Rucete ✏ AP Statistics In a Nutshell
2. Exploring Two-Variable Data — Practice Questions 2
This chapter introduces how to analyze relationships between two variables using two-way tables, scatterplots, correlation, regression, and residuals.
(Multiple Choice — Click to Reveal Answer)
1. A two-way table is also called a
(A) residual plot
(B) contingency table
(C) histogram
(D) boxplot
(E) stem plot
Answer
(B) — A two-way table is also called a contingency table.
2. In a two-way table, the row and column totals are called
(A) residuals
(B) outliers
(C) marginal frequencies
(D) regression coefficients
(E) z-scores
Answer
(C) — Row and column totals are marginal frequencies.
3. A conditional relative frequency is found by dividing a cell count by
(A) the grand total only
(B) the corresponding row or column total
(C) the number of rows
(D) the number of columns
(E) the mean of all cell counts
Answer
(B) — Conditional relative frequency uses the relevant row total or column total.
4. If two categorical variables have different conditional distributions, they are
(A) independent
(B) symmetric
(C) associated
(D) linear
(E) standardized
Answer
(C) — Different conditional distributions indicate association.
5. A segmented bar chart is most similar to a
(A) pie chart
(B) scatterplot
(C) histogram
(D) boxplot
(E) dotplot
Answer
(A) — It is like a pie chart shown as a rectangular bar.
6. In a mosaic plot, the size of each rectangle mainly represents
(A) the slope
(B) the median
(C) frequency or relative frequency
(D) the correlation
(E) the standard deviation
Answer
(C) — Rectangle area represents the cell information.
7. Simpson’s paradox occurs when
(A) the regression line is horizontal
(B) the correlation is negative
(C) a relationship reverses when groups are combined
(D) two variables are perfectly associated
(E) the residuals sum to 1
Answer
(C) — That is the definition of Simpson’s paradox.
8. A scatterplot is used to examine the relationship between
(A) two categorical variables
(B) two quantitative variables
(C) one variable only
(D) only time and frequency
(E) only row and column totals
Answer
(B) — Scatterplots are for two quantitative variables.
9. If larger x-values tend to be paired with larger y-values, the association is
(A) negative
(B) positive
(C) nonlinear only
(D) marginal
(E) influential
Answer
(B) — This is positive association.
10. If larger x-values tend to be paired with smaller y-values, the association is
(A) positive
(B) negative
(C) uniform
(D) conditional
(E) residual
Answer
(B) — This is negative association.
11. When describing a scatterplot, which feature should be included?
(A) Only the mode
(B) Only the mean
(C) Direction, form, strength, unusual features, and context
(D) Only the correlation
(E) Only the quartiles
Answer
(C) — That is the standard chapter framework.
12. Correlation measures the strength and direction of a
(A) causal relationship
(B) linear relationship
(C) categorical relationship
(D) nonlinear relationship only
(E) segmented relationship
Answer
(B) — Correlation is specifically for linear relationships.
13. Which statement is true?
(A) Correlation implies causation
(B) A high correlation proves causation
(C) Correlation does not imply causation
(D) Zero correlation means no relationship at all
(E) A nonlinear pattern always has high correlation
Answer
(C) — Correlation alone never proves causation.
14. The possible values of r are from
(A) 0 to 1
(B) -1 to 1
(C) -100 to 100
(D) 0% to 100%
(E) 1 to 10
Answer
(B) — Correlation always lies between -1 and 1.
15. A correlation near 0 can still occur when
(A) there is a strong nonlinear relationship
(B) the variables are identical
(C) the points all lie on a line
(D) the slope is positive
(E) there are no unusual points
Answer
(A) — Correlation measures only linear relationship.
16. The coefficient of determination is written as
(A) r
(B) r + 1
(C) r2
(D) 2r
(E) √r only
Answer
(C) — The coefficient of determination is r squared.
17. r2 is interpreted as the percentage of variation in
(A) x explained by y only
(B) y explained by the linear model
(C) the residuals explained by x
(D) the slope explained by the intercept
(E) all variables explained equally
Answer
(B) — It is the percentage of variation in the response variable explained by the linear model.
18. In the regression equation ŷ = a + bx, b represents
(A) the predicted y when x = 0
(B) the residual
(C) the change in predicted y for a one-unit increase in x
(D) the correlation
(E) the mean of x
Answer
(C) — That is the interpretation of slope.
19. In the regression equation ŷ = a + bx, a represents
(A) the change in y per unit x
(B) the predicted y when x = 0
(C) the correlation coefficient
(D) the residual mean
(E) the standard deviation of y
Answer
(B) — That is the y-intercept.
20. A residual is
(A) predicted minus observed
(B) observed minus predicted
(C) observed plus predicted
(D) x minus y
(E) slope minus intercept
Answer
(B) — Residual = observed − predicted.
21. A point below the regression line has a residual that is
(A) positive
(B) negative
(C) zero
(D) undefined
(E) always large
Answer
(B) — Below the line means observed is less than predicted.
22. A residual plot with no clear pattern suggests
(A) a nonlinear model is definitely better
(B) a linear model may be appropriate
(C) the slope must be zero
(D) r must equal 1
(E) the variables are independent
Answer
(B) — No pattern supports the use of a linear model.
23. A point with an x-value far from the mean x-value has
(A) no leverage
(B) high leverage
(C) no residual
(D) no influence possible
(E) perfect correlation
Answer
(B) — Such points have high leverage.
24. An influential point is one whose removal substantially changes the
(A) sample size only
(B) graph title
(C) regression results, such as slope or correlation
(D) units of measurement
(E) median of x only
Answer
(C) — Influential points noticeably change the regression results.
25. Which statement is correct?
(A) Every outlier is influential
(B) Every influential point is an outlier
(C) Outliers and high leverage points are often influential, but not always
(D) Outliers never affect correlation
(E) Leverage and residual mean the same thing
Answer
(C) — They are often influential, but not always.
26. In the “Cuteness Factor” table, what proportion of all 250 volunteers viewed tasty foods?
(A) 0.26
(B) 0.34
(C) 0.36
(D) 0.40
(E) 0.55
Answer
(D) — 100 out of 250 viewed tasty foods, so 100/250 = 0.40.
27. In the same table, what percentage of all volunteers had low focus?
(A) 26%
(B) 34%
(C) 36%
(D) 38%
(E) 40%
Answer
(C) — 90 out of 250 had low focus, so 90/250 = 36%.
28. In the same table, among those who viewed adult animals, what percent had high focus?
(A) 10.0%
(B) 17.6%
(C) 30.8%
(D) 35.3%
(E) 47.1%
Answer
(B) — 15/85 = 0.176 ≈ 17.6%.
29. In the same table, among those who viewed tasty foods, what percent had medium focus?
(A) 10%
(B) 17.6%
(C) 30.8%
(D) 35%
(E) 55%
Answer
(D) — 35/100 = 35%.
30. In Example 2.5, Dr. Patch’s overall survival rate was
(A) 70.8%
(B) 71.4%
(C) 76%
(D) 80%
(E) 88.2%
Answer
(D) — 200 survivors out of 250 gives 80%.
31. In Example 2.5, Dr. Fixit’s survival rate among patients in poor condition was
(A) 60/68 = 88.2%
(B) 130/182 = 71.4%
(C) 80/113 = 70.8%
(D) 190/250 = 76%
(E) 52/182 = 28.6%
Answer
(B) — In poor condition, Dr. Fixit had 130 survivors out of 182 patients.
32. In the teacher-characteristics table, what percentage of all surveyed people were administrators?
(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%
Answer
(B) — 50 of 500 were administrators, so 10%.
33. In the same table, what percentage of teachers picked enthusiastic?
(A) 12.5%
(B) 20%
(C) 25%
(D) 40%
(E) 50%
Answer
(C) — 50 of 200 teachers picked enthusiastic, so 25%.
34. In the same table, what percentage of students picked challenging?
(A) 10%
(B) 20%
(C) 25%
(D) 30%
(E) 50%
Answer
(B) — 50 of 250 students picked challenging, so 20%.
35. In the same table, what percentage of those who picked strict were administrators?
(A) 10%
(B) 20%
(C) 25%
(D) 30%
(E) 50%
Answer
(C) — 25 of the 100 people who picked strict were administrators, so 25%.
36. In Example 2.9, if r = 0.84, find r2.
Answer
0.7056 — r2 = (0.84)2 = 0.7056.
37. In Example 2.9, express r2 as a percentage.
Answer
70.56% — Multiply 0.7056 by 100.
38. In Example 2.11, the regression line is ŷ = -1.73 + 0.5492x. Predict y when x = 20.
Answer
9.25 — -1.73 + 0.5492(20) = -1.73 + 10.984 = 9.254, which rounds to 9.25.
39. In Example 2.11, interpret the slope 0.5492.
Answer
For each additional close friend, the model predicts about 0.5492 more evening Facebook checks on average. — That is the contextual meaning of slope.
40. In Example 2.12, the regression line for calories burned is ŷ = 23.8 + 6.55x. Predict calories burned for 50 minutes.
Answer
351.3 — 23.8 + 6.55(50) = 23.8 + 327.5 = 351.3.
41. In Example 2.12, the regression line for minutes from calories is ŷ = -0.829 + 0.1465x. Predict minutes for a 400-calorie food item.
Answer
57.77 minutes — -0.829 + 0.1465(400) = -0.829 + 58.6 = 57.771.
42. In Example 2.13, the regression line is ŷ = -0.03656 + 0.001582x. Predict the probability of dying for age 30.
Answer
0.0109 — -0.03656 + 0.001582(30) = -0.03656 + 0.04746 = 0.01090.
43. In Example 2.13, interpret the slope 0.001582.
Answer
For each additional year of age, the model predicts the probability of dying from the RNA viral disease increases by about 0.001582 on average. — That is the slope in context.
44. In Example 2.15, the regression line is ŷ = 389.19 - 5.9776x. Predict the skin cancer mortality rate at latitude 45.
Answer
120.20 — 389.19 - 5.9776(45) = 389.19 - 268.992 = 120.198, which rounds to 120.20.
45. In Example 2.15, if the observed mortality at latitude 45 was 130, find the residual.
Answer
+9.80 — Residual = observed − predicted = 130 - 120.20 = +9.80.
46. In Example 2.15, if R-Sq = 68.0%, what percent of the variation in the response remains unexplained?
Answer
32.0% — 100% - 68.0% = 32.0%.
47. In Example 2.15, the slope is negative. If R-Sq = 68.0%, what is r to three decimals?
Answer
-0.825 — r = -√0.68 ≈ -0.8246, which rounds to -0.825.
48. In Example 2.15, what does S = 19.115 represent?
Answer
It is the standard deviation of the residuals and gives a typical prediction error of about 19.115 in the response variable’s units. — It measures typical spread around the regression line.
49. In Example 2.11, if a student with 24 close friends actually checks Facebook 13 times, what is the residual?
Answer
+1.55 — Predicted is 11.45, so residual = 13 - 11.45 = +1.55.
50. In Example 2.11, if a student with 24 close friends actually checks Facebook 10 times, what is the residual?
Answer
-1.45 — Predicted is 11.45, so residual = 10 - 11.45 = -1.45.