Name _________________________

School _________________________

Date _________________________

Purpose The purpose of this survey is to indicate what you already know and think about probability and statistics.

Take your time The questions require you to read and think carefully about various situations. If you are unsure of what you are being asked to do, please raise you hand for assistance.

Part I

On the first few pages are a series of statements concerning beliefs or attitudes about probability, statistics and mathematics. Following each statement is an "agreement" scale which ranges from 1 to 5, as shown below.

1 2 3 4 5 Strongly Disagree Neither Agree Strongly Disagree Agree, nor Agree disagreeIf you strongly agree with a particular statement, circle the number 5 on the scale. If you strongly disagree with the statement, circling the number 1.

_____________________________________________________________ 1 2 3 4 5 Strongly Disagree Neither Agree Strongly Disagree Agree, nor Agree disagree _____________________________________________________________1. I often use statistical information in forming my opinions or making decisions.

1 2 3 4 52. To be an intelligent consumer, it is necessary to know something about statistics.

1 2 3 4 53. Because it is easy to lie with statistics, I don't trust them at all.

1 2 3 4 54. Understanding probability and statistics is becoming increasingly important in our society, and may become as essential as being able to add and subtract.

1 2 3 4 55. Given the chance, I would like to learn more about probability and statistics.

1 2 3 4 56. You must be good at mathematics to understand basic statistical concepts.

1 2 3 4 57. When buying a new car, asking a few friends about problems they have had with their cars is preferable to consulting an owner satisfaction survey in a consumer magazine.

1 2 3 4 58. Statements about probability (such as what the odds are of winning a lottery) seem very clear to me.

1 2 3 4 59. I can understand almost all of the statistical terms that I encounter in newspapers or on television.

1 2 3 4 510. I could easily explain how an opinion poll works.

1 2 3 4 5

1. A small object was weighed on the same scale separately by nine students in a science class. The weights (in grams) recorded by each student are shown below.

6.2 6.0 6.0 15.3 6.1 6.3 6.2 6.15 6.2The students want to determine as accurately as they can the actual weight of this object. Of the following methods, which would you recommend they use?

- _____ a. Use the most common number, which is 6.2.
- _____ b. Use the 6.15 since it is the most accurate weighing.
- _____ c. Add up the 9 numbers and divide by 9.
- _____ d. Throw out the 15.3, add up the other 8 numbers and divide by 8.

Listed below are several statements concerning this survey. Place a check by every statement that you agree with.

- _____ a. The average is based on teenagers' estimates of what they spend and therefore could be quite different from what teenagers actually spend.
- _____ b. They should have done the survey at more than 80 malls if they wanted an average based on teenagers throughout the country.
- _____ c. The sample of 2,050 teenagers is too small to permit drawing conclusions about the entire country.
- _____ d. They should have asked teenagers coming out of music stores.
- _____ e. The average could be a poor estimate of the spending of all teenagers given that teenagers were not randomly chosen to fill out the questionnaire.
- _____ f. The average could be a poor estimate of the spending of all teenagers given that only teenagers in malls were sampled.
- _____ g. Calculating an average in this case is inappropriate since there is a lot of variation in how much teenagers spend.
- _____ h. I don't agree with any of these statements.

- _____ a. H H H T T
- _____ b. T H H T H
- _____ c. T H T T T
- _____ d. H T H T H
- _____ e. All four sequences are equally likely

4. Select the alternative below that is the best explanation for the answer you gave for the item above.

- _____ a. Since the coin is fair, you ought to get roughly equal numbers of heads and tails.
- _____ b. Since coin flipping is random, the coin ought to alternate frequently between landing heads and tails.
- _____ c. Any of the sequences could occur.
- _____ d. If you repeatedly flipped a coin five times, each of these sequences would occur about as often as any other sequence.
- _____ e. If you get a couple of heads in a row, the probability of a tails on the next flip increases.
- _____ f. Every sequence of five flips has exactly the same probability of occurring.

- _____ a. H H H T T
- _____ b. T H H T H
- _____ c. T H T T T
- _____ d. H T H T H
- _____ e. All four sequences are equally unlikely

The Caldwells then talked to three friends, two Oldsmobile owners, and one former Buick owner. Both Oldsmobile owners reported having a few mechanical problems, but nothing major. The Buick owner, however, exploded when asked how he like his car: First, the fuel injection went out - $250 bucks. Next, I started having trouble with the rear end and had to replace it. I finally decided to sell it after the transmission went. I'd never buy another Buick.

The Caldwells want to buy the car that is less likely to require major repair work. Given what they currently know, which car would you recommend that they buy?

- _____ a. I would recommend that they buy the Oldsmobile, primarily because of all the trouble their friend had with his Buick. Since they haven't heard similar horror stories about the Oldsmobile, they should go with it.
- _____ b. I would recommend that they buy the Buick in spite of their friend's bad experience. That is just one case, while the information reported in Consumer Reports is based on many cases. And according to that data, the Buick is somewhat less likely to require repairs.
- _____ c. I would tell them that it didn't matter which car they bought. Even though one of the models might be more likely than the other to require repairs, they could still, just by chance, get stuck with a particular car that would need a lot of repairs. They may as well toss a coin to decide.

7. Half of all newborns are girls and half are boys. Hospital A records an average of 50 births a day. Hospital B records an average of 10 births a day. On a particular day, which hospital is more likely to record 80% or more female births?

- _____ a. Hospital A (with 50 births a day)
- _____ b. Hospital B (with 10 births a day)
- _____ c. The two hospitals are equally likely to record such an event.

The following question about the lottery appeared in The New York Times (May 22, 1990).

Are your odds of winning the lottery better if you play the same numbers week after week or if you change the numbers every week?

What do you think?

- a. I think the odds are better if you play the same numbers week after week.
- b. I think the odds are better if you change the numbers every week.
- c. I think the odds are the same for each strategy.

- _____ a. The sample of 500 is too small to permit drawing conclusions.
- _____ b. If a student decreased the amount of time spent watching television, his or her performance in school would improve.
- _____ c. Even though students who did well watched less television, this doesn't necessarily mean that watching television hurts school performance.
- _____ d. One month is not a long enough period of time to estimate how many hours the students really spend watching television.
- _____ e. The research demonstrates that watching television causes poorer performance in school.
- _____ f. I don't agree with any of these statements.

- _____ a. The no-sleep group did better because none of these students scored below 40 and the highest score was achieved by a student in this group.
- _____ b. The no-sleep group did better because its average appears to be a little higher than the average of the sleep group.
- _____ c. There is no difference between the two groups because there is considerable overlap in the scores of the two groups.
- _____ d. There is no difference between the two groups because the difference between their averages is small compared to the amount of variation in the scores.
- _____ e. The sleep group did better because more students in this group scored 80 or above.
- _____ f. The sleep group did better because its average appears to be a little higher than the average of the no-sleep group.

- ______a. There is a 5% chance that the new drug is more effective than the current treatment.
- _____b. If the current treatement and the new drug were equally effective, then 5% of the times we conducted the experiment we would observe a difference as big or bigger than the 15% we observed here.
- _____c. There is a 5% chance that the new drug is at least better than the current treatment by at least 15%.

- ______a. One can be 95% "confident" that between 55% and 61% of all adult Americans approve of the President's performance.
- ______b. One can be sure that between 55% and 61% of all adult Americans approve of the President's performance.
- ______c. The sample percentage of 58% could be off by 3% in either direction due to inaccuracies in the survey process.
- ______d. There is a 3% chance that the percentage of 58 is an inaccurate estimate of the population of all Americans who approve of President Clinton's performance as president.