking 2 miles a day lowered someone's blood pressure.Twenty people's blood pressure was measured. Then, ten of these individuals were randomly selected from the initial 20 people. These ten were told to walk 2 miles a day for 6 weeks and to eat as they normally did. The other ten were told to eat as they normally would. After six weeks, their blood pressure levels were measured again. What type of study is this? a. observational study b. experiment c. anecdotal evidence

b. experiment

(Module 7) A high positive correlation is found between college students' age and their GPA. However, if one student aged 44 with a high GPA is omitted from the study, the correlation all but disappears. This is an example of: a. extrapolation b. misuse of cause and effect c. influential outlier

b. misuse of cause and effect

(Module 7) A study found a strong positive correlation between ice cream consumption and the number of violent crimes committed each month.Some people may take this as an indication of how refined sugars make people violent. This is an example of: a. extrapolation b. misuse of cause and effect c. influential outlier

b. misuse of cause and effect

(Module 7) People who use artificial sweeteners in place of sugar tend to be heavier than people who use sugar, thus we can conclude that artificial sweeteners are detrimental to weight loss efforts. This is an example of: a. extrapolation b. misuse of cause and effect c. influential outlier

b. misuse of cause and effect

(Module 13) Tests for tuberculosis like all other diagnostic tests are not perfect. QFT-G is one of such tests for tuberculosis. Suppose that for the population of adults that is taking the test, 5% have tuberculosis. The test correctly identifies 74.6% of the time adults with a tuberculosis and correctly identifies those without tuberculosis 76.53% of the time. Suppose that POS stands for the test gives a positive result and S means that the adult really has tuberculosis. What is the probability of an adult getting a POS result and truly NOT having tuberculosis? a. 0.0373 b. 0.0127 c. 0.2230 d. 0.7270

c. 0.2230

(Module 12) The probability of selecting a particular color almond M&M (according to their website) from a bag of M&Ms is listed below. Let the probability of selecting each color be represented as BR= Brown, Y = Yellow, R = Red, BL = Blue, O= Orange, and G= Green. Suppose that you are selecting one M&M. P(brown) = 0.1 P(yellow) = 0.2 P(red) = 0.1 P(blue) = 0.2 P(orange) = 0.2 P(green) = 0.2 What is the P(R or G)? a. 0.2 b. 0.7 c. 0.3 d. 0.1

c. 0.3

(Module 15) A teacher is monitoring how often students visit the website of the course during the day. She finds the following probability distribution. Find the expected number of visits to the course website. P(0) = 0.45 P(1) = 0.35 P(2) = 0.15 P(3) = 0.05 a. 0.75 b. 0.25 c. 0.80 d. 0.85

c. 0.80

(Module 16) Using the Binomial Distribution Applet answer the following question, A basketball player makes 40% of his shots from the free throw line. Suppose that each of his shots can be considered independent and that he throws 3 shots. Let X = the number of shots that he makes. What is the probability that he makes 2 shots or less? a. 0.216 b. 0.648 c. 0.936 d. 1

c. 0.936

(Module 16) Scores on an exam follow an approximately Normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. What is the minimum score you would need to be in the top 7%? a. 0.93 b. 1.48 c. 85.4 d. 81.4

c. 85.4

(Module 9) At UF, there are always a few days between the end of classes and the beginning of final exams. These days are meant as a study period, but some students would prefer to take the exams as soon as possible, to have a longer vacation - in fact, some students even leave Gainesville during those days as a mini-vacation. To see if the student body supports abolishing "dead week", the Student Government decides to conduct a survey. They place an ad in the student newspaper, asking students to vote. After the votes are in, they randomly select half of them to draw their conclusions. Will this sample be representative of all UF students? a. Yes, since it was done at random. b. Yes, since anyone (student or not) could participate. c. No, since this is an example of voluntary response sample. d. No, since it was done by the student newspaper.

c. No, since this is an example of voluntary response sample.

(Module 13) Tests for tuberculosis like all other diagnostic tests are not perfect. QFT-G is one of such tests for tuberculosis. Suppose that for the population of adults that is taking the test, 5% have tuberculosis. The test correctly identifies 74.6% of the time adults with a tuberculosis and correctly identifies those without tuberculosis 76.53% of the time. Suppose that POS stands for the test gives a positive result and S means that the adult really has tuberculosis. Represent the "76.53%" using notation. a. P(S) b. P(Sc) c. P(POSc | Sc) d. P( POSc | C)

c. P(POSc | Sc)

(Module 8) A researcher for Coca-Cola is testing new flavors for an energy drink:lemon-lime, grape, strawberry and orange. Each participant tries each of the flavors and states which they like the best. What would be the appropriate graph to make of the sampled data? a. dotplot b. histogram c. pie chart d. scatterplot

c. pie chart

(Module 14) The bus you take every morning always arrives anywhere from 2 minutes early to 15 minutes late and it is equally likely that it arrives during any of those minutes. Suppose that you arrive at the bus stop five minutes early. What is the probability that the bus is more than five minutes late? a. 10% b. 10/15 c. 10/18 d. 10/17

d. 10/17

(Module 12) We will flip a balanced coin 3 times and for each toss, record whether we get a Head or a Tail. Write all possible outcomes of this experiment to find the probability that we get exactly 2 heads. a. 1/3 b. 1/8 c. 2/3 d. 3/8

d. 3/8

(Module 14) Scores on an exam follow an approximately Normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. What is the minimum score you would need to be in the top 5%? a. 1.645 b. 88.6 c. 66.37 d. 86.43

d. 86.43

(Module 15) A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independent and that she throws 3 shots. Let X = the number of shots that he makes. What is the probability that she makes 0 shots? a. 0.227 b. 0.435 c. 0.278 d. 0.059

a. 0.227

(Module 13) Suppose that a classroom has 10 light bulbs. The probability that each individual light bulb works is 0.6. Suppose that each light bulb works independently of the other light bulbs. What is the probability that all 10 of the light bulbs work? a. 0.0060 b. 0.10 c. 1.667 d. 0.000157

a. 0.0060

(Module 9) A survey asks participants if they support or oppose the building of new football stadium. If there are 200 respondents(selecting using a simple random sample) to a survey, what is the approximate margin of error? a. 0.07 b. 0.26 c. 0.005 d. 0.05

a. 0.07

(Module 10) Hydrogen peroxide decomposes back to water and oxygen when exposed to air and light. When bought at a pharmacy for home use, hydrogen peroxide is sold in dark bottles that are labeled as a concentration of 3% by weight. A chemistry student wants to test the concentration of hydrogen peroxide that has been decanted to light and dark bottles, and exposed to air for 10, 20 and 30 hours. The concentration is tested by titration with potassium permanganate, and each sample is tested twice. Match the part of the experiment above that goes with each of the following terms. control a. Control b. Randomization c. Replication 1. Bottles are bought and opened at the same time, all handled the same way, etc. 2. The way to determine which samples get which color bottle and what time exposure 3. Each sample is tested twice

a. Control = (1) Bottles are bought and opened at the same time, all handled the same way, etc. b. Randomization = (2) The way to determine which samples get which color bottle and what time exposure c. Replication = (3) Each sample is tested twice

(Module 9) A track and field coach wants to analyze the effect of sports drinks on the performance of his athletes. He decides to test three brands: Powerade, Gatorade and Vitaminwater. He will have each of the athletes complete a 400 meter run and record their times. Which of the following represents a confounding variable? Mark all that apply. a. He decides to give all male athletes Gatorade and the female athletes either Powerade or Vitaminwater. b. He allows each athlete to choose their favorite drink from a cooler. c. He has some of the athletes drink the sports drink two hours before running, others one hour before running, and the rest 30 minutes before running.. d. He has some of the athletes drink Gatorade two hours before running, others drink Powerade one hour before running, and the rest Vitaminwater half an hour before running. e. He has some of the athletes run in the morning, some midday and some in the afternoon. f. He has some of the athletes drink Vitaminwater and run in the morning, some drink Gatorade and run midday and some drink Powerade and run in the afternoon. g. He has all his athletes repeat the 400m on different days after having one of the three drinks - on Monday they all have Gatorade, on Wednesday Powerade and on Friday Vitaminwater.

a. He decides to give all male athletes Gatorade and the female athletes either Powerade or Vitaminwater. d. He has some of the athletes drink Gatorade two hours before running, others drink Powerade one hour before running, and the rest Vitaminwater half an hour before running. f. He has some of the athletes drink Vitaminwater and run in the morning, some drink Gatorade and run midday and some drink Powerade and run in the afternoon. g. He has all his athletes repeat the 400m on different days after having one of the three drinks - on Monday they all have Gatorade, on Wednesday Powerade and on Friday Vitaminwater.

(Module 3) Suppose that you had the following data set. 500 200 250 275 300 Suppose that the value 500 was a typo, and it was suppose to be negative (-500). How would the value of the standard deviation change? a. It would increase. b. It would decrease. c. It would stay the same. d. Unable to be determined.

a. It would increase.

(Module 10) An advertising firm wants to determine the effect of the length of a commercial and how frequently it is shown on the customers intent to buy a product. Are people more likely to buy a product after watching long versions of the commercial, or shorter ones? Do people prefer to see the same commercial many times, or fewer? Does the answer to the last question depend on how long the commercial is?They prepare two versions of a commercial for a soft drink - one a 30 second version, and the other a 45 second version. Then they prepare videotapes of a one-hour episode of a popular TV show, where they insert either the long or short versions of the commercial, either one, two or three times (in addition to commercials for other products that would normally advertise there.) Twenty-four people are then recruited to participate in the study, without telling them what the purpose of it is. Four people are selected at random to watch each one of the videotapes (and made to sit through the whole thing, including the commercials.) After watching the show, each person is asked (individually) how likely they are to purchase the soft drink: not at all, somewhat likely, very likely. Find the sections of the article that matches each of the terms below. a. Response Variable(s) b. Factor(s) c. Experimental Unit(s) d. Number of Treatment(s) 1. Intent to purchase 2. Length, number of times 3. 24 4. 6

a. Response Variable(s) = (1) Intent to purchase b. Factor(s) = (2) Length, number of times c. Experimental Unit(s) = (3) 24 d. Number of Treatment(s) = (4) 6

(Module 10) A car company is testing a new type of tire. They want to determine the average stopping distance in light rain, light snow and dry conditions. They test out tires on four randomly selected cars from the lot. They want to know if the stopping distance is significantly different under the three conditions. What is the factor? a. Road conditions b. Stopping Distance c. Four cars

a. Road conditions

(Module 9) Which of the following are probability samples? Mark all that apply. a. Simple Random Sample b. Convenience Sample c. Voluntary Response d.Sample e. Blind Sample f. Stratified Sample g. Cluster Sample

a. Simple Random Sample f. Stratified Sample g. Cluster Sample

(Module 10) What does it mean to find statistically significant results? a. We say we found statistically significant differences between treatments when the observed differences in the samples are too large to be attributed to chance, so we believe there are true differences in the populations. b. We say we found statistically significant differences between treatments when the observed differences in the samples are too small to be attributed to chance, so we believe there are true differences in the populations. c. We say we found statistically significant differences between treatments when the observed differences in the populations are too large to be attributed to chance, so we believe there are true differences in the samples. d. We say we found statistically significant differences between treatments when the observed differences in the populations are too small to be attributed to chance, so we believe there are true differences in the samples.

a. We say we found statistically significant differences between treatments when the observed differences in the samples are too large to be attributed to chance, so we believe there are true differences in the populations.

(Module 11) Answer the following questions regarding the article link below: http://www.gallup.com/poll/214250/say-tried-marijuana.aspx a. The main topic of this article is: b. The study was conducted by: c. The data was collected: d. Are the results of the study trustworthy?

a. What marijuana use looks like in America b. An independent and well respected polling organization c. Using methods that would likely yield a sample representative of the population d. Yes

(Module 8) The following is an excerpt from a paper published in BMJ (formerly the British Medical Journal) in 1994: Charig et al undertook a historical comparison of success rates in removing kidney stones. Open surgery had a success rate of 78% (273/350) while a minimally invasive procedure called percutaneous nephrolithotomy had a success rate of 83% (289/350), an improvement over the use of open surgery. However, the success rates looked rather different when stone diameter was taken into account. This showed that, for stones of <2 cm, 93% (81/87) of cases of open surgery were successful compared with just 83% (234/270) of cases of percutaneous nephrolithotomy. Likewise, for stones of >/=2 cm, success rates of 73% (192/263) and 69% (55/80) were observed for open surgery and percutaneous nephrolithotomy respectively. The main reason why the success rate reversed is because the probability of having open surgery or percutaneous nephrolithotomy varied according to the diameter of the stones. In observational (nonrandomised) studies comparing treatments it is likely that the initial choice of treatment would have been influenced by patients' characteristics such as age or severity of condition; so any difference between treatments could be accounted for by these original factors. Such a situation may arise when a new treatment is being phased in over time. Randomised trials are therefore necessary to demonstrate any treatment effect. This is an example of Simpson's paradox because: a. When the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them). b. When the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be more successful at removing them). c. When the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them). d. When the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be more successful at removing them).

a. When the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them).

(Module 3) Match each term on the left column with the appropriate description from the right column description. Each answer choice will only be used one time. a. mean b. median c. mode d. range e. variance f. standard deviation 1. Distances from the data points to this measure of center always add up two zero 2. This measure of center always has exactly 50% of the observations on either side 3. This measure of center represents the most common observation, or class of observations 4. This measure of spread is affected the most by outliers 5. Measure of spread around the mean, but its units are not the same as those of the data points 6. Is smaller for distributions where the points are clustered around the middle

a. mean = (1) Distances from the data points to this measure of center always add up two zero b. median = (2) This measure of center always has exactly 50% of the observations on either side c. mode = (3) This measure of center represents the most common observation, or class of observations d. range = (4) This measure of spread is affected the most by outliers e. Variance = (5) Measure of spread around the mean, but its units are not the same as those of the data points f. Standard Deviation = (6) Is smaller for distributions where the points are clustered around the middle

(Module 5) At most restaurants, the more food you order, the more money you have to pay. This is true whether you go to an overpriced "gourmet" restaurant where the plates are tiny but very expensive, or to a cafeteria where the portions are huge and the prices cheap. If you collect data at any ONE restaurant, the correlation between the amount of food served per person and the price paid for it should be: a. positive and fairly strong b. negative and fairly strong c. fairly weak

a. positive and fairly strong

(Module 11) Which of the following types of studies require approval by an Internal Review Board? (Select all that apply) a. research that poses risks to participants b. surveys not meant to be published c. data collected for instructional purposes only d. data collected on vulnerable populations e. data collected through phones or computers

a. research that poses risks to participants d. data collected on vulnerable populations

(Module 2) Suppose that someone made a graph of SAT scores from 100 randomly selected students from the state of Florida. Standardized test scores like those for the SAT are derived from the students' raw scores (number of questions answered correctly) and adjusted for slight differences in difficulties between versions. What shape would you expect the histogram of this data to be? a. symmetric b. right skewed c. left skewed d. uniform

a. symmetric

(Module 5) Find the equation of the Least Squares Regression line if: x-bar = 2 sx = 2.3 y-bar = 22 sy = 4.1 r = - 0.94 a. y-hat = 25.35 - 1.68x b. y-hat = 25.35x - 1.68 c. y-hat = 18.64 - 1.68x d. y-hat = 18.64x + 1.68

a. y-hat = 25.35 - 1.68x

(Module 14) X~N(145, 13). Find the z-score corresponding to an observation of 150. a. -0.3846 b. 0.3846 c. 0.88 d. -0.88

b. 0.3846

(Module 15) A basketball player makes 40% of his shots from the free throw line. Suppose that each of his shots can be considered independent and that he takes 3 shots. Let X = the number of shots that he makes. What is the mean for X? a. 0.4 b. 1.2 c. 0.849 d. 0.72

b. 1.2

(Module 12) Suppose that you are rolling a six sided dice. Let A = even. What is P(Ac)? a. 1/4 b. 1/2 c. 1/3 d. 1/6

b. 1/2

(Module 14) Scores on an exam follow an approximately Normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. What percent of students scored above 80 points? a. 72.24% b. 27.76% c. 59% d. 41%

b. 27.76%

(Module 6) A confidential and voluntary survey conducted in STA 3024 in the Spring of 1999 asked the students questions about their sex life. A simple linear regression analysis was conducted to predict the number of lifetime sexual partners a student has had based on the number of sexual partners the student has had in the past year. The analysis yielded an R-squared of 27.8%. Interpret R-squared. a. 27.8% of the variability in the student's number of sexual partners in the past year is explained by the number of lifetime sexual partners the student has had. b. 27.8% of the variability in the number of sexual partners students have had in their lifetime is explained by the number of sexual partners in the past year. c. As the student's number of lifetime sexual partners increases by one, the number of sexual partners in the past year increases by 27.8%. d. As the student's number of sexual partners in the past year increases by one, the number of lifetime sexual partners increases by 27.8%.

b. 27.8% of the variability in the number of sexual partners students have had in their lifetime is explained by the number of sexual partners in the past year.

(Module 6) A political scientist was interested in studying America's voting habits. So, he decided to make a least squares regression equation to predict the percentage of people in a state that would vote for Obama in 2012 based on the percentage of people in a state that voted for Obama in 2008. The least squares equation is y-hat = -4.599 +1.04x. In the state of Alabama, 37.74% voted for Obama in 2008; whereas, 38.35% voted for him in 2012. What is the value of the residual? a. 34.65 b. 3.70 c. -3.70 d. 4.02 e. -4.02

b. 3.70

(Module 5) A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says "The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero. Which of the following would be a correct interpretation of that statement? a. Professor McDaniel said that good researchers tend to be good teachers and vice versa. b. Professor McDaniel said that good researchers tend to be bad teachers and vice versa. c. Professor McDaniel said that bad researchers tend to be bad teachers and vice versa. d. Professor McDaniel said that, among good researchers, you can find both good and bad teachers and the same thing goes for bad researchers.

d. Professor McDaniel said that, among good researchers, you can find both good and bad teachers and the same thing goes for bad researchers.

(Module 2) An academic adviser wanted to investigate the amount of money spent by students on textbooks. She randomly sampled 25 students and asked how much they had spent on textbooks. Which of the following would be an appropriate graph to make of the sampled data? a. dotplot b. stemplot c. histogram d. all of the above

d. all of the above

(Module 4) The median is: a. the second quartile b. the 50th percentile c. the observation with half of the data on either side of it d. all of the above

d. all of the above

(Module 16) Scores on an exam follow an approximately Normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. What is the minimum score you would need to be in the top 5%? a. 1.645 b. 88.6 c. 66.37 e. 86.43

e. 86.43

(Module 4) In a boxplot you find 25% of the data: a. below Q1 b. above Q3 c. between Q1 and Q2 d. between Q2 and Q3 e. all of the above

e. all of the above

(Module 10) A track and field coach wants to analyze the effect of sports drinks on the performance of his athletes. He decides to test three brands: Powerade, Gatorade and Vitaminwater. He will have each of the athletes complete a 400 meter run and record their times. Which of the following represents a blocked design? Mark all that apply. a. He decides to give all male athletes Gatorade and the female athletes either Powerade or Vitaminwater. b. He has some of the athletes drink the sports drink two hours before running, and others one hour before running. c. He has some of the athletes drink Gatorade two hours before running, others drink Powerade one hour before running, and the rest Vitaminwater half an hour before running. d. He has some of the athletes run in the morning, some midday and some in the afternoon. e. He has some of the athletes drink Vitaminwater and run in the morning, some drink Gatorade and run midday and some drink Powerade and run in the afternoon. f. He has all his athletes repeat the 400m on different days after having one of the three drinks - on Monday they all have Gatorade, on Wednesday Powerade and on Friday Vitaminwater. g. He has all his athletes repeat the 400m on different days after having each of the three drinks - and uses randomization to determine which drink they have each day. h. He creates groups of three similar athletes after ranking them by speed, then randomly assigns one person from each group to get either Powerade, Gatorade, or Vitaminwater.

g. He has all his athletes repeat the 400m on different days after having each of the three drinks - and uses randomization to determine which drink they have each day. h. He creates groups of three similar athletes after ranking them by speed, then randomly assigns one person from each group to get either Powerade, Gatorade, or Vitaminwater.