Statistics Exam First Semester

AP Stats Midterm Review Name ______Chapters 1 – 8 Show all work for full credit. Treat this as an AP exam!! Show all formulas used and graphs where needed. For #1 – 4: Quiz Scores 1 4 5 5 6 7 7 7 8 9 3 4 5 6 6 7 7 8 8 9 3 4 5 6 6 7 7 8 8 10

1. Make a dotplot or a histogram (your choice) of the quiz scores.

2. Describe the distribution.

3. Find the mean and standard deviation of the quiz scores.

4. Make a boxplot of the quiz scores. Check for any outliers. Be sure to label the 5-number summary on your boxplot.

For #5 – 8, IQ is distributed normally with a mean of 100 and a standard deviation of 15.5.

5. What is the percentile rank of someone with an IQ of 112?

6. What IQ do you need to have to be in the top 5%?

7. What percent of the people have an IQ between 75 and 115?

8. What percent of the people have an IQ of at least 132? For #9 – 14: Big Ten Average Scores School Football Players’ SAT All Students’ SAT Illinois 872 1140 Indiana 741 1007 Michigan 826 1190 Michigan State 788 998 Minnesota 838 1050 Northwestern 1034 1250 Ohio State 820 986 Penn State 897 1083 Purdue 881 1009 Wisconsin 825 1090

9. Which university’s scores would be influential on a scatterplot?

10. Using football players’ SAT as your explanatory variable, find the LSRL for this data.

11. Interpret the correlation for the data.

12. Iowa’s football players have an average SAT score of 814. What score would you predict for the entire student body?

13. Find the residual for Penn State.

14. What is the coefficient of determination for this data? Describe its meaning. For #15 – 17:

Shipping Box Length (inches) Shipping Cost ($) 10 4.99 12 8.59 15 16.79 18 28.99 24 68.99

15. Perform a logarithmic transformation for an exponential model for this data. Show your work. Give me the linear equation of (x, log y) and the exponential equation.

16. Perform a logarithmic transformation for a power model for this data. Show your work. Give me the linear equation of (log x, log y) and the power equation.

17. Which model, exponential or power, is a better “fit” for this data? Justify. For #18 – 21: A researcher suspected a relationship between people’s preferences in movies and their preferences in pizza. A random sample of 100 people produced the following two-way table:

Favorite Movie Pepperoni Veggie Cheese Zorro 20 5 10 Chicken Little 8 15 12 Dreamer 15 2 13

18. Fill in the marginal distributions for this table.

19. What percent of these people prefer pepperoni pizza?

20. What percent of people who prefer veggie pizza like Zorro?

21. What percent of those who like Chicken Little prefer cheese pizza?

22. What is the difference between an observational study and an experiment?

23. Describe the difference between a SRS, stratified random sample, and a systematic random sample.

24. Describe the difference between a completely randomized design, block design, and a matched pairs design.

25. I want to test the effects of two new drug therapies on blood sugar levels. I have 96 men and 72 women whom I can use in my experiment. I need to check blood sugar levels both before and after treatment. Draw a chart for this experimental design. Include blocking. 26. You are going to roll a die three times and note how many odd numbers you get. What is the size of the sample space?

27. License plates have 3 numbers and 4 letters. How many different license plates can be made?

28. Give an example of complements.

29. Give an example of disjoint events that are not complements.

Probability of winning certain prizes in my fake raffle: Car Boat TV Can Opener 0.03 0.07 0.12 0.33

30. What is the probability of winning nothing?

31. What is the probability of winning the car or the TV?

32. What is the probability of not winning the car or the can opener?

33. Make a Venn diagram for the following: 31% of my students got an A on the exam 29% of my students studied for the exam 40% of my students bought me flowers 15% of my students studied for the exam, bought me flowers, and got an A 2% of my students got an A but did not study or buy me flowers 28% of my students bought me flowers and got an A 18% of my students studied and bought me flowers Number of family members (X) 2 3 4 5 6 7 Probability 0.05 ? 0.39 0.26 0.15 0.03

34. Find P(X > 4).

35. Find P(X < 5).

36. Find P(X  3).

37. Find the expected number of family members.

38. Find the standard deviation for the number of family members.

For #39 – 42: Liz can run the 400 meter dash in an average of 60 seconds with a standard deviation of 4 seconds. Paul can run it in 70 seconds with a standard deviation of 8 seconds.

39. If Liz and Paul are the first two legs of a 1600 m relay team, what is the mean and standard deviation of their times together?

40. Liz and Paul race each other. What is the mean and standard deviation of the difference in their times? 41. Paul drinks a 2-liter of Mountain Dew, so he now runs twice as fast. What are his new mean and standard deviation? (Careful…twice as fast does not mean twice as much time…)

42. Liz is penalized 10 seconds for jumping the gun. What are her new mean and standard deviation?

43. What are the four conditions of a binomial distribution?

44. What are the four conditions of a geometric distribution?

45. At an archaeological site that was an ancient swamp, the bones from 20 brontosaur skeletons have been unearthed. The bones do not show any sign of disease or malformation. It is thought that these animals wandered into a deep area of the swamp and became trapped in the swamp bottom. The 20 left femur bones (thigh bones) were located and 4 of these femurs are to be randomly selected without replacement for DNA testing to determine gender. Let X be the number out of the 4 selected left femurs that are from males. Based on how these bones were sampled, explain why the probability distribution of X is not binomial. The article “FBI says Fewer than 25 Failed Polygraph Test” (San Luis Obispo Tribune, July 29, 2001) described the impact of a new program that requires top FBI officials to pass a polygraph test. The article states that false-positives (i.e., tests in which an individual fails even though he or she is telling the truth) are relatively common and occur 15% of the time. Suppose that such a test is given to 10 trustworthy individuals.

46. What is the probability that no one fails?

47. What is the probability that more than 2 fail, even if they are all trustworthy?

48. The article indicated that 500 FBI agents were tested. Consider the random variable x = number of the 500 tested who fail. If all 500 agents tested are trustworthy, what are the mean and standard deviation of x?

49. The headline indicated that fewer than 25 of the 500 agents tested failed the test. Is this a surprising result if all 500 are trustworthy? Answer based on the values of the mean and standard deviation from #48. Selected boxes of a breakfast cereal contain a prize. Suppose that 5% of the boxes contain the prize and the other 95% contain the message, “Sorry, try again.” A consumer determined to find a prize decides to continue to buy boxes of cereal until a prize is found. Consider the random variable x, where x = number of boxes purchased until a prize is found.

50. What is the probability that at most two boxes must be purchased?

51. What is the probability that less than 2 boxes are needed?

52. What is the probability that exactly four boxes must be purchased?

53. What is the probability that more than four boxes must be purchased?

54. What is the expected number of boxes he would have to purchase before finding a prize?

55. Which topic or topics are you struggling with the most in this course and why? What would make this class better?