ap stats review
At a photography contest, entries are scored on a scale from 1 to 100. At a recent contest with 1000 entries, a score of 68 was at the 77th percentile of the distribution of all the scores. Which of the following is the best description of the 77th percentile of the distribution?
A. There were 770 entries with a score less than or equal to 68.
A roadrunner is a desert bird that tends to run instead of fly. While running, the roadrunner uses its tail as a balance. A sample of 10 roadrunners was taken, and the birds' total length in centimeters (cm), and tail length, in cm, were recorded. The output shown in the table is from a least-squares regression to predict tail length given total length. Suppose a roadrunner has a total length of 59.0 cm and tail length of 31.1 cm. Based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner?
A. Underestimate, because the residual is positive
A student is applying to two different agencies for scholarships. Based on the student's academic record, the probability that the student will be awarded a scholarship from Agency A is 0.55 and the probability that the student will be awarded a scholarship from Agency B is 0.40. Furthermore, if the student is awarded a scholarship from Agency A, the probability that the student will be awarded a scholarship from Agency B is 0.60. What is the probability that the student will be awarded at least one of the two scholarships?
B. 0.62
The following is a residual plot for a linear regression of y versus x. What is indicated by the plot?
B. A linear model is not appropriate
The following table shows the probability distribution for the number of books a student typically buys at the annual book fair held at an elementary school. Let the random variable B represent the number of books a student buys at the next book fair. What is the expected value of B?
C. 1.79
The following histogram shows the age, in years, of the people who attended a documentary at a movie theater. Based on the histogram, which of the following statements best describes the relationship between the mean and the median of the distribution of ages?
C. The mean is most likely less than the median because the distribution is skewed to the left.
For a random sample of 20 professional athletes, there is a strong, linear relationship between the number of hours they exercise per week and their resting heart rate. For the athletes in the sample, those who exercise more hours per week tend to have lower resting heart rates than those who exercise less. Which of the following is a reasonable value for the correlation between the number of hours athletes exercise per week and their resting heart rate?
D. -0.87
Of all the fish in a certain river, 20 percent are salmon. Once a year, people can purchase a fishing license that allows them to catch up to 8 fish. Assume each catch is independent. Which of the following represents the probability of needing to catch 8 fish to get the first salmon?
D. 0.2(0.8)^7
The following boxplot shows the typical gas mileage, in miles per gallon, for 20 different car models. Based on the boxplot, the top 25 percent of the cars have a typical mileage of at least how many miles per gallon?
D. 35
An observational study found that the amount of sleep an employee gets each night is associated with job performance. The correlation coefficient was found to be r = 0.86. A reader of the study concluded that more sleep causes employees to perform better. Why is such a conclusion not correct?
D. Causation cannot be determined from an observational study
The following list shows the number of video games sold at a game store each day for one week. 15,43,50,39,22,16,20 Which of the following is the best classification of the data in the list?
D. Quantitative and discrete
The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. Is Avery interpreting the probability correctly?
E. No, because 0.40 represents probability in the long run over many visits to the site
According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor's degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor's degree. What is the probability that B will equal 40?
A. (50 40) (0.31)^40 (0.69)^10
At a small coffee shop, the distribution of the number of seconds it takes for cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds?
A. 0.17
A market research firm is studying the effects of price and type of packaging on sales of a particular product. Twenty-seven stores with shoppers of similar characteristics will be sued in the study. The nine combinations of three price levels and three packaging types are the treatments of interest. Total sales of he product over a seven-week period will be recorded. Which of the following describes the best design to use for the study?
A. A completely randomized design. Randomly assign the nine combinations of price level and packaging type so that three stores use each combination
A certain country school district has 15 high schools. The high school seniors' plans after graduation in each school vary greatly from one school to the next. The county superintendent will select a sample of high school seniors from the district to survey about their plans after graduation. The superintendent will use a cluster sample with the high schools as clusters. A random sample of 5 high schools will be selected, and all seniors at those high schools will complete the survey. What is one disadvantage to selecting a cluster sample to investigate the superintendent's goal?
A. Cluster sampling is usually very expensive to implement and could cost the district too much money.
Clear-cut harvesting of wood from forests creates long periods of time when certain animals cannot use the forests as habitats. Partial-cut harvesting is increasingly used to lessen the effects of logging on the animals. The following scatterplot shows the relationship between the density of red squirrels, in squirrels per plot, 2 to 4 years after partial-cut harvesting, and the percent of trees that were harvested in each of 11 forests. Which of the following is the best description of the relationship displayed in the scatterplot?
A. Negative, linear, and strong
A high school science teacher has 78 students, Of those students, 35 are in the band and 32 are on a sports team. There are 16 students who are not in the band or on a sports team. One student from the 78 students will be selected at random. Let event B represent the event of selecting a student in the band, and let event S represent the event of selecting a student on a sports team. Are B and S mutually exclusive events?
A. No, because P(B S) - 5/78
A city has designed a survey to collect information about residents' opinions about city services. Which of the following describes a scenario in which nonresponse bias is likely present?
A. Surveys were mailed to 500 people, and 200 of the surveys were completed and returned
As part of a study on the relationship between the use of tanning booths and the occurrence of skin cancer, researchers reviewed the medical records of 1,436 people. The table below summarizes tanning booths use for people in the study who did not have skin cancer. Of the people in the study who had skin cancer, what fraction used a tanning booth?
B. 190/896
At a large collegiate women's swim meet, an official records the time it takes each swimmer to swim 100 meters for all swimmers who compete in only one stroke category. The following table shows the mean times and corresponding standard deviations for the collegiate women at the swim meet for each of the four stroke categories. For each of the 4 stroke categories, consider a random variable representing the time of a randomly selected swimmer in that category. What is the standard deviation of the sum of the 4 random variables?
B. 1.67 seconds
A statistician at a metal manufacturing plant is sampling the thickness of metal plates. If an outlier occurs within a particular sample, the statistician must check the configuration of the machine. The distribution of metal thickness has mean 23.5 mm and standard deviation 1.4 mm. Based on the two-standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine?
B. 20.6 mm
Roger claims that the two statistics most likely to change greatly when an outlier is added to a small data set are the mean and median. Is Roger's claim correct?
B. No, only the mean is likely to change greatly
The computer output below shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river. Which of the following statements is a correct interpretation of the value 19.0 in the output?
B. On average, there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead found in the fish.
A study was conducted on three types of home siding and the type of damage done to the siding by woodpeckers. Each hole made by a woodpecker was classified as either drumming (territorial signaling), foresting (looking for food), or nesting. The following bar chart shows the relative frequency of the holes for each type of siding. Which of the following statements is supported by the chart?
C. The proportion of holes created for drumming is least for grooved plywood.
The least-squares regression line y = 1.8 - 0.2x summarizes the relationship between velocity, in feet per second, and depth, in feet, in measurements taken for a certain river, where x represents velocity and y represents the depth of the river. What is the predicted value of y, in feet, when x = 5?
D. 0.8
Data were collected on the ages, in years, of the men and women enrolled in a large sociology course. Let the random variables M and W represent the ages of the men and women, respectively. The distribution of M has mean 20.7 years and standard deviation 1.73 years. The distribution of W has mean 20.2 years and standard deviation 1.60 years. Of all of those enrolled in the course, 54 percent are men and 46 percent are women. What is the mean age of the combined distribution of both men and women in the course?
D. 20.47 years
The following boxplot summarizes the heights of a sample of 100 trees growing on a tree farm. Emily claims that a tree height of 43 inches is an outlier for the distribution. Based on the 1.5 x IQR rule for outliers, is there evidence to support the claim?
D. No, because 43 is not greater than (Q3 + 1.5 x IQR)
The owner of a food store conducted a study to investigate whether displaying organic fruit at the front of the store rather than at the back of the store will increase sales of the fruit. At the beginning of each week, the organic fruit display was randomly assigned to either the front or back of the store, and sales for the week were recorded. At the end of 12 months, the owner determined that the average weekly sales of organic fruit displayed at the front of the store were greater than the average weekly sales of organic fruit displayed at the back of the store. The difference was statistically significant. What can be concluded from the study?
D. Placing the display at the front instead of the back of the store causes an increase, on average, of weekly sales of the organic fruit.
To estimate the percent of red marbles in a large bag of marbles, Margo will use the following sample method. She will randomly select a marble, record its color, put it back into the bag, shake the bag to throughly mix the marbles, and then repeat those steps. She will perform the procedure many times. What type of sampling method is Margo using?
D. Random sampling with replacement
A researcher is studying the effect of genetically modified (GM) and nongenetically modified (nGM) corn on the weight gain of lambs. The sex and genetics of the lambs can affect their weight gain. Five sets of male twin lambs and five sets of female twin lambs-- for a total of twenty lambs-- are available for the study. The lambs will be randomly assigned to a diet of either GM or nGM diet of corn. Weight gain will be recorded for each lamb after five weeks on the diet. Which of the following designs would be best to use in the study?
E. A matched pairs design. For each set of twins, randomly assign one twin to the GM diet and the other twin to the nGM diet
A researcher selects a simple random sample of 1,200 women who are students at Midwestern colleges in the United States to use for an observational study. Which of the following describes the population to which it would be most reasonable to generalize the results?
E. All women who are students at Midwestern colleges in the United States
In a study to determine whether miles driven is a good predictor of trade-in-value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in-value and mileage for those cars. Five of the points are labeled A, B, C, D, E, respectively. Which of the five labeled points is the most influential with respect to a regression of trade-in-value versus miles driven?
E. E
A sample of 100 students from Liberty High School and a sample of 60 students from Central High School were asked what they planned to do after graduation. Responses fell into five categories: four year university (4Y), community college (CC), join the workforce (W), join the military (M), or undecided (UD). The results are shown in the following bar chart. Which of the following statements is supported by the bar chart?
E. For the category undecided, the number of students from Liberty High School was 4 greater than the number of students from Central High School