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AP Statistics Midterm Review

Part I. Multiple Choice (1- 29) – Choose the answer that best fits.

  1. Which of the following does NOT describe the distribution of data for one variable statistics?

A. scatterplotC. standard deviation

B. range D. IQR E. None of the above

  1. Which of the following data display(s) have quantitative data that can be recovered?

A. dotplotC. stem-and-leaf plot

C. histogramD. A and CE. None of the above

For 3 and 4 use the situation described below.

3. His cousin also owns a small used car dealership in the next town. Suppose he wants to describe how business is going to his cousin. He is a bit competitive with his cousin. Which of following should he use to describe how many cars his dealership is selling a day?

A. meanC. IQR

B. medianD. standard deviationE. None of the above

4. The small used car dealer has a wife. She wants to renovate their home. She asks how business is going. Unlike his wife, he does not want to renovate their home. Which of the following should he use to describe how many cars his dealership is selling a day?

A. meanC. IQR

B. medianD. standard deviationE. None of the above

For 5 and 6 us the situation described below.

5. Which of the following points has the highest negative residual?

A. Point AC. Point C

B. Point BD. Point DE. Point E

6. Which of following best describes the correlation?

A. strong and positiveC. weak and negative

B. strong and negativeD. weak and positiveE. cannot be determined

Use the following scenario to answer questions 7-9:

A market research company employs a large number of typists to enter data into a computer data base. The time it takes for potential new typists to learn the computer system is known to have a normal distribution with a mean of 90 minutes and a standard deviation of 18 minutes. A candidate is automatically hired if she learns the computer system in less than 100 minutes. A cut-off time is set at the slowest 10% of the learning distribution. Anyone slower than this cut-off time is definitely not hired.

7. / What proportion of candidates takes more than two hours to learn the computer system?
A. / 0.048
B. / 0.452
C. / 0.711
D. / 0.952
8. / What proportion of candidates will be automatically hired?
A. / 0.048
B. / 0.711
C. / 0.452
D. / 0.952
9. / What is the cut-off time the market research company uses?
A. / 1 hour and 7 minutes.
B. / 1 hour and 53 minutes.
C. / 2 hours.
D. / 2 hours and 8 minutes.
10. / The mean age of five people in a room is 30 years. One of the people whose age is 50 years leaves the room. What is the mean age of the remaining four people in the room?
A. / 40 years
B. / 30 years
C. / 25 years
D. / This cannot be determined from the information given.
11. / The median age of five people in a meeting is 30 years. One of the people, whose age is 50 years, leaves the room. What is the median age of the remaining four people in the room?
A. / 40 years.
B. / 30 years.
C. / 25 years.
D. / This cannot be determined from the information given.
12. / A particularly common question in the study of wildlife behavior involves observing contests between “residents” of a particular area and “intruders.” In each contest, the “residents” either win or lose the encounter (assuming there are no ties). Observers might record several variables, some of which are listed below. Which of these variables is categorical?
A. / The duration of the contest (in seconds).
B. / The number of animals involved in the contest.
C. / Whether the “residents” win or lose.
D. / The total number of contests won by the “residents.”

13)Some descriptive statistics for a set of tests scores are shown above. For this test, a certain student has a standardized score of z = -1.2. What is the score did this student receive on the test.

A. 266.28C. 779.42

B. 729.24D. 1083.38E. 1311.98

Matching.

For questions 14-17 use the following list to identify which graphical display is most appropriate: a)Bar Graph, b)Dot Plot, c)Histogram, or d)Box & Whisker Plot

14. You have a small number of values and you want to see each individual

15. You have a large number of values, you don’t need to see individuals, and you want to see the overall shape

16. You have categorical data

17. You want to display the five number summary

For questions 18-21 use the following list to identify which sampling method is being described: a)Simple Random Sample, b)Stratified Random Sample, c)Cluster Sample, or d)Systematic Sample

18. Number all the students and select every third person after you chose where to randomly start

19. Write the name of all the baseball players on a sheet of paper and draw two from a hat

20. Organize the student body of OCHSA by conservatory and then randomly choose five students from each

21. Randomly choose five classrooms from the entire list of classrooms on campus

22. There are two games involving flipping a coin. In the first game you win a prize if

you can throw between 40% and 60% heads. In the second game you win if you can

throw more than 75% heads. For each game would you rather flip the coin 50 or 500

times?

  1. It does not matter.
  2. 50 times for each game
  3. 500 for each game
  4. 50 for the first game and 500 for the second
  5. 500 for the first game and 50 for the second

23. Given that 55% of the U.S. Population are female and 20% are older than age 65, can

we conclude that (.55)(.20) = 11% are women older than 65?

  1. yes, by the multiplication rule.
  2. Yes, by conditional probability
  3. Yes, by law of large numbers.
  4. No, because the events are not independent.
  5. No, because the events are independent.

24. A trucking firm determines that its fleet of trucks averages a mean of 18.2 miles per

gallon with a standard deviation of .8 miles per gallon on cross country hauls. What

is the probability that one of the trucks averages more than 19 miles per gallon? We can

assume that the mean number of miles driven per gallon is normally distributed.

  1. .212
  2. .788
  3. None of the answers is correct
  4. .159
  5. .841

25. The heart disease death rates per 100,000 people in the united states for certain years

were

year 1950 1960 1970 1975 1980

Death rate 307.6 286.2 253.6 217.8 202.0

Find the regression line and predict the death rate for the year 1983

  1. 145.8 per 100,000 people
  2. 188.6 per 100,000 people
  3. 196.8 per 100,000 people
  4. 198.5 per 100,000 people
  5. None of the above

26. Suppose that 25% of all business executives are willing to switch companies if

offered a higher salary. If a headhunter randomly contacts a random sample of 120

executives, what is the probability that over 42 executives will be willing to switch

companies if offered a higher salary?

  1. .0057
  2. .0075
  3. .0099
  4. .0040
  5. .0025

27. Which of the following statements about the correlation coefficient r are true?

  1. It is not affected by changes in the measurement units of the variables.
  2. It is not affected by which variable is called x and which is called y.
  3. It is not affected by extreme values.
  1. I only
  2. I and II
  3. I and III
  4. II and III
  5. I, II, and III

28. Each of the 7 basketball teams in the SFL has 12 players. A sample of 14 players is to be chosen as follows. Each team will be asked to place 12 cards with their players names into a hat and randomly draw out two names. The two names from each team will be combined to makeup the sample. Will this method result in a simple random sample of the 84 basketball players.

  1. Yes, because this is an example of stratified sampling, which is a special case of simple random sampling.
  2. No, because the teams are not chosen randomly.
  3. No, because not each group of 14 players has the same chance of being selected.
  4. Yes, because each player has the same chance of being selected.
  5. Yes, because each team is equally represented.

29. Under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling.

A. The population can be divided into large number of strata so that each stratum contains only a few individuals.

B. The population can be divided into a small number of strata so that each stratum contains a large number of individuals.

C. The population can divided into strata so that the individuals in each stratum are as much alike as possible.

D. The population can be divided into strata so that the individuals in each stratum are as different as possible.

E. The population can be divided into strata of equal sizes so that each individual in the population still has the same chance of being selected.

Part II. Free Response.

1) Taltson Lake is in the Canadian Northwest Territories. This lake has many Northern Pike. The following data was obtained by two fishermen visiting the lake. Let x = length of a northern Pike in inches and let y = weight in pounds.

x (inches) / 20 / 24 / 36 / 41 / 46
y (pounds) / 2 / 4 / 12 / 15 / 20
  1. Draw a scatter plot.
  1. Find
  1. Find the least squares line. Write out the equation, and graph it.
  1. Compute the sample correlation coefficient r.

e. Describe r in the context of the problem.

  1. If a 32 inch Northern Pike is caught, what is the weight in pounds as predicted by the least squares line?

2)Of those mountain climbers who attempt Mt. McKinley (Denali), only 65% reach the summit. In a random sample of 120 mountain climbers who are going to attempt Mt. McKinley, what is the probability that…

  1. 80 reach the summit?
  1. At least 80 reach the summit?
  1. No more than 80 reach the summit?
  1. From 70 to 80 reach the summit, including 70 and 80.

3) John and Joel are salesmen in different districts. In John’s district, the long term mean sales is $17,319 each month with standard deviation $684. In Joel’s district, the long term mean sales is $21, 971 each month with standard deviation $495. Assume that sales in both districts follow a normal distribution.

  1. Last month John sold $19,214 whereas Joel sold $22,718 worth of merchandise. Relative to the buying habits of customers in each district, does this mean Joel is a better salesman? Who is the better salesman in relation to their district? Explain.

4) . A common classroom practice is to have students exchange their quizzes for grading. This practice is hypothesized to reduce time between quiz and feedback to students, thus resulting in higher achievement. Your history teacher, aware of your statistical prowess, has asked you to design an experiment to test this theory. You have decided to use the final exam (not graded by students) as your response measure. Your history teacher has three classes, one early in the morning, one at noon, and one late in the afternoon. Each class contains 30 students.

(a) Describe the treatments you will use in your experiment

(b) One possible confounding variable is the time of day; students may

be more alert at certain times of the day than at other times. Describe a method

that could be used to control this variable. Students have already been assigned

their schedules, and these cannot be changed.

(c) Would it be a good idea to use a single blind or double blind in this experiment? Why or why not?

(c) Do you feel the results of your experiment could be generalized to

Math classes? Explain why or why not.