AP Stats Final Semester 1

At a small coffee shop. the distribution of the number of seconds it takes for a cashier to process an order is approx normal with mean 278 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?

0.95

A field researcher who studies lions conjectured that the more time a cub spends playing, the sooner the cub will begin to hunt. Based on the scatterplots, for which gender does there appear to be evidence that the more time a lion cub sends playing, the sooner the cub is likely yo begin hunting?

For female cubs only

According to a recent survey, 81 percent of adults in a certain state have graduated from high school. If 15 adults from the state are selected at random, what is the probability that 5 of them have nor graduated from high school?

(15 5) (0.19)^5 (0.81) ^10

At a large regional 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 slots 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 fo the 4 random variables?

1.67 seconds

The following is a residual plot for a linear regression of y versus x. What is indicated by the plot?

A linear model is not appropriate

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?

(50 40) (o.31)^40 (0.69)^10

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. 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?

-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?

0.2(0.8)^7

One student from a high school will be selected at random. let A be the event that the selected student is a student athlete, and let B be the event that the selected student drives to school. If P(A n B)= 0.08 and P(B|A) = 0.25, what is the probability that the selected student will be a student athlete?

0.32

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. What is the probability that the student will be awarded at least one of the two scholarships?

0.62

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 buy at the next book fair. What is the expected value of B?

1.79

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 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 in the mean age of the combined distribution of both men and women in the course?

20.47 years

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 millimeters and standard deviation 1.4 millimeters. 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?

20.6 mm

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 used in the study. The nine combinations of three price levels and three package types are the treatments of interest. Total sales of the product over a seven-week period will be recorded. Which of the following describes the best design to use for the study?

A completely randomized design. Randomly assign the nine combinations of price level and packaging type so that three stores use each combination

A researcher selects random sample of 1,200 women who are students at Midwestern colleges in the United States to use for an observational study. Which the following describes the population to which it would be most reasonable to generalize the results?

All women who are students at midwestern colleges in the United States

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?

0.8

A restaurant manager collected data to predict monthly sales for the restaurant from monthly advertising expenses. The model created from the data showed that 36% of the variation in monthly sales could be explained by monthly advertising expense. What was the value of the correlation coefficient?

0.60

A middle school chess club has 5 members: Adam, Bradley, Carol, Dave, and Ella. Two students from the club will be selected at random to participate in the county chess tournament. What is the probability that Adam and Ella will be selected?

1/10

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. Of the people in the study who has skin cancer, what fraction used a tanning booth?

190/896

The following boxplot shows the typical gas mileage, in miles per gallon, for 20 different car models. Based on the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon?

35

A certain monthly magazine has both print and online subscribers. Print subscribers are people who pay to have the magazine physically delivered to them each month. Which of the following is a sample of the population of interest?

50 online subscribers

A researcher is studying the effect of generally modified and nongenetically modified corn on the weight gain of lambs. The sex and genetics of the lambs can affect their weight gain. Which of the following designs would be the best to use in the study?

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.

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, and E, respectively. Which of the five points is the most influential with respect to a regression of trade-in value versus miles driven?

E

In a certain school district, students from grade 6 through 12 can participate in a school-sponsored community service activity. The following bar chart shows the relative frequencies of students from each grade who participate in the community service activity

Grade 11 had the greatest relative frequency of participating student

Clear-cut harvesting of wood from forests creates long periods of time when certain animals cannot use the forests as habitats. Which of the following is the best description of the relationship displayed in the scatterplot

Negative, linear, and strong

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?

No, because 0.40 represents probability in the long run over many visits to the site.

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 banc, and let event S represent the event of selecting a student on a sports team. Are B and S mutually exclusive events?

No, because P(BnS) = 5/78

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. The difference was statistically significant. What can be concluded from the study?

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

The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W = 7+ 2X. What are the mean and standard deviation of W?

The mean is 31, and the standard deviation is 3

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?

The mean is most likely less than the median because the distribution is skewed to the right

One way to measure the duration of subterranean disturbances such as earthquakes and mining is to calculate the root-mean-square time. The following histograms summarize the distribution of the root-mean-square time for two sources of disturbances.

The median of the earthquake disturbances is less than the median of the mining disturbances

A certain school district has 15 high schools. The high schools seniors' plans after graduation in each school vary greatly from one school to the next. The country superintendent will select a sample of high school seniors from the district to survey about their plans after graduation. The superintendent will use cluster sample with the high schools as clusters. A random sample of 5 highs 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?

The schools in the cluster sample might not be representative of the population of seniors

The quality-control manager of a large factory is concerned about the number of defective items produced by workers. Thirty workers at the factory agree to participate in a study of three different incentive plans to help reduce the number of defective items produced. The plans will be randomly assigned to the workers so that 10 workers received each plan. The reduction in the number of defective items produced by each worker will be recorded two weeks after the plans are implemented. Which of the following best describes why a completely randomized design is an appropriate design to use in this situation?

There is no blocking variable, and incentive plans will be randomly assigned to the workers

A roadrunner is a desert bird that tends to run instead of fly. While running, the roadrunner uses its tail as a balance. Suppose a roadrunner has a total length of 59.0 cm and tail length of 31.1 com. Based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner?

Underestimate, because the residual is positive

A school nutritionist was interested in how students at a certain school would feel after taking a nutritional supplement. The nutritionist selected a random sample of twenty students from the school to participate in the study. Participants were asked to keep a journal on how well they felt after taking the supplement each day. What possible source of bias is present in the method of data collection?

Response bias where responses are self-reported

A city designed a survey to collect information about resident's opinions about city services. Which of the following describes a scenario in which nonresponse bias is likely present?

Surveys were mailed to 500 people, and 200 of the surveys were completed and returned

One statistic calculated for pitchers in baseball is called the earned run average, or ERA. The following boxplots summarize the ERA for pitchers in two leagues, A and B. Based on the boxplots, which of the following statistics is the same for both leagues?

The interquartile range

A study was conducted on three types of home siding and the type of damage done to the siding by woodpeckers. The following bar charts shows the relative frequency of the holes for each type of siding. Which of the following statements is supported by the bar chart?

The proportion of holes created for drumming is least for grooved plywood

Eighteen individuals who use a particular form of social media were assigned a new user interface to use when logging in to their accounts. After using the new user interface for a week, each individual was asked to rate how easy or hard the new user interface was to use on a scale from 1 to 9. ,which of the following correctly identifies why this is not a well-designed experiment?

The study was not comparative---only one treatment was used

A chemist for a paint company conducted an experiment to investigate whether a new outdoor paint will last longer than the older paint. What can be concluded from the experiment?

There is not enough evidence to attribute the higher ratings to the new paint

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?

Causation cannot be determined from an observational study

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, community college, join the workforce, join the military, or undecided. The results are shown in the following bar chart. Which of the following statements is supported by the bar chart?

Foe the category undecided, the number of students from liberty High School was 4 greater than the number of students from Central High School

A store owner reports that the probability that a customer who purchases a lawn mower will also purchase an extended warranty is 0.68. Which of the following is the best interpretation of the probability 0.68 ?

For all customers who purchase a lawn mower, 68% will also purchase an extended warranty

A market researcher asked a group of men to choose their favorite color design from a sample of advertisements. The results are shown in the following table. Which of the following statements is not supported by the table?

For men, the number who chose a design with black was greater than the number who chose a design with blue

For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a fish based on its length. The biologist collects a random sample of this species of fish and finds that the lengths vary from 0.75 to 1.35 inches. The biologist uses the data from the sample to create a single linear regression model. Would it be appropriate to sue this model to predict the weight of a fish of this species that is 3 inches long

No, because 3 inches falls above the maximum value of lengths in the sample

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 * IQR rule for outliers, is there evidence to support the claim?

No, because 43 is not greater than (Q3+ 1.5 * IQR)

Roger claims that the two statistics most likely to change greatly when an outlier s added to a small data set are the mean and the median. Is Roger's claim correct?

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 from the concentration of lead, in ppm, found from a certain river. Which of the following statements is a correct interpretation of the value of 19.0 in the output?

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

The following list shows the number of video games sold at a game store each day for one week. Which of the following is the best classification of the data in the list?

Quantitative and discrete

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 thoroughly mix the marbles, and then repeat those steps. She will perform the procedure many times. What type of sampling method is Margo using?

Random sampling with replacement