AP STATS FINAL

44. The veterinary bills for the dogs are summarized in the ogive below. Estimate the IQR of these expenses.

$100

11. A relief fund is set up to collect donations for the families affected by recent storms. A random sample of 400 people shows that 28% of those 200 who were contacted by telephone actually made contributions compared to only 18% of the 200 who received first class mail requests. Which formula calculates the 95% confidence interval for the difference in the proportions of people who make donations if contacted by telephone or first class mail?

(0.28-0.18)+1.96 square root (0.28)(0.72)/200 + (0.18)(0.82)/200

53. A college alumni fund appeals for donations by phoning or emailing recent graduates. A random sample of 300 alumni shows that 40% of the 150 who were contacted by telephone actually made contributions compared to only 30% of the 150 who received email requests. Which formula calculates the 98% confidence interval for the difference in the proportions of alumni who may make donations if contacted by phone or by email?

(0.40-0.30)+2.33√(0.40)(0.60)/150)+(0.30)(0.70)/150

32. Which scatterplot shows a strong association between two variables even though the correlation is probably near zero?

(upside down U shaped graph)

36. A random sample of 120 classrooms at a large university found that 70% of them has been cleaned properly. What is the standard error of the sample proportion?

0.042

55. A random sample of 120 college seniors found that 30% of them has been offered jobs. What is the standard error of the sample proportion?

0.042

13. Five juniors and four seniors have applied for two open student council positions. School administrators have decided to pick the two new members randomly. What is the probability they are both juniors or both seniors?

0.444

18. The city council has 6 men and 3 women. If we randomly choose two of them to cochair a committee, what is the probability these chairpersons are the same gender?

1/2

17. A friend of yours plans to toss a fair coin 200 times. You watch the first 20 tosses and are surprised that she got 15 heads. But then you get bored and leave. How many heads do you expect her to have when she has finished all 200 tosses?

105

47. In an AP Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty six percent of students eat breakfast and floss their teeth. What is the probability that a student from this class eats breakfast but does not floss their teeth?

11%

37. A coffee house owner knows that customers pour different amounts of coffee into their cups. She samples cups from 10 customers she believes to be representative of the customers and weighs the cups, finding a mean of 12.5 ounces and standard deviation of 0.5 ounces. Assuming these cups of coffee can be considered a random sample of all cups of coffee which of the following formulas gives a 95% confidence interval for the mean weight of all cups of coffee?

12.5+2.262(0.5/√ 10)

24. The ages of people attending the opening show of a new movie are summarized in the ogive shown. Estimate the IQR of the ages.

13

41. We have calculated a confidence interval based on a sample of size n=100. Now we want to get a better estimate with a margin of error that is only one-fourth as large. How large does our new sample need to be?

1600

70. We have calculated a confidence interval based on a sample n=180. Now we want to get a better estimate with a margin of error only one third as large. We need a new sample with at least...

1620

25. A poll of 120 Ithacans found that 30 had visited the Museum of the Earth, and that 80 had been to Home Depot. If it appeared that going to Home Depot and going to the Museum of the Earth were Independent events, how many of those polled had been to both?

20

9. A professor was curious about her students' grade point averages (GPAs). She took a random sample of 15 students and found a mean GPA of 3.01 with a standard deviation of .534. Which of the following formulas gives a 99% confidence interval for the mean GPA of the professor's students?

3.01+2.977(.534/square root 15)

12. Six Republicans and four Democrats have applied for two open positions on a planning committee. Since all the applicants are qualified to serve, the City Council decides to pick the two new members randomly. What is the probability that both came from the same party?

42/90

21. A fair coin has come "heads" 10 times in a row. The probability that the coin will come heads on the next coin flip is

50%

52. We have calculated a confidence interval based upon a sample of n=200. Now we want to get a better estimated with a margin of error only one fifth as large. We need a new sample with at least

5000

3. Last weekend police ticketed 18 men whose mean spread was 72 miles per hour, and 30 women going an average of 64 mph. Overall, what was the mean speed of all the people ticketed?

67 mph

38. Insurance company records indicate that 12% of all teenage drivers have been ticketed for speeding and 9% for going through a red light. If 4% have been ticketed for both, what is the probability that a teenage driver has been issued a ticket for speeding but not for running a red light?

8%

46. A surgery of some AP Stats students recorded gender and whether the student was left of right-handed. Results were summarized in a table like the one shown. If it turned out that handedness was independent of gender, how many of the AP Stats students were lefty girls?

9

71. A friend of your plans to toss a fair coin 200 times. You watch the first 40 tosses, noticing that she got only 16 heads. But then you get bored and leave. If the coin I fair, how many heads do you expect her to have when she has finished the 200 tosses?

96

35. Which of the following is not a goal of re-expressing data?

All of these are goals of re-expressing data.

14. Which two events are most likely to be independent?

Having a driver's license, and having blue eyes

19. An online catalog company wants on-time delivery for at least 90% of the orders they ship. They have been shipping orders via UPS and FedEx but will switch to a more expensive service (ShipFast) if there is evidence that this service can exceed the 90% ontime goal. As a test the company sends a random sample of orders via ShipFast, and then makes follow-up phone calls to see if these orders arrived on time. Which hypothesis should they test?

Ho: p=0.90 Ha: p>0.90

68. A truck company want on-time delivery for 98% of the parts they order from a metal manufacturing plant. They have been ordering from Hudson Manufacturing but will switch to a new, cheaper manufacturer (Steel-R-Us) unless there is evidence that this new manufacturer cannot meet the 98% on-time goal. As a test the truck company purchases a random sample of metal parts from Steel-R-Us, and then determines if these parts were delivered on time, Which hypothesis should they test?

Ho: p=0.98 Ha: p<0.98

39. A residuals plot is useful because I. It wil help us to see whether our model is appropriate II. It might show a pattern in the data that was hard to see in the original scatterplot. III. It will clearly identify influential points.

I and II

2. Which statement correctly compares t-distributions to the Normal distribution? I. t distributions are also mound shaped and symmetric II. t distributions are more spread out than the normal distribution III. as degrees of freedom increase, the variance of t distributions becomes larger

I and II only

31. Which statement about residuals plots is true? I. A curved pattern indicates nonlinear association between the variables. II. A pattern of increasing speed indicates the predicted values become less reliable as the explanatory variable increase. III. Randomness in the residuals indicates the model will predict accurately.

I and II only

27. Hoping to get information that would allow them to negotiate new rates with their advertisers, Natural Health magazine phoned a random sample of 600 subscribers. 64% of those polled said they use nutritional supplements. Which is true? I. The population of interest is the people who read this magazine. II. "64%" is not a statistic, it's the parameter of interest III. Thie sampling design should provide the company with a reasonably accurate estimate of the percentage of all subscribers who use supplements.

I and III only

42. Which of the statements correctly compared t-distribtuions to the normal distribution? I. t distributions are also mound shaped and symmetric II. t distributions have less spread than the normal distribution III. as degrees of freedom increase, the variance of t distributions becomes smaller

I and III only

23. A certain population is strongly skewed to the left. We want to estimate its mean, so we collect a sample. Which should be true if we use a large sample rather than a small over? I. The distribution of our sample data will be more clearly skewed to the left. II. The sampling model of the sample means will be more skewed to the left. III. The variability of the sample means will greater.

I only

58. Among a dozen eggs, three are rotten. A cookie recipe calls for two eggs; they'll be selected randomly from that dozen. Which plan could be used to stimulate the number of rotten eggs that might be chosen? I. Let 0,1, and 2 represent the rotten eggs, and 3,4,...,11 the good eggs. Generate two random numbers 0-11, ignoring repeats. II. Randomly generate a 0,1,, or 2 to represent the number of rotten eggs you get. III. Since 25% of the eggs are rotten, let 0=rotten and 1,2,3=good. Generate two random numbers 0-3 and see how many 0's you get.

I only

61. Which of the following is true about Student's t-models? I. They are unimodal, symmetric, and bell shaped. II. They have fatter tails than the Normal model. III. As the degrees of freedom increase, the t-models look more and more like the Normal.

I, II, and III

40. We have calculated a 95% confidence interval and would prefer for our next confidence interval to have a smaller margin of error without losing any confidence. In order to do this, we can I. change the z* value to a smaller number II. take a larger sample III. take a smaller sample

II only

60. Which statement about bias is true? I. Bias results from random variation and will always be present. II. Bias results from a sampling method likely to produce samples that do not represent the population. III. Bias is usually reduced when sample size is larger.

II only

65. A basketball player has a 70% free throw percentage. Which plan could be used to stimulate the number of free throws she will make in her next five free throw attempts? I. Let 0,1 represent making the first shot, 2,3 represent making the second shot,...,8,9 represent making the fifth shot. Generate five random numbers 0-9, ignoring repeats. II. Let 0,1,2 represent missing a shot and 3,4,...,9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9. III. Let 0,1,2 represent missing a shot and 3,4,...,9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9, ignoring repeats.

II only

15. Which is true about a 95% confidence interval based on a given sample? I. The interval contains 95% of the population. II. Results from 95% of all samples will lie in the interval. III. The interval is narrower than a 98% confidence interval would be.

III only

29. Which is true about a 99% confidence interval based on a given sample? I. The interval contains 99% of the population. II. Results from 99% of all samples will lie in this interval. III. The interval is wider than a 95% confidence interval would be.

III only

45. Which is true about a 98% confidence interval for a population proportion based on a given sample?

III only

16. A philosophy professors wants to find out whether the mean age of the men in his large lecture class is equal to the mean age of the women in his class. After collecting data from a random sample of his students, the professor tested the hypothesis Ho-uW=0 against the alternative Ha:uM-uW does not equal 0. The p-value for the test was 0.003. Which is true?

It is very unlikely that the professor would see results like these if the mean age of men was equal to the mean age of women.

20. Two variables that are actually not related to each other may nonetheless have a very high correlation because they both result from some other, possibly hidden, factor. This is an example of:

Lurking variable

6. Researchers studying growth patterns of children collect data on the heights of fathers and sons. The correlation between the fathers' heights and the heights of their 16 year old sons is most likely to be....

Near +0.7

22. A factory has 20 assembly lines producing a popular toy. To inspect a representative sample of 100 toys, quality control staff randomly selected 5 toys from each line's output. Was this a sample random sample?

No, because not all combinations of 100 toys could have been chosen.

34. Suppose the state decides to randomly test high school wrestlers for steroid use. There are 16 team in the league, and each team has 20 wrestlers. State investigators plan to test 32 of these athletes by randomly choosing two wrestlers from each team. Is this a simple random sample?

No, because not all possible groups of 32 wrestlers could have been the sample.

1. A researcher found that a 98% confidence interval for the mean hours per week spent studying by college students was (13,17). Which is true?

None

56. Doctors at a technology research facility randomly assigned equal numbers of people to use computer keyboards in two rooms. In one room a group of people typed a manuscript using standard keyboards, while in the other room people typed using the same manuscript using ergonomic keyboards to see if those people could type more words per minute. After collecting data for several days the researchers tested the hypothesis Ho: u1-u2=0 against one-tail alternative and found a p-value of 0.22. Which is true?

None of these.

8. Of the following, which is not a critical part of designing a good experiment?

Random selection of subjects

7. All but one of the statements below contain a mistake. Which one could be true?

The correlation between blood alcohol level and reaction time is r=0.73.

43. All but one of the statements below contain a mistake. Which one could be true?

The correlation between weight and length of foot is 0.488.

4. We want to know the mean winning score at the US Open golf championship. An internet search gives us all the scores for the history of that tournament, and we create a 95% confidence interval based on a t-distribution. The procedure was not appropriate. Why?

The entire population of scores was gathered so there is no reason to do inference.

5. The residuals plot for a linear model is shown. Which is true?

The linear model is no good because of the curve in the residuals.

62. A correlation of zero between two quantitative variables means that

There is no linear association between the two variables

57. A marketing company reviewing the length of television commercials monitored a random sample of commercials over several days. They found that a 95% confidence interval for the mean length (in seconds) of commercials aired daily was (23,27). Which is true?

We're 95% sure that the mean commercial length is between 23 and 27 seconds.

66. A company checking the productivity of its assembly line monitored a random sample of workers for several days. They found that a 95% confidence interval for the mean number of items produced daily by each worker was (23,27). Which is true?

We're 95% sure that the mean daily worker output is between 23 and 27 items.

10. Which variable about German Shepards is most likely to be described by a normal model?

Weight

33. Suppose your local school district decides to randomly test high school students for attention deficit disorder (ADD). There are three high schools in the district, each with grades 912. The school board pools all of the students together and randomly samples 250 students. Is this a simple random sample?

Yes, because they could have chosen any 250 students throughout the district.

59. The SPCA collects the following data about the dogs they house. Which data is categorical?

breed

49. If we wish to compare the average PSAT scores of boys and girls taking AP Statistics at this high school, which would be the best way to gather these data?

census

69. We wish to compare the average ages of the math and science teachers at your school. Which is the best way to collect the data?

census

28. The correlation coefficient between the hours that a person is awake during a 24 hour period and the hours that same person is asleep during a 24 hour period is most likely to be

exactly -1.0

50. School administrators collect data on students attending the school. Which of the following variables is quantitative?

grade point average

54. Which of those variables is most likely to follow a Normal model?

head circumference

30. The mean number of hours worked for the 30 males was 6, and for the females was 9. The overall mean number of hours worked...

is 7.2

51. It takes a while for new factory workers to master a complex assembly line process. During the first month new employees work, the company tracks the number of days they have been on the job and the length of time it takes them to complete an assembly. The correlation is most likely to be

near -0.6

26. Which two events are most likely to be independent?

registering to vote; being left-handed

63. A company sponsoring a new Internet search engine wants to collect on the ease of using it. Which is the best way to collect data?

sample survey

64. Residuals are...

the difference between observed responses and values predicted by the model

48. The SPCA has kept these data records for the past 20 years. If they want to show the trend in the number of dogs they have housed, what kind of plot should they make?

timeplot

67. Which of the following variables would most likely follow a Normal model?

weights of adult male elephants