Learn Extracted exam questions AP Statistics 2017 Free Response
2017 Free Response
Source PDF on the left, extracted YAML on the right. Compare numbering, marks, options and text.
Researchers studying a pack of gray wolves in North America collected data on the length $x$, in meters, from nose to tip of tail, and the weight $y$, in kilograms, of the wolves. A scatterplot of weight versus length revealed a relationship between the two variables described as positive, linear, and strong.
For the situation described above, explain what is meant by each of the following words.
Positive:
Linear:
Strong:
The data collected from the wolves were used to create the least-squares equation $\hat{y} = -16.46 + 35.02x$.
Interpret the meaning of the slope of the least-squares regression line in context.
One wolf in the pack with a length of 1.4 meters had a residual of $-9.67$ kilograms. What was the weight of the wolf?
The manager of a local fast-food restaurant is concerned about customers who ask for a water cup when placing an order but fill the cup with a soft drink from the beverage fountain instead of filling the cup with water. The manager selected a random sample of 80 customers who asked for a water cup when placing an order and found that 23 of those customers filled the cup with a soft drink from the beverage fountain.
Construct and interpret a 95 percent confidence interval for the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain.
The manager estimates that each customer who asks for a water cup but fills it with a soft drink costs the restaurant $0.25. Suppose that in the month of June 3,000 customers ask for a water cup when placing an order. Use the confidence interval constructed in part (a) to give an interval estimate for the cost to the restaurant for the month of June from the customers who ask for a water cup but fill the cup with a soft drink.
A grocery store purchases melons from two distributors, J and K. Distributor J provides melons from organic farms. The distribution of the diameters of the melons from Distributor J is approximately normal with mean 133 millimeters (mm) and standard deviation 5 mm.
For a melon selected at random from Distributor J, what is the probability that the melon will have a diameter greater than 137 mm?
Distributor K provides melons from nonorganic farms. The probability is 0.8413 that a melon selected at random from Distributor K will have a diameter greater than 137 mm. For all the melons at the grocery store, 70 percent of the melons are provided by Distributor J and 30 percent are provided by Distributor K.
For a melon selected at random from the grocery store, what is the probability that the melon will have a diameter greater than 137 mm?
Given that a melon selected at random from the grocery store has a diameter greater than 137 mm, what is the probability that the melon will be from Distributor J?
The chemicals in clay used to make pottery can differ depending on the geographical region where the clay originated. Sometimes, archaeologists use a chemical analysis of clay to help identify where a piece of pottery originated. Such an analysis measures the amount of a chemical in the clay as a percent of the total weight of the piece of pottery. The boxplots below summarize analyses done for three chemicals—X, Y, and Z—on pieces of pottery that originated at one of three sites: I, II, or III.
[Three side-by-side sets of boxplots grouped by Site (Site I, Site II, Site III), each set showing boxplots for chemicals X, Y, Z on the x-axis. Shared y-axis "Percent of Total Weight" from 0 to 16 (gridlines every 2). A legend distinguishes Site I (open box), Site II (gray box), Site III (hatched box).
Site I: Chemical X — min 6, Q1 ≈ 6.5, median ≈ 7, Q3 ≈ 7.5, max 8. Chemical Y — min 11, Q1 ≈ 12, median ≈ 13, Q3 ≈ 14, max 15. Chemical Z — min 4, Q1 ≈ 5, median ≈ 7, Q3 ≈ 9, max 10.
Site II: Chemical X — min 3.5, Q1 ≈ 5, median ≈ 6, Q3 ≈ 6.5, max 7. Chemical Y — min 1.8, Q1 ≈ 2.5, median ≈ 3, Q3 ≈ 3.5, max 4.5. Chemical Z — min 6, Q1 ≈ 6.5, median ≈ 7, Q3 ≈ 7.5, max 8.
Site III: Chemical X — min 4.8, Q1 ≈ 5.5, median ≈ 6, Q3 ≈ 7, max 7.5. Chemical Y — min 6, Q1 ≈ 6.5, median ≈ 7, Q3 ≈ 7.5, max 8. Chemical Z — min 2.8, Q1 ≈ 5, median ≈ 7, Q3 ≈ 9, max 11.2.]
For chemical Z, describe how the percents found in the pieces of pottery are similar and how they differ among the three sites.
Consider a piece of pottery known to have originated at one of the three sites, but the actual site is not known.
Suppose an analysis of the clay reveals that the sum of the percents of the three chemicals X, Y, and Z is 20.5%. Based on the boxplots, which site—I, II, or III—is the most likely site where the piece of pottery originated? Justify your choice.
Suppose only one chemical could be analyzed in the piece of pottery. Which chemical—X, Y, or Z—would be the most useful in identifying the site where the piece of pottery originated? Justify your choice.
The table and the bar chart below summarize the age at diagnosis, in years, for a random sample of 207 men and women currently being treated for schizophrenia.
Age-Group (years)
| 20 to 29 | 30 to 39 | 40 to 49 | 50 to 59 | Total | |
|---|---|---|---|---|---|
| Women | 46 | 40 | 21 | 12 | 119 |
| Men | 53 | 23 | 9 | 3 | 88 |
| Total | 99 | 63 | 30 | 15 | 207 |
[100% stacked bar chart titled with y-axis "Percent of People" from 0% to 100% (gridlines every 20%), x-axis "Age-Group (years)" with categories 20 to 29, 30 to 39, 40 to 49, 50 to 59. Each bar is split into a gray "Men" segment (bottom) and a hatched "Women" segment (top). Approximate Men percentages by age group: 20 to 29 ≈ 53%, 30 to 39 ≈ 37%, 40 to 49 ≈ 30%, 50 to 59 ≈ 20% (Women is the remainder to 100% in each bar), consistent with the table counts.]
Do the data provide convincing statistical evidence of an association between age-group and gender in the diagnosis of schizophrenia?
Consider an experiment in which two men and two women will be randomly assigned to either a treatment group or a control group in such a way that each group has two people. The people are identified as Man 1, Man 2, Woman 1, and Woman 2. The six possible arrangements are shown below.
| Arrangement A | Treatment | Control |
|---|---|---|
| Man 1 | Woman 1 | |
| Man 2 | Woman 2 |
| Arrangement B | Treatment | Control |
|---|---|---|
| Man 1 | Man 2 | |
| Woman 1 | Woman 2 |
| Arrangement C | Treatment | Control |
|---|---|---|
| Man 1 | Man 2 | |
| Woman 2 | Woman 1 |
| Arrangement D | Treatment | Control |
|---|---|---|
| Woman 1 | Man 1 | |
| Woman 2 | Man 2 |
| Arrangement E | Treatment | Control |
|---|---|---|
| Man 2 | Man 1 | |
| Woman 2 | Woman 1 |
| Arrangement F | Treatment | Control |
|---|---|---|
| Man 2 | Man 1 | |
| Woman 1 | Woman 2 |
Two possible methods of assignment are being considered: the sequential coin flip method, as described in part (a), and the chip method, as described in part (b). For each method, the order of the assignment will be Man 1, Man 2, Woman 1, Woman 2.
For the sequential coin flip method, a fair coin is flipped until one group has two people. An outcome of tails assigns the person to the treatment group, and an outcome of heads assigns the person to the control group. As soon as one group has two people, the remaining people are automatically assigned to the other group.
Complete the table below by calculating the probability of each arrangement occurring if the sequential coin flip method is used.
| Arrangement | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| Probability |
For the sequential coin flip method, what is the probability that Man 1 and Man 2 are assigned to the same group?
The six arrangements are repeated below (same as shown above).
For the chip method, two chips are marked "treatment" and two chips are marked "control." Each person selects one chip at random without replacement.
Complete the table below by calculating the probability of each arrangement occurring if the chip method is used.
| Arrangement | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| Probability |
For the chip method, what is the probability that Man 1 and Man 2 are assigned to the same group?
Sixteen participants consisting of 10 students and 6 teachers at an elementary school will be used for an experiment to determine lunch preference for the school population of students and teachers. As the participants enter the school cafeteria for lunch, they will be randomly assigned to receive one of two lunches so that 8 will receive a salad, and 8 will receive a grilled cheese sandwich. The students will enter the cafeteria first, and the teachers will enter next. Which method, the sequential coin flip method or the chip method, should be used to assign the treatments? Justify your choice.