﻿ ﻿Take a Diagnostic Exam - Determine Your Test Readiness - 5 Steps to a 5 AP Statistics 2017 (2016)

## 5 Steps to a 5 AP Statistics 2017 (2016)

### STEP 2

CHAPTER 3 Take a Diagnostic Exam

### Take a Diagnostic Exam

IN THIS CHAPTER

Summary: The following diagnostic exam begins with 40 multiple-choice questions. The diagnostic exam also includes five free-response questions and one investigative task much like those on the actual exam. All of these test questions have been written to approximate the coverage of material that you will see on the AP exam but are intentionally somewhat more basic than actual exam questions (which are more closely approximated by the Practice Exams at the end of the book). Once you are done with the exam, check your work against the given answers, which also indicate where you can find the corresponding material in the book. You will also be given a way to convert your score to a rough AP score.

Key Ideas

Practice the kind of questions you will be asked on the real AP Statistics exam.

Answer questions that approximate the coverage of topics on the real exam.

Determine your areas of strength and weakness.

AP Statistics Diagnostic Test

AP Statistics Diagnostic Test

SECTION I

Time: 1 hour and 30 minutes

Number of questions: 40

Directions: Use the answer sheet provided on the previous page. All questions are given equal weight. There is no penalty for unanswered questions. One point is earned for every correct answer. The use of a calculator is permitted in all parts of this test. You have 90 minutes for this part of the test.

1. Eighteen trials of a binomial random variable X are conducted. If the probability of success for any one trial is 0.4, write the mathematical expression you would need to evaluate to find P (X = 7). Do not evaluate.
2. Two variables, x and y , seem to be exponentially related. The natural logarithm of each y value is taken and the least-squares regression line of ln(y ) on x is determined to be ln(y ) = 3.2 + 0.42x . What is the predicted value of ywhen x = 7?
3. 464.05
4. 1380384.27
5. 521.35
6. 6.14
7. 1096.63
8. You need to construct a 94% confidence interval for a population proportion. What is the upper critical value of z to be used in constructing this interval?
9. 0.9699
10. 1.96
11. 1.555
12. –1.88
13. 1.88

14. Which of the following best describes the shape of the histogram at the left?
15. Approximately normal
16. Skewed left
17. Skewed right
18. Approximately normal with an outlier
19. Symmetric
20. The probability is 0.2 that a value selected at random from a normal distribution with mean 600 and standard deviation 15 will be above what number?
21. 0.84
22. 603.80
23. 612.6
24. 587.4
25. 618.8
26. Which of the following are examples of continuous data?
27. The speed your car goes
28. The number of outcomes of a binomial experiment

III. The average temperature in San Francisco

1. The wingspan of a bird
2. The jersey numbers of a football team
3. I, III, and IV only
4. II and V only
5. I, III, and V only
6. II, III, and IV only
7. I, II, and IV only

Use the following computer output for a least-squares regression for Questions 7 and 8.

1. What is the equation of the least-squares regression line?
2. ŷ= –0.6442x + 22.94
3. ŷ= 22.94 + 0.5466x
4. ŷ= 22.94 + 2.866x
5. ŷ= 22.94 – 0.6442x
6. ŷ= –0.6442 + 0.5466x
7. Given that the analysis is based on 10 datapoints, what is the P -value for the t -test of the hypothesis H 0 : β = 0 versus H A : β ≠ 0?
8. 0.02 <P < 0.03
9. 0.20 <P < 0.30
10. 0.01 <P < 0.05
11. 0.15 <P < 0.20
12. 0.10 <P < 0.15
13. “A hypothesis test yields a P -value of 0.20.” Which of the following best describes what is meant by this statement?
14. The probability of getting a finding at least as extreme as that obtained by chance alone if the null hypothesis is true is 0.20.
15. The probability of getting a finding as extreme as that obtained by chance alone from repeated random sampling is 0.20.
16. The probability is 0.20 that our finding is significant.
17. The probability of getting this finding is 0.20.
18. The finding we got will occur less than 20% of the time in repeated trials of this hypothesis test.
19. A random sample of 25 men and a separate random sample of 25 women are selected to answer questions about attitudes toward abortion. The answers were categorized as “pro-life” or “pro-choice.” Which of the following is the proper null hypothesis for this situation?
20. The variables “gender” and “attitude toward abortion” are related.
21. The proportion of “pro-life” men is the same as the proportion of “pro-life” women.
22. The proportion of “pro-life” men is related to the proportion of “pro-life” women.
23. The proportion of “pro-choice” men is the same as the proportion of “pro-life” women.
24. The variables “gender” and “attitude toward abortion” are independent.
25. A sports talk show asks people to call in and give their opinion of the officiating in the local basketball team”s most recent loss. What will most likely be the typical reaction?
26. They will most likely feel that the officiating could have been better, but that it was the team”s poor play, not the officiating, that was primarily responsible for the loss.
27. They would most likely call for the team to get some new players to replace the current ones.
28. The team probably wouldn”t have lost if the officials had been doing their job.
29. Because the team had been foul-plagued all year, the callers would most likely support the officials.
30. They would support moving the team to another city.
31. A major polling organization wants to predict the outcome of an upcoming national election (in terms of the proportion of voters who will vote for each candidate). They intend to use a 95% confidence interval with margin of error of no more than 2.5%. What is the minimum sample size needed to accomplish this goal?
32. 1536
33. 39
34. 1537
35. 40
36. 2653
37. A sample of size 35 is to be drawn from a large population. The sampling technique is such that every possible sample of size 35 that could be drawn from the population is equally likely. What name is given to this type of sample?
38. Systematic sample
39. Cluster sample
40. Voluntary response sample
41. Random sample
42. Simple random sample
43. A teacher”s union and a school district are negotiating salaries for the coming year. The teachers want more money, and the district, claiming, as always, budget constraints, wants to pay as little as possible. The district, like most, has a large number of moderately paid teachers and a few highly paid administrators. The salaries of all teachers and administrators are included in trying to figure out, on average, how much the professional staff currently earn. Which of the following would the teachers” union be most likely to quote during negotiations?
44. The mean of all the salaries.
45. The mode of all the salaries.
46. The standard deviation of all the salaries.
47. The interquartile range of all the salaries.
48. The median of all the salaries.
49. Alfred and Ben don”t know each other but are each considering asking the lovely Charlene to the school prom. The probability that at least one of them will ask her is 0.72. The probability that they both ask her is 0.18. The probability that Alfred asks her is 0.6. What is the probability that Ben asks Charlene to the prom?
50. 0.78
51. 0.30
52. 0.24
53. 0.48
54. 0.54
55. A significance test of the hypothesis H 0 : p = 0.3 against the alternative H A : p > 0.3 found a value of = 0.35 for a random sample of size 95. What is the P -value of this test?
56. 1.06
57. 0.1446
58. 0.2275
59. 0.8554
60. 0.1535
61. Which of the following describe/s the central limit theorem?
62. The mean of the sampling distribution of x– is the same as the mean of the population.
63. The standard deviation of the sampling distribution of x– is the same as the standard deviation of x – divided by the square root of the sample size.

III. If the sample size is large, the shape of the sampling distribution of x – is approximately normal.

1. I only
2. I & II only
3. II only
4. III only
5. I, II, and III
6. If three fair coins are flipped, P (0 heads) = 0.125, P (exactly 1 head) = 0.375, P (exactly 2 heads) = 0.375, and P (exactly 3 heads) = 0.125. The following results were obtained when three coins were flipped 64 times:

What is the value of the X 2 statistic used to test if the coins are behaving as expected, and how many degrees of freedom does the determination of the P -value depend on?

1. 3.33, 3
2. 3.33, 4
3. 11.09, 3
4. 3.33, 2
5. 11.09, 4

For the histogram pictured above, what is the class interval (boundaries) for the class that contains the median of the data?

1. (5, 7)
2. (9, 11)
3. (11, 13)
4. (15, 17)
5. (7, 9)
6. Thirteen large animals were measured to help determine the relationship between their length and their weight. The natural logarithm of the weight of each animal was taken and a least-squares regression equation for predicting weight from length was determined. The computer output from the analysis is given below:

Give a 99% confidence interval for the slope of the regression line. Interpret this interval.

1. (0.032, 0.041); the probability is 0.99 that the true slope of the regression line is between 0.032 and 0.041.
2. (0.032, 0.041); 99% of the time, the true slope will be between 0.032 and 0.041.
3. (0.032, 0.041); we are 99% confident that the true slope of the regression line is between 0.032 and 0.041.
4. (0.81, 1.66); we are 99% confident that the true slope of the regression line is between 0.032 and 0.041.
5. (0.81, 1.66); the probability is 0.99 that the true slope of the regression line is between 0.81 and 1.66.
6. What are the mean and standard deviation of a binomial experiment that occurs with probability of success 0.76 and is repeated 150 times?
7. 114, 27.35
8. 100.5, 5.23
9. 114, 5.23
10. 100.5, 27.35
11. The mean is 114, but there is not enough information given to determine the standard deviation.
12. Which of the following is the primary difference between an experiment and an observational study?
13. Experiments are only conducted on human subjects; observational studies can be conducted on nonhuman subjects.
14. In an experiment, the researcher manipulates some variable to observe its effect on a response variable; in an observational study, he or she simply observes and records the observations.
15. Experiments must use randomized treatment and control groups; observational studies also use treatment and control groups, but they do not need to be randomized.
16. Experiments must be double-blind; observational studies do not need to be.
17. There is no substantive difference—they can both accomplish the same research goals.
18. The regression analysis of question 20 indicated that “R-sq = 98.1%.” Which of the following is (are) true?
19. There is a strong positive linear relationship between the explanatory and response variables.
20. There is a strong negative linear relationship between the explanatory and response variables.

III. About 98% of the variation in the response variable can be explained by the regression on the explanatory variable.

1. I and III only
2. I or II only
3. I or II (but not both) and III
4. II and III only
5. I, II, and III
6. A hypothesis test is set up so that P (rejecting H 0 when H 0 is true) = 0.05 and P (failing to reject H 0 when H 0 is false) = 0.26. What is the power of the test?
7. 0.26
8. 0.05
9. 0.95
10. 0.21
11. 0.74
12. For the following observations collected while doing a chi-square test for independence between the two variables A and B , find the expected value of the cell marked with “X .”
13. 4.173
14. 9.00
15. 11.56
16. 8.667
17. 9.33
18. The following is a probability histogram for a discrete random variable X.
19. 3.5
20. 4.0
21. 3.7
22. 3.3
23. 3.0
24. A psychologist believes that positive rewards for proper behavior are more effective than punishment for bad behavior in promoting good behavior in children. A scale of “proper behavior” is developed. μ 1 = the “proper behavior” rating for children receiving positive rewards, and μ 2 = the “proper behavior” rating for children receiving punishment. If H 0 : μ 1μ 2 = 0, which of the following is the proper statement of H A ?
25. HA : μ 1μ 2 > 0
26. HA : μ 1μ 2 < 0
27. HA : μ 1μ 2 ≠ 0
28. Any of the above is an acceptable alternative to the given null.
29. There isn”t enough information given in the problem for us to make a decision.
30. Estrella wants to become a paramedic and takes a screening exam. Scores on the exam have been approximately normally distributed over the years it has been given. The exam is normed with a mean of 80 and a standard deviation of 9. Only those who score in the top 15% on the test are invited back for further evaluation. Estrella received a 90 on the test. What was her percentile rank on the test, and did she qualify for further evaluation?
31. 13.35; she didn”t qualify.
32. 54.38; she didn”t qualify.
33. 86.65; she qualified.
34. 84.38; she didn”t qualify.
35. 88.69; she qualified.
36. Which of the following statements is (are) true?
37. In order to use aχ 2 procedure, the expected value for each cell of a one- or two-way table must be at least 5.
38. In order to useχ 2 procedures, you must have at least 2 degrees of freedom.

III. In a 4 × 2 two-way table, the number of degrees of freedom is 3.

1. I only
2. I and III only
3. I and II only
4. III only
5. I, II, and III
6. When the point (15,2) is included, the slope of regression line (y = a + bx ) is b = –0.54. The correlation is r = –0.82. When the point is removed, the new slope is –1.04 and the new correlation coefficient is –0.95. What name is given to a point whose removal has this kind of effect on statistical calculations?
7. Outlier
8. Statistically significant point
9. Point of discontinuity
10. Unusual point
11. Influential point
12. A one-sided test of a hypothesis about a population mean, based on a sample of size 14, yields a P -value of 0.075. Which of the following best describes the range of t values that would have given this P -value?
13. 1.345 <t < 1.761
14. 1.356 <t < 1.782
15. 1.771 <t < 2.160
16. 1.350 <t < 1.771
17. 1.761 <t < 2.145
18. Use the following excerpt from a random digits table for assigning six people to treatment and control groups:
98110 35679 14520 51198 12116 98181 99120 75540 03412 25631
The subjects are labeled: Arnold: 1; Betty: 2; Clive: 3; Doreen: 4; Ernie: 5; Florence: 6. The first three subjects randomly selected will be in the treatment group; the other three in the control group. Assuming you begin reading the table at the extreme left digit, which three subjects would be in the control group?
19. Arnold, Clive, Ernest
20. Arnold, Betty, Florence
21. Betty, Clive, Doreen
22. Clive, Ernest, Florence
23. Betty, Doreen, Florence
24. A null hypothesis, H 0 : μ = μ 0 is to be tested against a two-sided hypothesis. A sample is taken; x – is determined and used as the basis for a C -level confidence interval (e.g., C = 0.95) for μ . The researcher notes that μ 0 is not in the interval. Another researcher chooses to do a significance test for μ using the same data. What significance level must the second researcher choose in order to guarantee getting the same conclusion about H 0 : μ = μ 0 (that is, reject or not reject) as the first researcher?
25. 1 –C
26. C
27. α
28. 1 –α
29. α= 0.05
30. Which of the following is not required in a binomial setting?
31. Each trial is considered either a success or a failure.
32. Each trial is independent.
33. The value of the random variable of interest is the number of trials until the first success occurs.
34. There is a fixed number of trials.
35. Each trial succeeds or fails with the same probability.
36. X and Y are independent random variables with μ X = 3.5, μ Y = 2.7, σ X = 0.8, and σ Y = 0.65. What are μ X +Y and σ X +Y ?
37. μX +Y = 6.2, σ X +Y = 1.03
38. μX +Y = 6.2, σ X +Y = 1.0625
39. μX +Y = 3.1, σ X +Y = 0.725
40. μX +Y = 6.2, σ X +Y = 1.45
41. μX +Y = 6.2, σ X +Y cannot be determined from the information given.
42. A researcher is hoping to find a predictive linear relationship between the explanatory and response variables in her study. Accordingly, as part of her analysis she plans to generate a 95% confidence interval for the slope of the regression line for the two variables. The interval is determined to be (0.45, 0.80). Which of the following is (are) true? (Assume conditions for inference are met.)
43. She has good evidence of a linear relationship between the variables.
44. It is likely that there is a non-zero correlation (r) between the two variables.

III. It is likely that the true slope of the regression line is 0.

1. I and II only
2. I and III only
3. II and III only
4. I only
5. II only
6. In the casino game of roulette, there are 38 slots for a ball to drop into when it is rolled around the rim of a revolving wheel: 18 red, 18 black, and 2 green. What is the probability that the first time a ball drops into the red slot is on the 8th trial (in other words, suppose you are betting on red every time—what is the probability of losing 7 straight times before you win the first time)?
7. 0.0278
8. 0.0112
9. 0.0053
10. 0.0101
11. 0.0039
12. You are developing a new strain of strawberries (say, Type X) and are interested in its sweetness as compared to another strain (say, Type Y). You have four plots of land, call them A, B, C, and D, which are roughly four squares in one large plot for your study (see the figure below). A river runs alongside of plots C and D. Because you are worried that the river might influence the sweetness of the berries, you randomly plant type X in either A or B (and Y in the other) and randomly plant type X in either C or D (and Y in the other). Which of the following terms best describes this design?
13. A completely randomized design
14. A randomized study
15. A randomized observational study
16. A block design, controlling for the strain of strawberry
17. A block design, controlling for the effects of the river
18. Grumpy got 38 on the first quiz of the quarter. The class average on the first quiz was 42 with a standard deviation of 5. Dopey, who was absent when the first quiz was given, got 40 on the second quiz. The class average on the second quiz was 45 with a standard deviation of 6.1. Grumpy was absent for the second quiz. After the second quiz, Dopey told Grumpy that he was doing better in the class because they had each taken one quiz, and he had gotten the higher score. Did he really do better? Explain.
19. Yes. zDopey is more negative than z Grumpy .
20. Yes. zDopey is less negative than z Grumpy .
21. No. zDopey is more negative than z Grumpy .
22. Yes. zDopey is more negative than z Grumpy .
23. No. zDopey is less negative than z Grumpy .
24. A random sample size of 45 is obtained for the purpose of testing the hypothesis H 0 : p = 0.80. The sample proportion is determined to be = 0.75. What is the value of the standard error of for this test?
25. 0.0042
26. 0.0596
27. 0.0036
28. 0.0645
29. 0.0055

SECTION II—PART A, QUESTIONS 1–5

Spend about 65 minutes on this part of the exam. Percentage of Section II grade—75.

Directions: Show all of your work. Indicate clearly the methods you use because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation.

1. The ages (in years) and heights (in cm) of 10 girls, ages 2 through 11, were recorded. Part of the regression output and the residual plot for the data are given below.
2. What is the equation of the least-squares regression line for predicting height from age?
3. Interpret the slope of the regression line in the context of the problem.
4. Suppose you wanted to predict the height of a girl 5.5 years of age. Would the prediction made by the regression equation you gave in (a) be too small, too large, or is there not enough information to tell?
5. You want to determine whether a greater proportion of men or women purchase vanilla lattes (regular or decaf). To collect data, you hire a person to stand inside the local Scorebucks for 2 hours one morning and tally the number of men and women who purchase the vanilla latte, as well as the total number of men and women customers: 63% of the women and 59% of the men purchase a vanilla latte.
6. Is this an experiment or an observational study? Explain.
7. Based on the data collected, you write a short article for the local newspaper claiming that a greater proportion of women than men prefer vanilla latte as their designer coffee of choice. A student in the local high school AP Statistics class writes a letter to the editor criticizing your study. What might the student have pointed out?
8. Suppose you wanted to conduct a study less open to criticism. How might you redo the study?
9. Sophia is a nervous basketball player. Over the years she has had a 40% chance of making the first shot she takes in a game. If she makes her first shot, her confidence goes way up, and the probability of her making the second shot she takes rises to 70%. But if she misses her first shot, the probability of her making the second shot she takes doesn”t change—it”s still 40%.
10. What is the probability that Sophia makes her second shot?
11. If Sophia does make her second shot, what is the probability that she missed her first shot?
12. A random sample of 72 seniors taken 3 weeks before the selection of the school Homecoming Queen identified 60 seniors who planned to vote for Buffy for queen. Unfortunately, Buffy said some rather catty things about some of her opponents, and it got into the school newspaper. A second random sample of 80 seniors taken shortly after the article appeared showed that 56 planned to vote for Buffy. Does this indicate a serious drop in support for Buffy? Use good statistical reasoning to support your answer.
13. Some researchers believe that education influences IQ. One researcher specifically believes that the more education a person has, the higher, on average, will be his or her IQ. The researcher sets out to investigate this belief by obtaining eight pairs of identical twins reared apart. He identifies the better educated twin as Twin A and the other twin as Twin B for each pair. The data for the study are given in the table below. Do the data give good statistical evidence, at the 0.05 level of significance, that the twin with more education is likely to have the higher IQ? Give good statistical evidence to support your answer.

SECTION II—PART B, QUESTION 6

Spend about 25 minutes on this part of the exam. Percentage of Section II grade—25.

Directions: Show all of your work. Indicate clearly the methods you use because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation.

1. A paint manufacturer claims that the average drying time for its best-selling paint is 2 hours. A random sample of drying times for 20 randomly selected cans of paint are obtained to test the manufacturer”s claim. The drying times observed, in minutes, were: 123, 118, 115, 121, 130, 127, 112, 120, 116, 136, 131, 128, 139, 110, 133, 122, 133, 119, 135, 109.
2. Obtain a 95% confidence interval for the true mean drying time of the paint.
3. Interpret the confidence interval obtained in part (a) in the context of the problem.
4. Suppose, instead, that a significance test at the 0.05 level of the hypothesisH 0 : μ = 120 was conducted against the alternative H A : μ ≠ 120. What is the P -value of the test?
5. Are the answers you got in part (a) and part (c) consistent? Explain.
6. At the 0.05 level, would your conclusion about the mean drying time have been different if the alternative hypothesis had beenH A : μ > 120? Explain.

END OF DIAGNOSTIC EXAM

1. c
2. a
3. e
4. d
5. c
6. a
7. d
8. b
9. a
10. b
11. c
12. c
13. e
14. e
15. b
16. b
17. d
18. a
19. e
20. c
21. c
22. b
23. c
24. e
25. d
26. d
27. a
28. c
29. b
30. e
31. d
32. e
33. a
34. c
35. a
36. a
37. c
38. e
39. c
40. b

SOLUTIONS TO DIAGNOSTIC TEST—SECTION I

1. From Chapter 10

The correct answer is (c). If X has B (n, p ), then, in general,

In this problem, n = 18, p = 0.4, x = 7 so that

1. From Chapter 7

The correct answer is (a). ln (y ) = 3.2 + 0.42(7) = 6.14⇒y = e 6.14 = 464.05.

1. From Chapter 11

The correct answer is (e). For a 94% z -interval, there will be 6% of the area outside of the interval. That is, there will be 97% of the area less than the upper critical value of z . The nearest entry to 0.97 in the table of standard normal probabilities is 0.9699, which corresponds to a z -score of 1.88.

(Using the TI-83/84, we have invNorm(0.97) = 1.8808 .)

1. From Chapter 6

The correct answer is (d). If the bar to the far left was not there, this graph would be described as approximately normal. It still has that same basic shape but, because there is an outlier, the best description is: approximately normal with an outlier.

1. From Chapter 9

The correct answer is (c). Let x be the value in question. If there is 0.2 of the area above x , then there is 0.8 of the area to the left of x . This corresponds to a z -score of 0.84 (from Table A, the nearest entry is 0.7995). Hence,

(Using the TI-83/84, we have invNorm(0.8) = 0.8416 .)

1. From Chapter 5

The correct answer is (a). Discrete data are countable; continuous data correspond to intervals or measured data. Hence, speed, average temperature, and wingspan are examples of continuous data. The number of outcomes of a binomial experiment and the jersey numbers of a football team are countable and, therefore, discrete.

1. From Chapter 7

The correct answer is (d). The slope of the regression line. –0.6442, can be found under “Coef” to the right of “x .” The intercept of the regression line, 22.94, can be found under “Coef” to the right of “Constant.”

1. From Chapter 13

The correct answer is (b). The t statistic for H 0 : β = 0 is given in the printout as –1.18. We are given that n = 10 ⇒ df = 10 – 2 = 8. From the df = 8 row of Table B (the t Distribution Critical Values table), we see, ignoring the negative sign since it”s a two-sided test,

1.108 < 1.18 < 1.397 ⇒ 2(0.10) < P < 2(0.15),

which is equivalent to 0.20 < P < 0.30. Using the TI-83/84, we have 2 × tcdf (-100, –1.18,8) = 0.272.

1. From Chapter 12

The correct answer is (a). The statement is basically a definition of P -value. It is the likelihood of obtaining, by chance alone, value as extreme or more extreme as that obtained if the null hypothesis is true. A very small P -value sheds doubt on the truth of the null hypothesis.

1. From Chapter 14

The correct answer is (b). Because the samples of men and women represent different populations, this is a chi-square test of homogeneity of proportions: the proportions of each value of the categorical variable (in this case, “pro-choice” or “pro-life”) will be the same across the different populations. Had there been only one sample of 50 people drawn, 25 of whom happened to be men and 25 of whom happened to be women, this would have been a test of independence.

1. From Chapter 8

The correct answer is (c). This is a voluntary response survey and is subject to voluntary response bias. That is, people who feel the most strongly about an issue are those most likely to respond. Because most callers would be fans, they would most likely blame someone besides the team.

1. From Chapter 11

The correct answer is (c). The “recipe” we need to use is n ≥ . Since we have no basis for an estimate for P * , we use P * = 0.5. In this situation the formula reduces to

Since n must be an integer, choose n = 1537.

1. From Chapter 8

The correct answer is (e). A random sample from a population is one in which every member of the population is equally likely to be selected. A simple random sample is one in which every sample of a given size is equally likely to be selected. A sample can be a random sample without being a simple random sample.

1. From Chapter 6

The correct answer is (e). The teachers are interested in showing that the average teacher salary is low. Because the mean is not resistant, it is pulled in the direction of the few higher salaries and, hence, would be higher than the median, which is not affected by a few extreme values. The teachers would choose the median. The mode, standard deviation, and IQR tell you nothing about the average salary.

1. From Chapter 9

The correct answer is (b). P (at least one of them will ask her) = P (A or B) = 0.72.

P (they both ask her) = P (A and B) = 0.18.

P (Alfred asks her) = P (A) = 0.6.

In general, P (A or B) = P (A) + P (B) – P (A and B). Thus, 0.72 = 0.6 + P (B) – 0.18 ⇒ P (B) = 0.30.

1. From Chapter 12

(Using the TI-83/84, we find normalcdf(1.06,100) = 0.1446. )

1. From Chapter 10

The correct answer is (d). Although all three of the statements are true of a sampling distribution, only III is a statement of the central limit theorem.

1. From Chapter 14

(This calculation can be done on the TI-83/84 as follows: let L1 = observed values; let L2 = expected values; let L3 = (L2-L1 )2 /L2 ; Then χ 2 = LIST MATH sum(L3) =3.33. )

In a chi-square goodness-of-fit test, the number of degrees of freedom equals one less than the number of possible outcomes. In this case, df = n –1 = 4 – 1 = 3.

1. From Chapter 6

The correct answer is (e). There are 101 terms, so the median is located at the 51st position in an ordered list of terms. From the counts given, the median must be in the interval whose midpoint is 8. Because the intervals are each of width 2, the class interval for the interval whose midpoint is 8 must be (7, 9).

1. From Chapter 13

The correct answer is (c). df = 13 – 2 = 11 ⇒ t * = 3.106 (from Table B; if you have a TI-84 with the invT function, t * = in v T(0.995,11 )). Thus, a 99% confidence interval for the slope is:

0.0365 ± 3.106(0.0015) = (0.032, 0.041).

We are 99% confident that the true slope of the regression line is between 0.032 units and 0.041 units.

1. From Chapter 10
2. From Chapter 8

The correct answer is (b). In an experiment, the researcher imposes some sort of treatment on the subjects of the study. Both experiments and observational studies can be conducted on human and nonhuman units; there should be randomization to groups in both to the extent possible; they can both be double blind.

1. From Chapter 7

The correct answer is (c). III is basically what is meant when we say R-sq = 98.1%. However, R-sq is the square of the correlation coefficient.

could be either positive or negative, but not both. We can”t tell direction from R 2 .

1. From Chapter 11

The correct answer is (e). The power of a test is the probability of correctly rejecting H 0 when H A is true. You can either fail to reject H 0 when it is false (Type II), or reject it when it is false (Power). Thus, Power = 1 – P (Type II) = 1 – 0.26 = 0.74.

1. From Chapter 14

The correct answer is (d). There are 81 observations total, 27 observations in the second column, 26 observations in the first row. The expected number in the first row and second column equals

1. From Chapter 9

μ X = 2(0.3) + 3(0.2) + 4(0.4) + 5(0.1) = 3.3.

1. From Chapter 12

The correct answer is (a). The psychologist”s belief implies that, if she”s correct, μ 1 > μ 2 . Hence, the proper alternative is H A : μ 1μ 2 > 0.

1. From Chapter 6

Because she had to be in the top 15%, she had to be higher than the 85th percentile, so she was invited back.

1. From Chapter 14

The correct answer is (b). I is true. Another common standard is that there can be no empty cells, and at least 80% of the expected counts are greater than 5. II is not correct because you can have 1 degree of freedom (for example, a 2 × 2 table). III is correct because df = (4 – 1) (2 – 1) = 3.

1. From Chapter 7

The correct answer is (e). An influential point is a point whose removal will have a marked effect on a statistical calculation. Because the slope changes from –0.54 to –1.04, it is an influential point.

1. From Chapter 12

The correct answer is (d). df = 14 – 1 = 13. For a one-sided test and 13 degrees of freedom, 0.075 lies between tail probability values of 0.05 and 0.10. These correspond, for a one-sided test, to t * values of 1.771 and 1.350. (If you have a TI-84 with the invT function, t * = invT(1 -0.075,13) = 1.5299. )

1. From Chapter 8

The correct answer is (e). Numbers of concern are 1, 2, 3, 4, 5, 6. We ignore the rest. We also ignore repeats. Reading from the left, the first three numbers we encounter for our subjects are 1, 3, and 5. They are in the treatment group, so numbers 2, 4, and 6 are in the control group. That”s Betty, Doreen, and Florence. You might be concerned that the three women were selected and that, somehow, that makes the drawing nonrandom. However, drawing their three numbers had exactly the same probability of occurrence as any other group of three numbers from the six.

1. From Chapter 11

The correct answer is (a). If a significance test at level a rejects a null hypothesis (H 0 : μ = μ 0 ) against a two-sided alternative, then μ 0 will not be contained in a C = 1 – α level confidence interval constructed using the same value of . Thus, α = 1 – C .

1. From Chapter 10

The correct answer is (c). The statement in (c) describes the random variable for a geometric setting. In a binomial setting, the random variable of interest is the number count of successes in the fixed number of trials.

1. From Chapter 9

μ X+Y is correct for any random variables X and Y . However, σ X+Y is correct only if X and Y are independent .

1. From Chapter 14

The correct answer is (a). Because 0 is not in the interval (0.45, 0.80), it is unlikely that the true slope of the regression line is 0 (III is false). This implies a non-zero correlation coefficient and the existence of a linear relationship between the two variables.

1. From Chapter 10

The correct answer is (c). This is a geometric setting (independent trials, each succeeding or failing with the same probability).

(On the TI-83/84, this is found as geometpdf(18/38,8) .)

1. From Chapter 8

The correct answer is (e). The choice is made here to treat plots A and B as a block and plots C and D as a block. That way, we are controlling for the possible confounding effects of the river. Hence the answer is (c). If you answered (e), be careful of confusing the treatment variable with the blocking variable.

1. From Chapter 6 The correct answer is (c).

They are both below average, but Grumpy”s z score puts him slightly above Dopey. Note that if Grumpy had been 4 points above the mean on the first test and Dopey 5 points above the mean on the second, then Dopey would have done slightly better than Grumpy.

1. From Chapter 12

The standard error of for a test of H 0 : p = p 0 is

If you got an answer of 0.0645, it means you used the value of rather than the value of p 0 in the formula for s .

SOLUTIONS TO DIAGNOSTIC TEST—SECTION II, PART A

1. a.
2. For each additional year of age, the height (in cm) is predicted to increase by 6.36 cm.

We would expect the residual for 5.5 to be in the same general area as the residuals for 4, 5, 6, and 7 (circled on the graph). The residuals in this area are all positive ⇒ actual – predicted > 0 ⇒ actual > predicted. The prediction would probably be too small.

1. a. It is an observational study. The researcher made no attempt to impose a treatment on the subjects in the study. The hired person simply observed and recorded behavior.
2. • The article made no mention of the sample size. Without that you are unable to judge how much sampling variability there might have been. It”s possible that the 63–59 split was attributable to sampling variability.
• The study was done atone Scorebucks, on one morning, for a single 2-hour period. The population at that Scorebucks might differ in some significant way from the patrons at other Scorebucks around the city (and there are many, many of them). It might have been different on a different day or during a different time of the day. A single 2-hour period may not have been enough time to collect sufficient data (we don”t know because the sample size wasn”t given) and, again, a 2-hour period in the afternoon might have yielded different results.
1. You would conduct the study at multiple Scorebucks, possibly blocking by location if you believe that might make a difference (i.e., would a working-class neighborhood have different preferences than the ritziest neighborhood?). You would observe at different times of the day and on different days. You would make sure that the total sample size was large enough to control for sampling variability (replication).
2. From the information given, we have
• P(hit the first and hit the second) = (0.4) (0.7) = 0.28
• P(hit the first and miss the second) = (0.4) (0.3) = 0.12
• P(miss the first and hit the second) = (0.6) (0.4) = 0.24
• P(miss the first and miss the second) = (0.6) (0.6) = 0.36

This information can be summarized in the following table:

1. P(hit on second shot) = 0.28 + 0.24 = 0.52
2. P(miss on first | hit on second) = (0.24)/(0.52) = 6/13 = 0.46.
3. Let p 1 be the true proportion who planned to vote for Buffy before her remarks. Let p 2 be the true proportion who plan to vote for Buffy after her remarks.

We want to use a 2-proportion z test for this situation. The problem tells us that the samples are random samples.

Now, 72(0.83), 72(1 – 0.83), 80(0.70), and 80(1 – 0.70) are all greater than 5, so the conditions for the test are present.

Because P is very low, we reject the null. We have reason to believe that the level of support for Buffy has declined since her “unfortunate” remarks.

1. The data are paired, so we will use a matched pairs test.

Let μ d = the true mean difference between Twin A and Twin B for identical twins reared apart.

We want to use a one-sample t -test for this situation. We need the difference scores:

A dotplot of the difference scores shows no significant departures from normality:

The conditions needed for the one sample t -test are present.

(from Table B; on the TI-83/84, tcdf(2.39,100,7) =0.024 ).

Because P < 0.05, reject H 0 . We have evidence that, in identical twins reared apart, the better educated twin is likely to have the higher IQ score.

1. a. = 123.85, s = 9.07. We are told that the 20 cans of paint have been randomly selected. It is reasonable to assume that a sample of this size is small relative to the total population of such cans. A boxplot of the data shows no significant departures from normality. The conditions necessary to construct a 95% t confidence interval are present.
2. We are 95% confident that the true mean drying time for the paint is between 119.6 minutes and 128.1 minutes. Because 120 minutes is in this interval, we would not consider an average drying time of 120 minutes for the population from which this sample was drawn to be unusual.

(On the TI-83/84, we find P -value = 2 × tcdf(1.90,100,19) = 0.073. )

1. We know that if a two-sidedα -level significance test rejects (fails to reject) a null hypothesis, then the hypothesized value of μ will not be (will be) in a C = 1 – α confidence interval. In this problem, 120 was in the C = 0.95 confidence interval and a significance test at α = 0.05 failed to reject the null as expected.
2. For the one-sided test,t = 1.90, df = 19 ⇒ 0.025 < P -value < 0.05

(On the TI-83/84, we find P -value = tcdf(1.90,100,19) = 0.036. )

For the two-sided test, we concluded that we did not have evidence to reject the claim of the manufacturer. However, for the one-sided test, we have stronger evidence (P < 0.05) and would conclude that the average drying time is most likely greater than 120 minutes.

Scoring Sheet for Diagnostic Test

Section I: Multiple-Choice Questions

Section II: Free-Response Questions

Composite Score

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