AP Stats - Midterm
79. Which of the following are true statements? I. Correlation requires that there are clearly identified explanatory and response variables. II. Scatterplots require that both variables be quantitative. III. Every least-squares regression line passes through (x, y).
c. II and III only
89. Which of the following statements about high-leverage points and outliers are true? I. An influential point always has a large residual. II. Outliers are always high-leverage points. III. Removing an influential point always causes a marked change in either the correlation, the regression equation, or both.
c. III only
82. A least-squares regression line for predicting weights of basketball players based upon their heights was computed and further analysis yielded the residual plot shown below. What does the residual plot tell you about the linear model?
c. The curved pattern in the residual plot suggests that the linear model is not appropriate.
98. We measure a response variable y at several different times. A residual plot of log y versus time of measurement is created to determine if an exponential model is appropriate to model the relationship between time and the response variable. The residual plot displays random scatter about the line residual = 0. Which one of the following conclusions can be made?
c. The model is appropriate because the residual plot displays random scatter about the line residual = 0.
38. A recent investigation of prices for five-year-old Toyota Camrys in Montgomery, Alabama, and New York, New York, revealed that the mean price in Montgomery was $13,200 with a standard deviation of $1,000. In New York, the mean price was $12,800 with a standard deviation of $1,800. Which of the following statements is true?
c. The standardized score for a car priced at $15,000 would be higher in Montgomery than in New York
93. Suppose we measure a response variable Y for several values of an explanatory variable X. A scatterplot of log Y versus log X displays a negative association and is roughly linear. We may conclude that
c. a power model would approximately describe the relationship between Y and X.
32. A percentile is a measure of
c. location.
6. X and Y are two categorical variables. The best way to determine if there is a relation between them is to
c. make a two-way table of the X and Y values.
21. The standard deviation of a random sample of 16 peoples' weights (in pounds) is computed to be 5.4. The units for the sample variance of these measurements is
c. pounds squared.
67. Data was recorded on wine consumption (in liters per person per year) and death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed Western countries and a scatterplot was constructed. If heart disease death rate were expressed as deaths per 1,000 people instead of as deaths per 100,000 people, how would the correlation r between wine consumption and heart disease death rate change?
c. r would not change.
90. The correlation between the heights of fathers and the heights of their (fully grown) sons is r = 0.52. This value was based on both variables being measured in inches. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be
c. unchanged: equal to 0.52.
7. A review of voter registration records in a small town yielded the following table of the number of males and females registered as Democrat, Republican, or some other affiliation.
d. 0.30
29. The following is a boxplot of the birth weights (in ounces) of a sample of 160 infants born in a local hospital. What is the approximate value of the median birth weight? Is this value a statistic or a parameter?
d. 110 ounces, statistic
58. Let X denote the time taken for a computer link to be made between the terminal in an executive's office and the computer at a remote factory site. It is known that X has a Normal distribution with a mean of 15 seconds and a standard deviation of 3 seconds. On 90% of the occasions the computer link is made in less than how many seconds?
d. 18.84
95. Using least-squares regression on data from 1990 through 2019, I determine that the (base 10) logarithm of the population of a country is approximately described by the equation log(population) = -13.5 + 0.01(year). Which of the following is the predicted population of the country in the year 2020?
d. 5,011,872
80. One characteristic of roller coasters that contributes to the maximum speed of the ride is the track's maximum height. Shown below is a regression analysis and residual plot for a regression of maximum speed (in miles/hours) on maximum height (in feet) for nine roller coasters that opened recently around the world. The circled point represents a roller coaster in the Philippines whose maximum height is 70 ft. What is the observed speed of this roller coaster closest to?
d. 55 mi/h
13. Below is a histogram of the heights of gold-medal-winning high jumps in the Olympic Games since 1896. Based on this histogram, what is the percentage of the winning jumps that were at least 80 inches?
d. 55%
34. The cumulative relative frequency graph at right shows the distribution of lifespans for 39 U.S. presidents. Which of the following is closest to the 70th percentile of this distribution?
d. 77 years
49. If a store runs out of advertised material during a sale, customers become upset, and the store loses not only the sale but also goodwill. From past experience, a music store finds that the mean number of CDs sold in a sale is 845, the standard deviation is 15, and a histogram of the demand is approximately Normal. The manager is willing to accept a 2.5% chance that a CD will be sold out. About how many CDs should the manager order for an upcoming sale?
d. 875
8. Mr. Swartzentruber selects a random sample of 100 students in grades 10 through 12 and asks their year in school and whether they were involved in interscholastic sports, intramural sports, or no sports. The results are summarized in the segmented bar graph below.
d. Juniors have the highest percentage participation in intramurals.
99. Use of smartphones increased rapidly from 2000 to 2019. A scatterplot of this growth shows a strongly nonlinear pattern. The data were fit with 3 different models. Here is a description of the variables, the residual plot and the r 2 value for each of the models: Which model does the best job at summarizing the relationship between year and number of smartphone users?
d. None of the provided models does a good job at summarizing the relationship between year and number of smartphone users because none of the r 2 values are 1.0.
23. A company produces packets of soap powder that are labeled "Giant Size 32 Ounces." A random sample of 10 packets has a mean of 33 oz. and a standard deviation of 0.7 ounces. Which of the following is a correct interpretation of the sample standard deviation?
d. The distance between the weight of each packet of soap powder and the mean weight was, on average, about 0.7 ounces
30. Different writers have different styles. One way to quantify this difference is to compare the distribution of word lengths in their work. Below are parallel boxplots describing the distributions of word lengths for the first 60 words in Henry James's The Turn of the Screw, J.K. Rowling's Harry Potter and the Chamber of Secrets, and Chapter 1 of your statistics textbook (labeled "Starnes"). Based on the graphs, which one of the following statements must be true?
d. The median word length for Rowling is longer than for either Starnes or James.
86. The computer output shown below gives the least-squares regression line for calories and protein (in grams) in one cup of 11 varieties of dried beans. Which of the following best describes what the number S = 3.376 represents?
d. The standard deviation of the residuals is 3.376.
5. The bar graph below summarizes responses of dog owners to the question, "Where in the car do you let your dog ride?
d. The vertical scale of this graph exaggerates the difference between the percentage who let their dogs ride in the driver's lap versus a passenger's lap.
35. Consider the following cumulative relative frequency graph of the scores of children who played the game Skeeball at a birthday party. What are the approximate values of the median and interquartile range of this distribution?
d. median = 70; interquartile range = 20
36. An ecologist who was studying starfish populations collected starfish of the species Pisaster. He was interested in the distribution of sizes of this species of starfish. One measure of size is "arm length." Below is a cumulative relative frequency graph for the arm length, in centimeters, of 102 Pisaster individuals. The Pisaster arm length of a particular starfish is 15.20 cm. Is this starfish unusually large?
d. no, this star fish is approximately at the 50th percentile for Pisaster arm length.
65. The height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. The goal is to determine if volume of usable lumber can be estimated from the height of a tree. If the data point (65, 70) were removed from this study, how would the value of the correlation r change?
d. r would be larger, because this point does not fall in the pattern of the rest of the data.
42. Suppose a data set consists of 25 positive integers. If every value in the data set is multiplied by negative 2, which of the following values would be negative?
d. the mean
53. The area under the standard Normal curve corresponding to z > -1.22 is closest to what value?
e. 0.8888
43. For this density curve, what percent of the observations lie between x = 0.2 and x = 3.8?
e. 72%
63. The height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. The goal is to determine if volume of usable lumber can be estimated from the height of a tree. Which of the following statements are supported by the scatterplot? I. There is a positive association between height and volume. II. There is an outlier in the plot. III. As the height of a cherry tree increases, the volume of useable lumber it yields increases.
e. I, II, and III
88. A regression of the amount of calories in a serving of breakfast cereal vs. the amount of fat (in grams) gave the following results: predicted calories = 97.1053 + 9.6525(fat). Which of the following is false?
e. If one cereal has 140 calories and 5 g of fat. Its residual is 4.5 calories.
60. When a basketball player makes a pass to a teammate who then scores, he earns an "assist." Below is a Normal probability plot for the number of assists earned by all players in the National Basketball Association during the 2010 regular season.
e. The distribution is skewed.
24. You catch 10 cockroaches in your bedroom and measure their lengths in centimeters. Which of these sets of numerical descriptions are all measured in centimeters?
e. both (b) and (c)
39. The distribution of a data set is Normally distributed with a mean of 25 and a standard deviation of 8. If you calculate the standardized score of every observation in this data set, what will the mean and standard deviation of the resulting scores be?
e. mean = 0; standard deviation = 1
78. You are interested in predicting the cost of heating houses on the basis of how many rooms the house has. A scatterplot of 25 houses reveals a strong linear relationship between these variables, so you calculate a least-squares regression line. "Least-squares" refers to
e. minimizing the sum of the squares of the residuals.
41. A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for this year. 28 31 34 35 37 41 42 42 42 47 49 51 52 52 60 61 67 72 75 77 Suppose each employee in the company receives a $3,000 raise for next year (each employee's salary is increased by $3,000). The interquartile range of the salaries for the employees will
a. be unchanged.
1. A survey typically records many variables of interest to the researchers involved. Below are some of the variables from a survey conducted by the U.S. Postal Service. Which of the variables is categorical?
a. county of residence
22. All of the following small data sets have a mean of 5. Which one has the smallest standard deviation?
b. 1 3 5 5 5 7 9
94. Like most animals, small marine crustaceans are not able to digest all the food they eat. Moreover, the percentage of food eaten that is assimilated (that is, digested) decreases as the amount of food eaten increases. A scatterplot of ln(assimilation) versus ln(food intake) is strongly linear, suggesting that a linear regression of these transformed variables may be more appropriate. Below is a computer regression analysis of the transformed data (note that natural logarithms are used). When food intake is 250 g/day, what is the predicted assimilation rate from this model?
b. 15.4%
50. Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a Normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. Approximately what percent of the bags will likely be underweight (that is, less than 16 ounces)?
b. 16%
72. Suppose a straight line is fit to data having response variable y and explanatory variable x. Predicting values of y for values of x outside the range of the observed data is called
b. extrapolation.
26. Mrs. Temple has just finished grading a quiz for a class of 26 students and has calculated measures of center and spread on the scores. While writing the grades on the quizzes, she realizes she made a mistake, and the highest grade should be 10 points higher. Which one of the following sets of measurements will he have to recalculate?
b. the mean and standard deviation
14. A policeman records the speeds of cars on a certain section of roadway with a radar gun. The histogram below shows the distribution of speeds for 251 cars. The maximum value is 35 mph. If the value, 35 mph, was actually 29 mph, how would the mean and standard deviation change?
b. the mean would decrease and the standard deviation would decrease
31. The five-number summary of the distribution of scores on the final exam in Psych 001 last semester was: 18, 39, 62, 76, and 100. Which of the following best describes the location of the 80th percentile?
d. The 80th percentile is between 76 and 100.
70. All but one of the following statements contains an error. Which statement could be correct?
e. The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r = 0.53.
2. You measure the age (years), weight (pounds), and marital status (single, married, divorced, or widowed) of 1400 women. How many variables did you measure?
3
74. A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is y134419x. On a day when the temperature is 20F, the regression line predicts that gas used will be about
d. 964 cubic feet.
48. The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. Only about 5% of young men have heights outside the range
b. 63 inches to 73 inches.
45. For the density curve shown, which statement is true?
c. The mean and median are equal.
18. For the histogram below, what are the correct locations of the mean and median? Note that the graph is NOT numerically precise—only the relative positions are important.
d. II is the mean and III is the median.
46. Which of the following properties is true for all Normal density curves? I. They are symmetric. II. The curve reaches its peak at the mean. III. 95% percent of the area under the curve is within one standard deviation of the mean.
c. I and II only
28. Mrs. Richardson asked the 26 seniors in her statistics class how many AP® courses they had taken during high school. Below is a dotplot summarizing the results of her survey.
B
3. Deciduous forests in the Eastern United States often have many different species of oak trees. Below is a frequency distribution for five different species of oaks found in sample plots of a certain forest.
C
4. Below is a pie chart of how a randomly selected group of people described the cost of their health insurance. Which of the following bar graphs is equivalent to the pie chart?
E
47. Which of the following dotplots would best be approximated by a Normal distribution?
E
64. The following table and scatter plot present data on wine consumption (in liters per person per year) and death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed Western countries. Which country is represented by the clear triangle in the scatter plot?
b. Canada
83. A fisheries biologist studying whitefish in a Canadian Lake collected data on the length (in centimeters) and egg production for 25 female fish. A computer regression analysis of egg production versus fish length are given below. Note that number of eggs is given in thousands (i.e., "40" means 40,000 eggs). Which of the following statements can be made based upon the computer output?
b. 69.7% of the variability in egg production can be accounted for by the linear regression with x = fish length.
57. The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?
b. 78.4 minutes
15. The population of the United States is aging, though less rapidly than in other developed countries. Below is a stemplot of the percentages of residents aged 65 and older in each of the 50 states, according to the 2010 census. There are three outliers: Alaska has the lowest percentage of older residents, Utah had the second lowest, and Florida has the highest. What is the percentage for Utah?
b. 9%
17. Which statement is true?
b. Fifty percent of the scores in a distribution are between the first and third quartile.
55. A company produces packets of soap powder labeled "Giant Size 32 Ounces." The actual weight of soap powder in a box has a Normal distribution with a mean of 33 oz. and a standard deviation of 0.8 oz. What proportion of packets are underweight (i.e., weigh less than 32 oz.)?
a. 0.106
51. Birthweights at a local hospital have a Normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. Which of the following is the proportion of infants with birthweights under 95 oz.?
a. 0.160
52. IQs among undergraduates at Mountain Tech are approximately Normally distributed. The mean undergraduate IQ is 110. About 95% of undergraduates have IQs between 100 and 120. What is the approximate value of the standard deviation of these IQs?
a. 5
33. Here are the exam scores for the 15 students in Mr. Kirk's statistics class: 72 75 75 78 81 81 85 89 90 90 90 91 95 95 98. Karen was at the 20th percentile of the distribution. What score did Karen earn on the exam?
a. 75
73. A linear regression equation was computed to predict the final exam score in a statistics class from the score on the first test. The equation of the least-squares regression line was y 10 0.9x where y represents the predicted final exam score and x is the score on the first exam. Suppose Joe scores a 90 on the first exam. What is the predicted value of his score on the final exam?
a. 91
81. Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows random scatter?
a. A straight line is a good model for the data.
27. Mr. Affie records the heights (in centimeters) of the male and female students in his class and summarizes the results in the following boxplots: Which of the following conclusions can be drawn from this graph?
b. About 25% of the male students are taller than the tallest female student.
71. Consider the scatter plot below for a very small data set, consisting of the heights of five fathers (x) and their sons (y). The "M" in the plot indicates the point (x, y). The letters A - E are labels for the five father-son pairs. Which father-son pair contributes the largest positive quantity to the correlation between father and son heights?
a. Pair A
44. For the density curve shown below, which statement is true?
a. The area under the curve between 0 and 1 is 1.
77. There is an approximate linear relationship between the height of females and their age (from 5 to 18 years) described by the equation = 50.3 + 6.1(Age), where height is measured in centimeters and age in years. Which one of the following statements must be true?
a. The estimated slope is 6.1, which implies that female children between the ages of 5 and 18 increase in height by about 6.1 cm for each year they grow older.
68. Consider the following scatterplot, which describes the relationship between stopping distance (in feet) and air temperature (in degrees Celsius) for a certain 2,000-pound car traveling 40 mph. If another data point is added with an air temperature of 0°C and a stopping distance of 80 feet, the correlation would
a. decrease, because this new point is an outlier that does not follow the pattern in the data.
62. Other things being equal, larger automobile engines are less fuel-efficient. You are planning an experiment to study the effect of engine size (in liters) on the fuel efficiency (in miles per gallon) of sport utility vehicles. In this study,
a. gas mileage is a response variable, and you expect to see a negative association.
92. The intensity of a light bulb is related to distance from the bulb by the model intensity a distance 2 a(distance) 2 . An engineer collected data on the amount of intensity measured for various distances from the bulb for a random sample of a new brand of LED light bulbs. The scatterplot for (distance)-2 and intensity is roughly linear. The regression analysis produced the following output. Which of the following is the correct equation of the least-squares regression line for this data?
a. intensity = 87.947 + 0.0609 (distance)-2
20. The mean speed of vehicles in the "cars only" lanes of the New Jersey turnpike is 68 miles per hour. The mean speed of vehicles in the "any vehicle" lanes is 64 miles per hour. What must be true about the mean speed of all vehicles on the turnpike, assuming these are the only types of lanes?
a. it could be any number between 64 and 68 miles per hour
66. The following scatter plot presents data on wine consumption (in liters per person per year) and death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed Western countries. The correlation between wine consumption and heart disease deaths is one of the following values. From the scatterplot, which must it be?
a. r = -0.84
12. Mr. Lee has just collected his last batch of 24 English essays, all of them as computer files. He's curious about how long the papers are, but he doesn't want to be fooled by large font sizes, so he uses the word processing software's word count feature. Below is a histogram of the word counts for the 24 essays Which of the following best describes the distribution the variable number of words in these essays?
a. skewed to the right, centered at about 750, with one high outlier
11. Below is a two-way table summarizing the number of cylinders in selected car models manufactured in six different countries. From this table, we might conclude that
a. there is a strong association between country of origin and number of cylinders.
61. A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. The response variable in this study is the
a. yield of the crop.
37. The mean number of days that the midge Chaoborus spends in its larval stage is 14.1 days, with a standard deviation of 2.2 days. This distribution is skewed toward higher values. What is the z-score for an individual midge that spends 12.7 days in its larval stage?
b. -0.64
19. The mean age of four people in a room is 30 years. A new person whose age is 55 years enters the room. What is the mean age of the five people now in the room?
b. 35
9. A company manufactures special plastic containers that hold a specified volume of hazardous material. Some containers do not meet specifications because they are either too small or too large. Are there differences between the sizes of containers produced by the daylight (8am), evening (4pm), and midnight shifts? Here is a mosaic plot of the results after inspecting 1500 randomly selected containers. Which of the following is the best evidence that there is an association between conformance to specifications and shift?
b. Knowing whether a container was too small, within specifications, or too large is helpful for predicting what shift produced it.
85. Students with above-average scores on Exam 1 in STAT 001 tend to also get above-average scores on Exam 2. But the relationship is only moderately strong. In fact, a linear relationship between Exam 2 scores and Exam 1 scores explains only 36% of the variance of the Exam 2 scores.
b. The correlation between Exam 1 scores and Exam 2 scores is r = 0.6.
16. There are 10 students in Mrs. Thomas's afternoon Statistics class. The maximum point total for the most recent quarter was 200 points. The point totals for the 10 students are given in the stemplot below. The mean score is 134.4 points and the standard deviation is 18.64 points. If the score of 179 was supposed to be 129 how would the value of the mean and standard deviation change?
b. The mean would decrease and the standard deviation would decrease.
25. A small company that prints custom t-shirts has 6 employees, one of whom is the owner and manager. Suppose the owner makes $120,000 per year and the other employees make between $40,000 and $50,000 per year. One day, the owner decides to give himself a $30,000 raise. Which of the following describes how the company's mean and median salaries would change?
b. The mean would increase by $5,000 and the median would not change.
69. Fifty randomly selected subjects had their systolic blood pressure (SBP) recorded twice, once at 9:00 a.m. and again at 2:00 p.m. If one were to examine the relationship between the morning and afternoon readings, then one might expect the correlation to be
b. high and positive, as those with relatively high readings in the morning will tend to have relatively high readings in the afternoon
40. A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for this year. 28 31 34 35 37 41 42 42 42 47 49 51 52 52 60 61 67 72 75 77 Suppose each employee in the company receives a $3,000 raise for next year (each employee's salary is increased by $3,000). The mean salary for the employees will
b. increase by $3,000.
84. The correlation between the age and height of children is found to be about r = 0.7. Suppose we use the age x of a child to predict the height y of the child. We conclude that
b. the percent of the variability in heights explained by the least-squares regression line is 0.49.
76. A study of child development measures the age (in months) at which a child begins to talk and the child's score on an ability test given several years later. The study asks whether the age at which a child talks helps predict the later test score. The least-squares regression line useful for predicting test score from age is y 1101.3x. According to this regression line, what happens (on the average) to children who talk one month later than other children?
b. their predicted test score goes down 1.3 points
54. The proportion of observations from a standard Normal distribution that take values larger than -0.75 is closest to what value?
c. 0.7734
75. Consider the following scatterplot of amounts of CO (carbon monoxide) and NOX (nitrogen oxide) in grams per mile driven in the exhausts of cars. The least-squares regression line has been drawn in the plot. What is the approximate value of the intercept of the least-squares regression line?
c. 1.8
91. A researcher wishes to study how the average weight y (in kilograms) of children changes during the first year of life. He plots these averages versus the age x (in months) and decides to fit a least-squares regression line to the data with x as the explanatory variable and y as the response variable. He computes the following quantities. r = correlation between x and y = 0.9 x = mean of the values of x = 6.5 y = mean of the values of y = 6.6 sx = standard deviation of the values of x = 3.6 sy = standard deviation of the values of y = 1.2 What is the y-intercept of the least-squares regression line?
c. 4.65
97. Use of the internet worldwide increased steadily from 1990 to 2019. A scatterplot of ln(Internet users) (in millions) versus year is strongly linear, suggesting that a linear regression of this transformation may be more appropriate. Below is a computer regression analysis of the transformed data (note that natural logarithms are used).
c. 4.92
56. The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade?
c. 44
10. Below is a two-way table summarizing the number of cylinders in selected car models manufactured in six different countries What percentage of all cars listed in the table have 4-cylinder engines?
c. 50%
87. A fisheries biologist studying whitefish in a Canadian Lake collected data on the length (in centimeters) and egg production for 25 female fish. A computer regression analysis of egg production versus fish length are given below. Note that number of eggs is given in thousands (i.e., "40" means 40,000 eggs). On average, how far are the predicted y-values from the actual y-values?
c. 6.751
59. Mrs. Sawyer is chatting with the principal of Scarborough High School. The topic of SAT math scores comes up, and the principal mentions that SAT math scores at the school are Normally distributed. He doesn't remember the mean or the standard deviation, but he does remember that the upper and lower quartiles are 500 and 600. The standard deviation of SAT math scores is closest to what value?
c. 75 points
96. Use of the Internet worldwide increased steadily from 1990 to 2002. A scatterplot of this growth shows a strongly nonlinear pattern. However, a scatterplot of ln(Internet users) versus year is much closer to linear. Below is a computer regression analysis of the transformed data (note that natural logarithms are used).
c. A random scattering of points on either side of the line residual = 0.
