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AP Statistics Practice Exam 2: printable

▶ Section I: multiple choice ✎ Section II: free response Answers and scoring guide

AP Statistics Practice Exam 2

Name: ______________________   Date: __________

Multiple choice: 42 questions (two sets of 3 on one prompt), 90 minutes, graphing calculator. Free response: 4 questions, 10 points each, 90 minutes, graphing calculator. steplyclass.com/ap-statistics/practice-exam-2/

Section I: multiple choice

  1. Seven runners finished a race in 34, 28, 41, 37, 30, 45 and 39 minutes. What is the median time, in minutes?
    1. A) 36.29
    2. B) 17
    3. C) 37
    4. D) 38
  2. A sample of five bus trips ran 4, 7, 10, 7 and 12 minutes late. What is the sample standard deviation, to one decimal place?
    1. A) 2.8
    2. B) 8
    3. C) 9.5
    4. D) 3.1
  3. Nine phone batteries lasted 22, 15, 30, 18, 27, 35, 12, 25 and 20 hours. What is the first quartile, Q1?
    1. A) 18
    2. B) 22
    3. C) 16.5
    4. D) 28.5
  4. A shop's sales on nine days were 52, 55, 57, 58, 60, 61, 63, 64 and 90. Using the 1.5 × IQR rule, which values are outliers?
    1. A) none
    2. B) 90 only
    3. C) 52 and 90
    4. D) 64 and 90
  5. Apples from an orchard have mean weight 70 grams and standard deviation 8 grams. What is the z-score of an apple that weighs 82 grams?
    1. A) 12
    2. B) −1.5
    3. C) 1.5
    4. D) 10.25
  6. Scores on an exam have mean 200 and standard deviation 20. Which score has a z-score of −1.5?
    1. A) 170
    2. B) 230
    3. C) 198.5
    4. D) 180
  7. The data are 10, 12, 13, 15 and 60. The value 60 is removed. How do the mean and the median change?
    1. A) mean: down 60, median: down 0.5
    2. B) mean: down 9.5, median: no change
    3. C) mean: down 0.5, median: down 9.5
    4. D) mean: down 9.5, median: down 0.5
  8. 250 adults were chosen at random from a city. Half of them chose to ride a bike to work, and the bike group felt less stressed. Which conclusion does the study support?
    1. A) causes it, for the whole city
    2. B) linked in the city, maybe not caused
    3. C) causes it, for people like these
    4. D) linked, for people like these
  9. 60 patients at a clinic volunteered for a study. Half of them were chosen at random to do a daily stretch, and the stretch group had less back pain. Which conclusion does the study support?
    1. A) causes it, for the whole clinic
    2. B) causes it, for people like these
    3. C) linked, for people like these
    4. D) linked in the clinic, maybe not caused
  10. 120 seedlings were picked at random from a nursery. Half of them were picked at random to get extra light, and the extra light group grew taller. Which conclusion does the study support?
    1. A) linked, for people like these
    2. B) linked in the nursery, maybe not caused
    3. C) causes it, for people like these
    4. D) causes it, for the whole nursery
  11. Seven shops sold 15, 22, 9, 30, 18, 25 and 12 umbrellas on a rainy day. What is the five-number summary?
    1. A) min 9, Q1 13.5, median 18, Q3 23.5, max 30
    2. B) min 9, Q1 15, median 18, Q3 22, max 30
    3. C) min 9, Q1 12, median 18, Q3 25, max 30
    4. D) min 9, Q1 12, median 18.71, Q3 25, max 30
  12. (Questions 12-14 use this.) At a school, 18 juniors ride the bus and 12 come by car; 10 seniors ride the bus and 20 come by car. One of these 60 students is picked at random. What is the probability that the student rides the bus?
    1. A) 715
    2. B) 35
    3. C) 13
    4. D) 815
  13. (Same students.) A senior is picked at random. What is the probability that the senior rides the bus?
    1. A) 13
    2. B) 16
    3. C) 514
    4. D) 23
  14. (Same students.) A bus rider is picked at random. What is the probability that the bus rider is a senior?
    1. A) 13
    2. B) 16
    3. C) 514
    4. D) 914
  15. A basketball player makes 60% of free throws, independently. In 5 throws, what is the probability that the player makes exactly 3?
    1. A) 0.216
    2. B) 0.6
    3. C) 0.3456
    4. D) 0.03456
  16. X is the number of books a student borrows in a week: P(X = 1) = 0.1, P(X = 2) = 0.3, P(X = 3) = 0.4, P(X = 4) = 0.2. What is the mean of X?
    1. A) 2.5
    2. B) 2.7
    3. C) 3
    4. D) 0.25
  17. Times to put together a desk are normal with mean 100 minutes and standard deviation 15 minutes. What is the probability that a desk takes more than 130 minutes?
    1. A) 0.9772
    2. B) 0.0456
    3. C) 0.1587
    4. D) 0.0228
  18. Lengths of bolts are normal with mean 60 mm and standard deviation 5 mm. What length has 95% of the bolts below it?
    1. A) 69.8
    2. B) 68.225
    3. C) 51.775
    4. D) 65
  19. A population has mean 30 and standard deviation 9. For random samples of 36, what is the probability that the sample mean is less than 32?
    1. A) 0.5879
    2. B) 0.9772
    3. C) 0.0918
    4. D) 0.9082
  20. Of 60 people, 32 like tea, 24 like coffee and 10 like both. One person is picked at random. What is the probability that the person likes neither?
    1. A) 2330
    2. B) 16
    3. C) 115
    4. D) 730
  21. In a random sample of 500 shoppers, 150 used a coupon. What is a 95% confidence interval for the proportion of all shoppers who use a coupon?
    1. A) (0.2663, 0.3337)
    2. B) (0.2598, 0.3402)
    3. C) (0.2795, 0.3205)
    4. D) (0.25, 0.35)
  22. In a random sample of 220 households, 66 have a pet. What is a 90% confidence interval for the proportion of all households that have a pet?
    1. A) (0.2492, 0.3508)
    2. B) (0.2394, 0.3606)
    3. C) (0.2691, 0.3309)
    4. D) (0.2984, 0.3016)
  23. A test of H0: p = 0.2 against Ha: p > 0.2 uses a random sample of 270 households, of which 63 own a dog. At α = 0.05, what is the conclusion?
    1. A) Reject H0
    2. B) Do not reject H0
    3. C) Accept H0: exactly 20% own a dog
    4. D) Accept Ha because 63270 is more than 0.2
  24. A town says 60% of its residents support a new park. In a random sample of 200 residents, 105 support it. A test of H0: p = 0.6 against Ha: p < 0.6 is done at α = 0.05. What is the conclusion?
    1. A) Reject H0: there is convincing evidence that fewer than 60% support the park
    2. B) Do not reject H0
    3. C) Accept H0: 60% support the park
    4. D) Accept Ha because 105 is more than half of 200
  25. In a random sample of 400 voters, 230 favour a plan. A test of H0: p = 0.5 against Ha: p ≠ 0.5 is done at α = 0.01. What is the conclusion?
    1. A) Do not reject H0
    2. B) Accept Ha only at α = 0.05, not at α = 0.01
    3. C) Accept H0
    4. D) Reject H0
  26. In a random sample of 160 city drivers, 32 had an accident last year; in a random sample of 160 country drivers, 48 did. A test of H0: p1 = p2 against Ha: p1 < p2 (1 = city) is done at α = 0.05. What is the conclusion?
    1. A) Do not reject H0
    2. B) Reject H0
    3. C) Accept H0
    4. D) Accept Ha because 32 is less than 48
  27. Men: 40 said yes and 60 said no; women: 50 said yes and 50 said no. A chi-square test of independence is done at α = 0.05. What is the conclusion?
    1. A) Reject H0
    2. B) Accept H0
    3. C) Do not reject H0
    4. D) Accept Ha because more women said yes
  28. A pollster wants a 95% confidence interval for a proportion with a margin of error of at most 0.04, and has no earlier estimate of p. What is the smallest sample size?
    1. A) 600
    2. B) 25
    3. C) 601
    4. D) 423
  29. Young people: 26 drink tea and 24 drink coffee; older people: 15 drink tea and 35 drink coffee. A chi-square test of independence is done at α = 0.05. What is the conclusion?
    1. A) Do not reject H0
    2. B) Accept H0
    3. C) Reject H0
    4. D) Accept Ha because more older people drink coffee
  30. A random sample of 25 batteries has mean life 72 hours and standard deviation 10 hours. What is a 95% t-interval for the mean life of all such batteries?
    1. A) (68.08, 75.92)
    2. B) (70, 74)
    3. C) (51.36, 92.64)
    4. D) (67.872, 76.128)
  31. A random sample of 16 workers takes a mean of 15 minutes to finish a task, with standard deviation 4 minutes. What is a 90% t-interval for the mean time?
    1. A) (13.355, 16.645)
    2. B) (13.04, 16.96)
    3. C) (7.988, 22.012)
    4. D) (13.247, 16.753)
  32. H0: μ = 20, Ha: μ > 20. A random sample of 25 has mean 22 and standard deviation 5. At α = 0.05, what is the conclusion?
    1. A) Reject H0
    2. B) Do not reject H0
    3. C) Accept H0
    4. D) Accept Ha because 22 is more than 20
  33. H0: μ = 100, Ha: μ ≠ 100. A random sample of 25 has mean 97 and standard deviation 9. At α = 0.05, what is the conclusion?
    1. A) Do not reject H0
    2. B) Reject H0
    3. C) Accept H0: the mean is 100
    4. D) Accept Ha because 97 is not 100
  34. Five students took a reading test before and after a summer course. Before: 12, 15, 11, 14, 16. After: 14, 16, 13, 17, 19. A paired t-test of whether scores went up is done at α = 0.05. What is the conclusion?
    1. A) Do not reject H0
    2. B) Accept H0
    3. C) Reject H0
    4. D) Accept Ha because every score went up
  35. Plants on a new fertiliser: mean height 79 cm, standard deviation 10 cm, n = 40. Plants on the old one: mean 74 cm, standard deviation 12 cm, n = 45. A test of H0: μ1 = μ2 against Ha: μ1 > μ2 is done at α = 0.05. What is the conclusion?
    1. A) Do not reject H0
    2. B) Reject H0
    3. C) Accept H0
    4. D) Accept Ha because 79 is more than 74
  36. Weekly spending in a population has mean $120 and standard deviation $18. For random samples of 36, what are the mean and the standard deviation of the sample mean?
    1. A) mean 120, SD 18
    2. B) mean 120, SD 3
    3. C) mean 120, SD 0.5
    4. D) mean 20, SD 3
  37. (Questions 37-39 use this.) Five students give hours studied x and quiz score y: (1, 3), (2, 5), (3, 6), (4, 9), (5, 12). What is the correlation r, to three decimal places?
    1. A) 0.968
    2. B) −0.984
    3. C) 2.2
    4. D) 0.984
  38. (Same five students.) Which is the least-squares regression line?
    1. A) y = 2.2x + 0.4
    2. B) y = 2x + 1
    3. C) y = 2.2x
    4. D) y = 0.4x + 2.2
  39. (Same five students.) Using the line y = 2.2x + 0.4, what is the residual for the student who studied 3 hours and scored 6?
    1. A) −1
    2. B) 1
    3. C) 7
    4. D) 0
  40. Points (0, 5), (1, 15), (2, 45), (3, 135), (4, 405). Which model fits them best?
    1. A) linear
    2. B) quadratic
    3. C) exponential
    4. D) neither
  41. Five points (x, y): (1, 10), (2, 8), (3, 9), (4, 5), (5, 3). What is the correlation r, to three decimal places?
    1. A) −0.922
    2. B) 0.922
    3. C) −1.7
    4. D) 0.85
  42. A regression line is y = 3x + 5. For the point (4, 15), what is the residual?
    1. A) −2
    2. B) 17
    3. C) 2
    4. D) 15

Section II, part A

Question 1: Library app survey (10 points)

A city library has an app for borrowing e-books. The city has four districts, and the library thinks the use of the app may be very different from one district to another. The library wants to survey 200 adults who live in the city.

(a) Write an investigative question that the survey could answer.

(b) Describe how to choose a stratified random sample of 200 adults, using the four districts.

(c) Give one reason why a stratified sample is a better choice here than a simple random sample of 200 adults.

(d) At first the library planned to ask the first 200 adults who walk into the main library. Explain why this is not a good sample, and say whether the estimate of app use would likely be too high or too low.

Question 2: Delivery times (10 points)

A random sample of 9 food deliveries in a town took these times, in minutes: 18, 22, 25, 19, 30, 21, 24, 20, 46.

(a) Find the mean delivery time.

(b) Use the 1.5 × IQR rule to decide whether any of the times is an outlier. Show the quartiles and the fences.

(c) The median time is 22 minutes. Compare the mean and the median, and say what this tells you about the shape of the distribution.

(d) The town wants one number for a typical delivery time and one for how much the times vary. Which measures should it report? Explain.

Question 3: Weight of snack bags (10 points)

The label on a bag of crisps says 50 grams. A consumer group buys a random sample of 20 bags from shops across a country. The sample mean weight is 48.6 grams and the sample standard deviation is 2.5 grams. A dotplot of the 20 weights shows no strong skew and no outliers.

(a) Name the inference procedure that gives an interval estimate of the mean weight, and say what the parameter is.

(b) Check the conditions for the procedure.

(c) Construct a 95% confidence interval for the mean weight.

(d) Does the interval give convincing evidence that the mean weight of all bags is not 50 grams? Explain.

Question 4: Radio adverts and new customers (10 points)

A shop runs adverts on a local radio station. For five weeks it records the number of adverts x and the number of new customers y:

adverts x2022242628
new customers y3035374345

(a) Find the least-squares regression line for predicting y from x.

(b) Interpret the slope of the line in context.

(c) Find the residual for the week with 24 adverts, and say what it means.

(d) Find the correlation r and describe the relationship. Should the shop use the line to predict new customers in a week with 40 adverts? Explain.

Answer key

Section I: multiple choice

  1. C
  2. D
  3. C
  4. B
  5. C
  6. A
  7. D
  8. B
  9. B
  10. D
  11. C
  12. A
  13. A
  14. C
  15. C
  16. B
  17. D
  18. B
  19. D
  20. D
  21. B
  22. A
  23. B
  24. A
  25. D
  26. B
  27. C
  28. C
  29. C
  30. D
  31. D
  32. A
  33. A
  34. C
  35. B
  36. B
  37. D
  38. A
  39. A
  40. C
  41. A
  42. A

Section II

Question 1: Library app survey (10 points)

(a) Write an investigative question that the survey could answer.

Example: "For adults who live in this city, what proportion use the library's app to borrow e-books?"

A good question names the group (adults in the city) and the variable (uses the app or not), and asks about all of them, not one person.

Scoring guide (2 points):

  • 1 point: names the group: adults who live in the city
  • 1 point: names the variable (app use) and asks about the whole group

(b) Describe how to choose a stratified random sample of 200 adults, using the four districts.

Treat each district as a stratum (a group).

In each district, number the adults on a list of residents and use a random number generator to pick 50 different adults.

The 4 × 50 = 200 adults chosen this way are the sample.

Scoring guide (3 points):

  • 1 point: the districts are the strata
  • 1 point: a random method inside every district (numbers + random number generator, no repeats)
  • 1 point: 50 from each district, 200 in all

(c) Give one reason why a stratified sample is a better choice here than a simple random sample of 200 adults.

App use may be very different from district to district.

A stratified sample makes sure every district is in the sample, so the estimate for the whole city varies less from sample to sample.

Scoring guide (2 points):

  • 1 point: app use differs between the districts
  • 1 point: every district is included, so the estimate is more precise (less variable)

(d) At first the library planned to ask the first 200 adults who walk into the main library. Explain why this is not a good sample, and say whether the estimate of app use would likely be too high or too low.

This is a convenience sample: the adults are not chosen at random.

People who walk into the library already use the library more than other adults, so they are more likely to use its app.

So the estimate of the proportion who use the app would likely be too high.

Scoring guide (3 points):

  • 1 point: not random (convenience sample)
  • 1 point: a reason in context: library visitors differ from other adults
  • 1 point: the estimate would likely be too high

Question 2: Delivery times (10 points)

(a) Find the mean delivery time.

mean = 25

Scoring guide (2 points):

  • 1 point: working: one mark for each right line (Check my steps)
  • 1 point: the right answer, finished

(b) Use the 1.5 × IQR rule to decide whether any of the times is an outlier. Show the quartiles and the fences.

outlier: 46

Scoring guide (3 points):

  • 1 point: Q1 = 19.5 and Q3 = 27.5, so IQR = 8
  • 1 point: fences 19.5 − 12 = 7.5 and 27.5 + 12 = 39.5
  • 1 point: 46 is above 39.5, so 46 is an outlier (and no other time is)

(c) The median time is 22 minutes. Compare the mean and the median, and say what this tells you about the shape of the distribution.

The mean (25 minutes) is larger than the median (22 minutes).

The long time of 46 minutes pulls the mean up, so the distribution is skewed to the right.

Scoring guide (2 points):

  • 1 point: the mean is larger than the median, with the numbers
  • 1 point: skewed to the right (because of the large value 46)

(d) The town wants one number for a typical delivery time and one for how much the times vary. Which measures should it report? Explain.

The median (22 minutes) for the typical time and the IQR (8 minutes) for the spread.

The data are skewed and have an outlier (46).

The median and the IQR are not pulled by the outlier; the mean and the standard deviation are.

Scoring guide (3 points):

  • 1 point: median for the centre
  • 1 point: IQR for the spread
  • 1 point: the reason: skew and the outlier pull the mean and the SD, not the median and the IQR

Question 3: Weight of snack bags (10 points)

(a) Name the inference procedure that gives an interval estimate of the mean weight, and say what the parameter is.

A one-sample t-interval for a population mean.

μ = the mean weight of all bags of these crisps sold in the country.

Scoring guide (2 points):

  • 1 point: one-sample t-interval for a mean (t, because σ is not known)
  • 1 point: μ defined in context (all bags of these crisps)

(b) Check the conditions for the procedure.

Random: the bags are a random sample. 10%: 20 bags are less than 10% of all bags sold.

Normal: n = 20 is less than 30, but the dotplot shows no strong skew and no outliers, so a t-interval is reasonable.

Scoring guide (2 points):

  • 1 point: random and 10% conditions
  • 1 point: the normal condition, using the dotplot (n is under 30)

(c) Construct a 95% confidence interval for the mean weight.

(47.43, 49.77)

Scoring guide (4 points):

  • 1 point: df = 20 − 1 = 19 and t× = 2.093
  • 1 point: standard error 2.5/√20 ≈ 0.559
  • 1 point: margin of error 2.093 × 0.559 ≈ 1.17
  • 1 point: the interval (47.43, 49.77)

(d) Does the interval give convincing evidence that the mean weight of all bags is not 50 grams? Explain.

Yes. 50 grams is not in the interval (47.43, 49.77): every plausible value is below 50.

So there is convincing evidence that the mean weight of all bags of these crisps is less than 50 grams.

Scoring guide (2 points):

  • 1 point: 50 is not in the interval
  • 1 point: the conclusion in context (the mean of all bags is not 50 g; below 50)

Question 4: Radio adverts and new customers (10 points)

(a) Find the least-squares regression line for predicting y from x.

y = 1.9x − 7.6

Scoring guide (3 points):

  • 1 point: the means 24 and 38 (the line goes through (24, 38))
  • 1 point: slope 7640 = 1.9
  • 1 point: y = 1.9x − 7.6

(b) Interpret the slope of the line in context.

For each extra advert in a week, the shop is predicted to get about 1.9 more new customers.

("Predicted": the line gives an average pattern, not the exact count in each week.)

Scoring guide (2 points):

  • 1 point: 1.9 more new customers for each extra advert
  • 1 point: said as a prediction, in context

(c) Find the residual for the week with 24 adverts, and say what it means.

Predicted: 1.9 × 24 − 7.6 = 45.6 − 7.6 = 38 new customers. Actual: 37.

Residual = actual − predicted = 37 − 38 = −1: that week the shop got 1 new customer fewer than the line predicts.

Scoring guide (2 points):

  • 1 point: residual = 37 − 38 = −1
  • 1 point: the meaning: 1 new customer fewer than predicted

(d) Find the correlation r and describe the relationship. Should the shop use the line to predict new customers in a week with 40 adverts? Explain.

r ≈ 0.988

Scoring guide (3 points):

  • 1 point: r ≈ 0.988
  • 1 point: a strong, positive, linear relationship
  • 1 point: no: 40 adverts is far outside the 20 to 28 adverts in the data (extrapolation)

Every answer solved step by step: steplyclass.com/ap-statistics/practice-exam-2/answers/

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