AP Stat Packet

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    Pont. Max.

    Preston H. Earle

    AP Statics Summer Work

    Preliminary Exercises

    P.1. Jamies preference is not good evidence that most young people prefer Jolt to Coke or

    Pepsi because Jamie and her friends do not accurately represent the whole of the population. This

    population could very easily lead to bias because the sample taken is of a small and very specific

    group of people. The sample should be random.

    P.2. a. The study of a direct correlation between the use cell phones and brain cancer is

    observational because the conclusion is drawn using pre-existing data rather than actually

    conducting an experiment.

    b. No, the conclusion that there is a direct correlation between cell phone usage and brain

    cancer would be imprudent. Irrefutable scientific conclusions must be made from precise, welldeveloped experiments.

    P.3. a. The study of the effectiveness of an educational software companys computer

    animation program for biology as opposed to a textbook presentation is an experiment. This is an

    experiment because the software company actually conducted tests on two random groups of

    high school juniors and then drew conclusions.

    b. If the group of high school juniors using the computer program achieved a much

    higher average than that of the juniors using the textbook, then the conclusion could be made that

    the computer animation software is more effective than the traditional textbook.

    P.4. a. If someone was to find out if people were generally satisfied with how things are going

    in the country right now, then a survey would need to be conducted. The reason a survey would

    need to be carried out rather than an experiment or observational study is that this is a simple

    question being posed to the population. There are no variables to test or behaviors or correlations

    to analyze.

    b. If someone to test whether college students learn accounting better in a classroom or

    using an online course, then an experiment would need to be conducted. The reason an

    experiment would need to be conducted rather than a survey or observational study is that this

    must be tested. There are variables to test and data to analyze in order to draw a conclusion. No

    simple question can be asked nor can this be analyzed because students could easily show bias

    towards one option or the other.

    c. If someone wanted to determine how long teachers wait on average after they ask their

    classes a question, then an observational study would be the most logical decision. This fact can

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    easily be discovered by observing teachers. A question cannot be asked and an experiment is not

    necessary because it is a simple observation, not a test or comparison.

    P.5. a. In an observational study of the health of people who drink wine as opposed to people

    who drink beer, some rather unorthodox methods would have to be used. Observing in this

    case would be viewing health records, physicals, or some other medical examination that wouldidentify the good or bad health of the random strangers found at a bar or other location which

    provides alcohol. In an observational study, there is now empirical data to show how often the

    person drinks or if that person exclusively drinks one type of alcohol. An experiment, the more

    rational choice, would entail selecting a group people who are carefully monitored and analyzed

    in a controlled environment. These people would be split into two equal but separate groups, and

    their health would be tested before, during, and after the experiment. This controlled

    environment would allow for precise conclusion; whereas, the observational study would have

    too many variables which could not be controlled.

    b. One could infer that people who drink wine are slightly wealthier than people whodrink beer by virtue of the fact that wine is generally more expensive. People who can afford the

    finer things like wine could also afford good health insurance and good doctors. They could

    also afford healthier, organic food which would lead to better health.

    P.6. According to the National Center for Education Statistics, 76 percent of all full-time

    dependent students worked while enrolled in college in the year 2000. However, a study

    conducted by Upromise Incorporated under the direction of Jonathan M. Orszag, Peter R.

    Orszag, and Diane M. Whitmore concluded that the numbers were significantly lower. In the

    graph below, the conclusion was drawn that the college employment rate never reached above 60

    percent.

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    P.7. a.

    b. It is obvious that the colors which are the most subtle and ordinary are also the most

    popular. Silver and White, two very common, ordinary colors, were by far the most popular. Onecan see that the more vibrant and further away from the grayscale the car is, the less popular it

    becomes. It is also interesting to note that this small amount of colors take over 85 percent of the

    entire 2003 model year. All other colors combined only add up to 14.2 percent.

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    P.8. a.

    b. It is clear that the data from P.7 correlates to the data in P.8. Silver and White are again

    the most popular for both Luxury and SUV cars. It also seems that the more subtle colors, Silver,White, Black, and Gray are more popular in Luxury cars; whereas, the slightly more vibrant

    Blue, Green, and Red are more popular in the SUV/Truck/Van category.

    P.9. a.

    Dot Plot of U.S Womens Soccer Scores (Differential)

    b. This dot plot shows that only a few games were lost, and only a few games were tied.

    Most of the games were won and generally by small margins. There is a steady declining trend

    which develops from 1 onto 8. Fewer games are one at high score differences.

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    P.10. a.This dot plot shows the amount of gold medals earned by a set of 30 countries. Most ofthe countries did not win any gold medals, and most of the data lies between 0 and 9. One

    extreme outlier, the United States, won 35 medals. Because of the great amount of 0s and large

    range, the distribution of this graph is not even.

    b. Yes, the sample is an accurate representation of the larger population by virtue of the

    amount of teams who did not win any gold medals. An inaccurate representation would have

    included mostly teams who won gold medals.

    P.11. Class Survey

    Who- The students in the AP Statistics Class What- Variables

    o Categorical Variables- gender, hand, genre of musico Quantitative Variables- Height (inches), Homework Time

    (minutes), coins (individual coins, currency and type of coin

    are not specified)

    Why- The teacher most likely wants to gather anonymous informationabout his students

    When- On the first day of class Where- The data is collected from the teachers AP Statistics students

    and is gathered anonymously

    How- The data was gathered through an anonymous survey of thewhole AP Statistics class

    By Whom- The surveyor is the teacher of the classP.12. Medical Study Variables

    Categorical Quantitative

    Gender Age

    Race Systolic Blood Pressure

    Smoker/Non-smoker Calcium Level in Blood

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    P.13. Two categorical variables which could be used in a TV viewing habits study would

    include gender and the genre of television being watched; two quantitative variables could be

    time spent watching television each day and how many days a week the person watches

    television.

    P.14. The probability of rolling a 6 on a six-sided die is 1/6. This is the case because it is one

    number being rolled for out of 6 possible outcomes. Theoretical ly, the die should on the 6 one

    out of every six times; however, this does not manifest itself after only 6 rolls. In order for this

    probability to be seen, the die must be rolled many times. The more the die is rolled, the more

    accurate the probability will become.

    P.15. 14 out 21 identifications would clearly be the better outcome. This would show that Mr.

    Bullards class could more easily identify the type of water being tasted. As the the number of

    students that can identify the water type increases, the likelihood that people can taste the

    difference also increases.

    P.16. I dont imagine the probability being any higher than 0.05. It is very unlikely that 11 or

    more children guessed correctly. It is more likely that the students could distinguish the different

    types of water.

    P.17.

    Coin Flipping

    Toss Number Heads Tails

    1 - +

    2 + -

    3 + -

    4 - +

    5 - +

    6 + -

    7 + -

    8 - +

    9 - +

    10 - +

    11 + -

    12 - +

    13 - +

    14 + -

    15 + -16 - +

    17 + -

    18 - +

    19 + -

    20 + -

    Total- 20 10 10

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    a.

    b. The proportion ended in exactly half (0.5).

    c. The conclusion can be made that the more times the coin is flipped, the closer the

    proportion comes to 0.5. This seen through the data provided. The proportions deviation slowlydecreases until it reaches a precise .

    P.18. a. No, if Gallup asked all teens aged 13 to 17, their number would be at least slightly

    different because all samples have different variability.