AP STATS FALL FINAL
A least squares regression line was fitted to the weights (in pounds) versus age (in months) of a group of many young children. The equation of the line is y(hat)= 16.6 + 0.65t where yˆ is the predicted weight and t is the age of child. A 20-month-old child in this group has an actual weight of 25 pounds. Which of the following is the residual weight, in pounds, for this child?
-4.60
A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water?
0.0915
Ms. Tucker travels through two intersections with traffic lights as she drives to the market. The traffic lights operate independently. The probability that both lights will be red when she reaches them is 0.22. The probability that the first light will be red and the second light will not be red is 0.33. What is the probability that the second light will be red when she reaches it?
0.40
The probability that a new microwave oven will stop working in less than 2 years is 0.05. The probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. The probability that a new microwave oven is damaged during delivery is 0.10. Given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years?
0.40
A contestant's final winnings on a game show are determined by a random selection of a base amount and a possible multiplier. For the base amount, the contestant randomly selects one of four cards, where two cards are marked $1,000, one card is marked $2,000, and one card is marked $5,000. After choosing the card, the contestant randomly selects one of five chips, where three chips are red and two chips are white. If the selected chip is red, the contestant's final winnings are twice the value of the base amount. If the selected chip is white, the contestant's final winnings are the value of the base amount. What is the probability that a contestant's final winnings are exactly $2,000?
0.400
The correlation between two scores X and Y equals 0.8. If both the X scores and the Y scores are converted to z-scores, what is the correlation between the z-scores for X and the z-scores for Y?
0.8
A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year?
0.922
A large store has a customer service department where customers can go to ask for help with store-related issues. According to store records, approximately 1/4 of all customers who go to the service department ask for help finding an item. Assume the reason each customer goes to the service department is independent from customer to customer. Based on the approximation, what is the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item?
1- (3/4)^4
There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model: y(hat) = 25.2 + 3.3x 9 < x < 25 where x is the number of chirps per minute and y(hat) is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?
16.5 degrees Fahrenheit.
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 booth use for people in the study who did and did not have skin cancer. Of the people in the study who had skin cancer, what fraction used a tanning booth?
190/896
A mathematics competition uses the following scoring procedure to discourage students from guessing (choosing an answer randomly) on the multiple-choice questions. For each correct response, the score is 7. For each question left unanswered, the score is 2. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest?
2
The height of 3-year-old boys is approximately normally distributed. Duncan and Shane are 3-year-old boys. Duncan is 32.0 inches tall and is at the 32nd percentile of the distribution. Shane is 34.0 inches tall and is at the 62nd percentile of the distribution. What is closest to the mean of the height distribution?
33.21 inches
The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachel is at the 99th percentile in height for adult women, find her height in inches.
70
The distribution of weights of female college cross-country runners is approximately normal with mean 122 pounds and standard deviation 8 pounds. What is closest to the percent of the runners who weigh between 114 pounds and 138 pounds?
82%
Research indicates that the standard deviation of typical human body temperature is 0.4 degree Celsius (C). What is the standard deviation of typical human body temperature in degrees Fahrenheit (F), where F=9/5 C + 32
9/5 (0.4)
Ali surveyed 200 students at a school and recorded the eye color and the gender of each student. Of the 80 male students who were surveyed, 60 had brown eyes. If eye color and gender are independent, how many female students surveyed would be expected to have brown eyes?
90
In the scatterplot of y versus x shown below, the least squares regression line is superimposed on the plot. Which of the following points has the largest residual?
A
A florist wanted to investigate whether a new powder added to the water of cut flowers helps to keep the flowers fresh longer than just water alone. For a shipment of roses that was delivered to the store, the florist flipped a coin before placing each rose in its own individual container with water. If the coin landed heads up, the rose was placed in water with the new powder; otherwise, the rose was placed in water alone. What experimental method should the florist use?
An experiment with a completely randomized design
Suppose that 30 percent of the subscribers to a cable television service watch the shopping channel at least once a week. You are to design a simulation to estimate the probability that none of five randomly selected subscribers watches the shopping channel at least once a week. For the assignments of the digits 0 through 9, what would be appropriate for modeling an individual subscriber's behavior in this simulation?
Assign "0, 1, 2" as watching the shopping channel at least once a week and "3, 4, 5, 6, 7, 8, and 9" as not watching,
A high school physics teacher was conducting an experiment with his class on the length of time it will take a marble to roll down a sloped chute. The class ran repeated trials in order to determine the relationship between the length, in centimeters, of the sloped chute and the time, in seconds, for the marble to roll down the chute. A linear relationship was observed and the correlation coefficient was 0.964. After discussing their results, the teacher instructed the students to convert all of the length measurements to meters but leave the time in seconds. What effect will this have on the correlation of the two variables?
Because changing from centimeters to meters does not affect the value of the correlation, the correlation will remain 0.964.
Automobile brake pads are either metallic or nonmetallic. An experiment is to be conducted to determine whether the stopping distance is the same for both types of brake pads. In previous studies, it was determined that car size (small, medium, large) is associated with stopping distance, but car type (sedan, wagon, coupe) is not associated with stopping distance. What type of experiment would be best done?
By blocking on car size
What are/are not characteristics of stratified random sampling?
Every possible subset of the population, of the desired sample size, has an equal chance of being selected.
As part of a community service program, students in three middle school grades (grade 6, grade 7, grade 8) each chose to participate in one of three school-sponsored volunteer activities. The graph below shows the distribution for each class for the three activities. Compare the grade levels and activities.
For students in grade 7, the number who chose activity C was greater than the number who chose activity B.
Gina's doctor told her that the standardized score (z-score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.50. What is the interpretation of this standardized score?
Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.
A set of residuals is created for a least-squares regression model. What does a negative residual indicate?
Has over predicted the response variable
63. Jason wants to determine how age and gender are related to political party preference in his town. Voter registration lists are stratified by gender and age-group. Jason selects a simple random sample of 50 men from the 20 to 29 age-group and records their age, gender, and party registration (Democratic, Republican, neither). He also selects an independent simple random sample of 60 women from the 40 to 49 age-group and records the same information. What is the most important observation about Jason's plan?
He will be unable to tell whether a difference in party affiliation is related to differences in age or to the difference in gender.
Which of the following statements is (are) correct? I. Correlation makes no distinction between explanatory and response variables. II. The sign of r reflects the strength of the association. III. r measures the strength of the linear relationship only.
I and III
A local television news station includes a viewer survey question about a current issue at the beginning of every evening news broadcast. Viewers are invited to use social media to respond to the question. The results of the survey are shared with the audience at the end of each broadcast. In relation to the opinions of the population of the region, which of the following is a possible reason why the results of such surveys could be biased? I. Viewers with strong opinions about the current issue are more likely to respond than are viewers without strong opinions. II. The opinions of viewers of one television station are not necessarily representative of the population of a region. III. Viewers with access to social media are not necessarily representative of the population of a region.
I, II, and III
Researchers wanted to investigate whether babies have a sense of right and wrong. They showed each of 60 babies a puppet show in which a red puppet was trying to open a heavy box lid. A second puppet, called the helper, would try to help the red puppet open the box, while a third puppet, called the hinderer, would try to slam the box lid down. After watching the show, each baby was presented with a tray containing the helper puppet and the hinderer puppet, and the researchers recorded which puppet the baby reached for. The researchers wanted to determine whether the babies would reach for the helper puppet more than for the hinderer puppet. As part of the show, a green puppet and a yellow puppet served as the helper and hinderer. For each baby, a coin was tossed to determine which color would serve which role. Which of the following is the most important reason for the random assignment of color to role in the study?
If the same role is played by the same color puppet, the babies might show a preference for the color instead of a preference for the role.
In a standard golf tournament, golfers play 18 holes of golf on each of 4 consecutive days. For each hole, golfers keep track of the number of times they hit the ball (strokes) before the ball goes into the cup. A golfer's score for the tournament is the total number of strokes needed to complete the tournament. The boxplots below summarize the scores for golfers who competed in tournament 1 and golfers who competed in tournament 2. Using the boxplots, compare and describe the distributions.
In both tournaments, at least half the golfers completed the tournament with a score less than 288.
A factory has two machines, A and B, making the same part for refrigerators. The number of defective parts produced by each machine during the first hour of operation was recorded on 19 randomly selected days. The scatterplot below shows the number of defective parts produced by each machine on the selected days. Compare machine A's defective parts to machine B
Machine A usually, but not always, produced fewer defective parts than machine B.
For a set of values, suppose the mean is 10 and the standard deviation is 2. If each value is multiplied by 9, what will be the mean and standard deviation for this new set of values?
Mean 90; Standard Deviation 18
Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of 14. If 4 is added to each score, what will be the mean and the standard deviation of the distribution of new scores?
Mean of 51 and Standard Deviation of 14
Summary statistics are calculated for a data set that includes an outlier. If the outlier is removed, which summary statistic would be least affected?
Median
If one wanted to calculate summary statistics for salaries at a large company where there are many people with modest salaries and a few people with very high salaries, which would be the most appropriate measures of center and spread?
Median and interquartile range
Two variables, x and y, were measured for a random sample of 25 subjects, and two separate regression models were fit to the data. Least squares estimation of the parameters in Model A yielded the following equation and residual plot. Least squares estimation of the parameters in Model B yielded the following equation and residual plot. Which model is appropriate and why?
Model B is appropriate, since the relationship between x and log y is linear.
A tropical storm is classified as major if it has sustained winds greater than 110 miles per hour. Based on data from the past two decades, a meteorologist estimated the following percentages about future storms. - 20% of all tropical storms will originate in the Atlantic Ocean, of which 20% will be classified as major. - 30% of all tropical storms will originate in the eastern Pacific Ocean, of which 15% will be classified as major. - 50% of all tropical storms will originate in the western Pacific Ocean, of which 25% will be classified as major. Based on the meteorologist's estimates, approximately what is the probability that a future tropical storm will originate in the Pacific Ocean and be classified as major?
Probability that a future tropical storm will originate in the Pacific Ocean and be classified as major is 0.170
A new medication has been developed to treat sleep-onset insomnia (difficulty in falling asleep). Researchers want to compare this drug to a drug that has been used in the past by comparing the length of time it takes subjects to fall asleep. What is the best method for obtaining this information?
Randomly assign the subjects to two groups, giving the new drug to one group and the old drug to the other group, and then compare the results.
A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman, sophomore, junior, and senior classes to complete the survey. This plan is an example of which type of sampling?
Stratified random
At a large airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as the time required to deliver all the baggage items on the flight to the baggage claim area. A scatterplot of the two variables indicated a strong, positive linear association between the variables. What is a correct interpretation of the word "strong" in the description of the association?
The actual time required to deliver all the items to the baggage claim area based on the number of items unloaded will be very close to the time predicted by a least-squares model.
Researchers working for a certain airline are investigating the weight of carry-on bags. The researchers will use the mean weight of a random sample of 800 carry-on bags to estimate the mean weight of all carry-on bags for the airline. Describe the effect on the bias and the variance of the estimator if the researchers increase the sample size to 1,300?
The bias will remain the same and the variance will decrease.
An airline recorded the number of on-time arrivals for a sample of 100 flights each day. The boxplot below summarizes the recorded data for one year. Find median, Q1, Q3, min, max, range, and IQR.
The difference between the median and the lower quartile for the number of on-time arrivals is less than 2.
A scientist recorded the duration of the eruptions of the Old Faithful geyser in Yellowstone National Park that occurred during a one-month time period. The histogram below shows the distribution of the duration, in seconds, of the eruptions. Describe the distribution.
The distribution displays two clusters, with one cluster centered at about 125 seconds and the other centered at about 260 seconds, and has a range of at most 250 seconds.
Based on records kept at a gas station, the distribution of gallons of gas purchased by customers is skewed to the right with mean 10 gallons and standard deviation 4 gallons. A random sample of 64 customer receipts was selected, and the sample mean number of gallons was recorded. Suppose the process of selecting a random sample of 64 receipts and recording the sample mean number of gallons was repeated for a total of 100 samples. Describe a dotplot created from the 100 sample means.
The dotplot is approximately normal with mean 10 gallons and standard deviation 0.5 gallon.
In a certain computer card game, the player is awarded 5 points for each card that is moved to a correct position. The player is penalized 10 points for each minute the game is played. Let the random variable X represent the number of cards moved to a correct position, and let the random variable Y represent the number of minutes the game is played. The means and standard deviations of the random variables for a particular player are shown in the table below. Assume that X and Y are independent. What are the expected value and the standard deviation of the points per game for the player?
The expected value is -6.5, and the standard deviation is 65.4.
An agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian pine. A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. Based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the Australian pine based on the age, in years, of the tree. predicted height = 0.29 + 0.48(age). Interpret the slope and the y-intercept.
The height increases, on average, by 0.48 meter each year.
The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y?
The mean is 22 and the standard deviation is 100.
In northwest Pennsylvania, a zoologist recorded the ages, in months, of 55 bears and whether each bear was male or female. The data are shown in the back-to-back stemplot below. Based on the stemplot, compare the medians of the bears.
The median age and the range of ages are both greater for female bears than for male bears.
The number of siblings was recorded for each student of a group of 80 students. Some summary statistics and a histogram displaying the results are shown below. An outlier is often defined as a number that is more than 1.5 times the interquartile range below the first quartile or above the third quartile. Using the definition of an outlier and the given information, what can be concluded?
The median is less than the mean, and the distribution has two outliers.
Staff members of a high school newspaper want to obtain an estimate of the average number of years teachers in the state have been teaching. At an educational conference attended by many teachers in the state, the staff members randomly selected 50 conference attendees and asked the attendees how long they have been teaching. Describe the sample and the population to which it would be most reasonable for the staff members to generalize the results.
The sample is the 50 conference attendees, and the population is all conference attendees.
Some contact lens wearers report problems with dryness in their eyes. A study was conducted to evaluate the effectiveness of a new eye-drop solution to relieve dryness for contact lens wearers. Twenty-five volunteers who wore contact lenses agreed to use the new solution for one month. At the end of the month, 36 percent of the volunteers reported that the new solution was effective in relieving dryness. The company that produced the new eye-drop solution concluded that using the new solution is more effective in relieving dryness than using no solution. Why the study does not support such a conclusion?
The study had no control group.
A game of chance is played in which X, the number of points scored in each game, has the distribution shown below. If the game is played twice, make the probability distribution of the sum, Y, of the scores?
Y takes on values 0, 1, 2, 3, 4 with respective probabilities 0.09, 0.24, 0.34, 0.24, and 0.09.
A researcher wanted to estimate the average amount of money spent on extracurricular activities per school in a certain region. The researcher randomly selected 20 public schools and 20 private schools in the region to use for a sample. What type of sample that was taken?
a stratified sample
At a large conference of teachers from a variety of subjects, a random sample of 50 mathematics teachers attending the conference was selected. Among the selected mathematics teachers, 28 percent had taken one or more courses in statistics. For what population is 28 percent a reasonable estimate of the percentage of those who have taken one or more courses in statistics?
all mathematics teachers who attended the conference
In a certain school, students can choose whether to eat in the school's cafeteria. A reporter working for the school's newspaper polled students on their reactions to changes in the menu at the cafeteria. For each student leaving the cafeteria in one 30-minute time period, the reporter used a coin to determine whether to stop the student and ask how he or she felt about the new menu. In the reporter's article it was stated that a random sample of the students showed that 89 percent of the school's student population was happy with the new menu. Is this biased and why? Name the type. How will the sample proportion compare to the population proportion?
because students self- selected whether to eat in the cafeteria the sampling method might be biased and the sample might not be representative of all students in the school
A volunteer for a mayoral candidate's campaign periodically conducts polls to estimate the proportion of people in the city who are planning to vote for this candidate in the upcoming election. Two weeks before the election, the volunteer plans to double the sample size in the polls. The main purpose of this is to:
decrease the standard deviation of the sampling distribution of the sample proportion
Three brands of candy pieces—X, Y, and Z—are made in many colors. Shaela bought one bag of each brand and counted the number of pieces of each color. The graph below shows the relative frequency distribution of colors for each bag. Compare the red candy pieces to green candy pieces in the bag for the different brands
for brand y, there were more red candy pieces than green candy pieces in the bag
88. A field researcher who studies lions conjectured that the more time a cub spends playing, the sooner the cub will begin to hunt. Observational data were collected from 20 lion cubs. The researcher recorded how long they spent playing and the age when they began hunting. Because male and female lions have different hunting behaviors, the researcher recorded the data for males and females separately. The two scatterplots show the data for the 10 female lions and the 10 male lions. Based on the scatterplots, for which gender does there appear to be evidence that the more time a lion cub spends playing, the sooner the cub is likely to begin hunting?
for female cubs only
The probability of winning a certain game is 0.5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are: n=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?
n=10 only
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. Interpret the value 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.
A television news editor would like to know how local registered voters would respond to the question, "Are you in favor of the school bond measure that will be voted on in an upcoming special election?" A television survey is conducted during a break in the evening news by listing two telephone numbers side by side on the screen, one for viewers to call if they approve of the bond measure, and the other to call if they disapprove. This survey method could produce biased results for a number of reasons. Name the type of bias and explain how it could skew the results
people who feel strongly about the issue are more likely to repspond
The prices, in thousands of dollars, of the 35 used cars at a certain car dealership are shown in the table below. Describe the shape of the distribution of used car prices at the dealership?
skewed to the right (positively skewed)
A graduate student conducted a study of field mice in rural Kansas. The student obtained a sample of 100 field mice and recorded the weight, in grams, of each mouse. After the measurements were taken, it was discovered that the scale was not calibrated correctly. The student adjusted the 100 recorded measurements by subtracting 3 grams from each measurement. Which of the following statistics for the weight, in grams, of the field mice has the same value before and after the adjustment?
the IQR
The stemplot below shows the yearly earnings per share of stock for two different companies over a sixteen-year period. Describe the distributions of the two companies.
the mean of the earrings of company A is greater than the mean of the earnings of company B.
The number of tickets purchased by a customer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer. Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is the mean cost per customer for the performance?
$29.40
A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below. The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y?
$432.00
In a carnival game, a person can win a prize by guessing which one of 5 identical boxes contains the prize. After each guess, if the prize has been won, a new prize is randomly placed in one of the 5 boxes. If the prize has not been won, then the prize is again randomly placed in one of the 5 boxes. If a person makes 4 guesses, what is the probability that the person wins a prize exactly 2 times?
(4)(0.2) ^2 (0.8)^2 2
An urn contains exactly three balls numbered 1, 2, and 3, respectively.
(fill in)
Draw a residual plot which provides the strongest evidence that its regression line is an appropriate model for the data.
(fill in)
Sketch a scatterplot for which the correlation between x and y closest to 0.
(fill in)
The distribution of the diameters of a particular variety of oranges is approximately normal with a standard deviation of 0.3 inch. How does the diameter of an orange at the 67th percentile compare with the mean diameter?
0.132 inch above the mean
The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. If the student leaves home at 8:25 A.M., what is the probability that the student will arrive at the college campus later than 9 A.M.?
0.16
The distribution of monthly rent for one-bedroom apartments in a city is approximately normal with mean $936 and standard deviation $61. A graduate student is looking for a one-bedroom apartment and wants to pay no more than $800 in monthly rent. Of the following, which is the best estimate of the percent of one- bedroom apartments in the city with a monthly rent of at most $800?
1.3%
A company ships gift baskets that contain apples and pears. The distributions of weight for the apples, the pears, and the baskets are each approximately normal. The mean and standard deviation for each distribution is shown in the table below. The weights of the items are assumed to be independent. Let the random variable W represent the total weight of 4 apples, 6 pears, and 1 basket. What is the standard deviation of W?
1.97 ounces
A fair coin is to be flipped 5 times. The first 4 flips land "heads" up. What is the probability of "heads" on the next (5th) flip of this coin?
1/2
Tristan the biologist is measuring bacteria growth. He makes a measurement each hour and observes an exponential growth pattern. To model this growth he linearizes his data using a natural logarithm. The equation he finds is: ln(y(hat)) = −0.5742 + 0.1498(x) where y is the size of the bacteria (measured in cm) and x is the number of hours. If Tristan observes the bacteria after 20 hours, what is the predicted size?
11.27 cm
80. The caffeine content of 8-ounce cans of a certain cola drink is approximately normally distributed with mean 33 milligrams (mg). A randomly selected 8-ounce can containing 35 mg of caffeine is 1.2 standard deviations above the mean.
12%
a random sample of 374 united states pennies were collected, and the age of each penny was determines. According to the boxplot below, what is the approximate interquartile range (IQR) of the ages?
16
A sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. Assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies?
16.5
A random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X - Y?
17.5
The weight of adult male grizzly bears living in the wild in the continental United States is approximately normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds. Approximately, what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear with a weight of 530 pounds?
324 pounds
The weights of a population of adult male gray whales are approximately normally distributed with a mean weight of 18,000 kilograms and a standard deviation of 4,000 kilograms. The weights of a population of adult male humpback whales are approximately normally distributed with a mean weight of 30,000 kilograms and a standard deviation of 6,000 kilograms. A certain adult male gray whale weighs 24,000 kilograms. This whale would have the same standardized weight (z-score) as an adult male humpback whale whose weight, in kilograms, is equal to what weight?
39,000
A professor teaches two statistics classes. The morning class has 25 students and their average on the first test was 82. The evening class has 15 students and their average on the same test was 74. What is the average on this test if the professor combines the scores for both classes?
79
Which of the following can be used to show a cause-and-effect relationship between two variables?
A controlled experiment
A study was conducted to evaluate the impact of taking a nutritional supplement on a person's reaction time. One hundred volunteers were placed into one of three groups according to their athletic ability: low, moderate, or high. Participants in each group were randomly assigned to take either the nutritional supplement or a placebo for six weeks. At the end of the six weeks, participants were given a coordination task. The reaction time in completing the task was recorded for each participant. The study compared the reaction times between those taking the supplement and those taking the placebo within each athletic ability level. Describe the study.
A randomized block design
72. Each of 100 laboratory rats has available both plain water and a mixture of water and caffeine in their cages. After 24 hours, two measures were recorded for each rat: the amount of caffeine the rat consumed, X, and the rat's blood pressure, Y. The correlation between X and Y was 0.428. Find and interpret the coefficient of determination.
About 18 percent of the variation in blood pressure can be explained by a linear relationship between blood pressure and caffeine consumed.
55. What are key distinctions between well designed experiments and observational studies?
An experiment can show a direct cause-and-effect relationship, whereas an observational study cannot.
Measurements of water quality were taken from a river downstream from an abandoned chemical dumpsite. Concentrations of a certain chemical were obtained from 9 measurements taken at the surface of the water, 9 measurements taken at mid-depth of the water, and 9 measurements taken at the bottom of the water. What type of study was conducted, and what is the response variable of the study?
An observational study was conducted, and the response variable is the concentration of the chemical.
The SC Electric Company has bid on two electrical wiring jobs. The owner of the company believes that the probability of being awarded the first job (event A) is 0.75; the probability of being awarded the second job (event B) is 0.5; and the probability of being awarded both jobs (event (A and B)) is 0.375. If the owner's beliefs are correct, are A and B mutually exclusive, independent, both or neither?
Event A and event B are not mutually exclusive and are independent.
Exercise physiologists are investigating the relationship between lean body mass (in kilograms) and the resting metabolic rate (in calories per day) in sedentary males. Predictor Coef StDev T P Constant 264.0 276.9 0.95 0.363 Mass 22.563 6.360 3.55 0.005 s=144.9 R-sq=55.7% R-sq(adj)=51.3% Based on the computer output above, Interpret the value of the slope of the regression line?
For each additional kilogram of lean body mass, the resting metabolic rate increases on average by 22.563 calories per day.
A wildlife biologist is interested in the relationship between the number of chirps per minute for crickets (y) and temperature. Based on the collected data, the least squares regression line is y(hat)=10.53+3.41x , where x is the number of degrees Fahrenheit by which the temperature exceeds 50 degrees. Interpret the meaning of the slope of the least squares regression line.
For each increase in temperature of 1 degree F, the estimated number of chirps per minute increases by 3.41.
An experiment has three mutually exclusive outcomes, A, B, and C. If P(A) = 0.12, P(B) = 0.61, and P(C) = 0.27, which of the following must be true? I. A and C are independent. II. P(A and B) = 0 III. P(B or C) = P(B) + P(C)
II and III only
Data on homes recently sold in a certain town included the area of the home, reported in square feet. The table below shows summary statistics of the reported areas, in square feet. An auditor determined that an error was made in the reported areas and that all of the areas should have been 100 square feet greater than what was reported. The areas were corrected and new summary statistics were reported. What are the interquartile range (IQR) and the standard deviation of the corrected areas?
IQR 102, standard deviation 61.0723
Can two events that are mutually exclusive be independent if each has a probability greater than 0?
If the events are mutually exclusive, they cannot be independent.
A local company is interested in supporting environmentally friendly initiatives such as carpooling among employees. The company surveyed all of the 200 employees at the downtown offices. Employees responded as to whether or not they own a car and to the location of the home where they live. The results are shown in the table below. What can you conclude about a person who owns a car?
If the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city
One hundred people were interviewed and classified according to their attitude toward small cars and their personality type. The results are shown in the table below. What association can you make about the attitude of the three groups?
Of the three attitude groups, the group with the neutral attitude has the highest proportion of type B personality types.
Let X represent a random variable whose distribution is normal, with a mean of 100 and a standard deviation of 10. What is equivalent to P(X > 115)?
P (X<85)
Events D and E are independent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true? Find P(E), P(D), P(D or E).
P(D or E) = 0.72
A group of students has 60 houseflies in a large container and needs to assign 20 to each of the three groups labeled A, B, and C for an experiment. They can capture the flies one at a time when the flies enter a side chamber in the container that is baited with food. How would you randomize to be most likely to result in three comparable groups of 20 houseflies each?
Place each fly in its own numbered container (numbered from 1 to 60) in the order that it was caught. Write the numbers from 1 to 60 on slips of paper, put the slips in a jar, and mix them well. Pick 20 numbers out of the jar. Assign the flies in the containers with those numbers to group A. Pick 20 more numbers and assign the flies in the containers with those numbers to group B. Assign the remaining 20 flies to group C.
A small town employs 34 salaried, nonunion employees. Each employee receives an annual salary increase of between $500 and $2000 based on a performance review by the mayor's staff. Some employees are members of the mayor's political party, and the rest are not. Students at the local high school form two lists, A and B, one for the raises granted to employees who are in the mayor's party, and the other for raises granted to employees who are not. They want to display a graph (or graphs) of the salary increases in the student newspaper that readers can use to udge whether the two groups of employees have been treated in a reasonably equitable manner. What display is least likely to be useful to readers for this purpose?
Scatterplot of B versus A
A newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. The editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. Describe how you would implement such design.
Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.
Lauren is enrolled in a very large college calculus class. On the first exam, the class mean was 75 and the standard deviation was 10. On the second exam, the class mean was 70 and the standard deviation was 15. Lauren scored 85 on both exams. Assuming the scores on each exam were approximately normally distributed, on which exam did Lauren score better relative to the rest of the class?
She scored about equally well on both exams.
Nutritionists examined the sodium content of different brands of potato chips. Each brand was classified as either healthy or regular based on how the chips were marketed to the public. The sodium contents, in milligrams (mg) per serving, of the chips are summarized in the boxplots below. Based on the boxplots, compare the two classifications of the sodium content of the chips
The interquartile range (IQR) of the brands classified as healthy is greater than the IQR of the brands classified as regular.
Grain moisture is a characteristic of grain that affects the price paid for the grain. A random sample of 28 loads of corn was evaluated for moisture as a percent of the total weight. A different random sample of 28 loads of soybeans was also evaluated for moisture. The data are displayed in the dotplots below. Compare the median, Q1, Q3, min, max, range, and IQR.
The range
At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the chemistry final and 84 on the calculus final. Relative to the students in each respective class, in which subject did this student do better?
The student did equally well in each course.
A botanist is studying the petal lengths, measured in millimeters, of two species of lilies. The boxplots below illustrate the distribution of petal lengths from two samples of equal size, one from species A and the other from species B. Based on these boxplots, what can you conclude about the data collected in this study?
There are more petal lengths that are less than 30 mm for species B than there are for species A.
The figure below shows a cumulative relative frequency histogram of 40 scores on a test given in an AP Statistics class. What can the graph show you about the variability in the lower 20 test scores than in the higher 20 test scores?
There is greater variability in the lower 20 test scores than in the higher 20 test scores.
A nonprofit organization plans to hold a raffle to raise funds for its operations. A total of 1,000 raffle tickets will be sold for $1.00 each. After all the tickets are sold, one ticket will be selected at random and its owner will receive $50.00. The expected value for the net gain for each ticket is -$0.95. What is the meaning of the expected value in this context?
They to get owners lose an average of $.95 per raffle ticket
A study of existing records of 27,000 automobile accidents involving children in Michigan found that about 10 percent of children who were wearing a seatbelt (group SB) were injured and that about 15 percent of children who were not wearing a seatbelt (group NSB) were injured. What can you NOT conclude about this study?
This study demonstrates clearly that seat belts save children from injury.
The manager of a public swimming pool wants to compare the effectiveness of two laundry detergents, Detergent A and Detergent B, in cleaning the towels that are used daily. As each dirty towel is turned in, it is placed into the only washing machine on the premises. When the washing machine contains 20 towels, the manager flips a coin to determine whether Detergent A or Detergent B will be used for that load. The cleanliness of the load of towels is rated on a scale of 1 to 10 by a person who does not know which detergent was used. The manager continues this experiment for many days. What type of study did the manager implement?
a completely randomized design
Researchers conducted a telephone survey of 427 adults living in a large city. The adults were asked whether they planned to purchase a smart watch in the next year. The table shows the responses categorized by the region of the city in which the residents live. What is the most appropriate graphical displays for comparing the proportions of those surveyed who plan to purchase a smart watch within the four regions?
a segmented bar chart
Athletes in a particular sport are classified as either offense or defense. The distribution of weights for the athletes classified as offense is approximately normal, centered at 200 pounds, and ranges from 150 pounds to 250 pounds. The distribution of weights for the athletes classified as defense is approximately normal, centered at 300 pounds, and ranges from 250 pounds to 350 pounds. There are 1,000 athletes in each classification. What is the best description of a histogram of the weights of all 2,000 athletes?
bimodal
A researcher conducting a telephone survey is concerned about possible sources of bias. Explain how nonresponse is a possible source of bias.
many of the people selected to participate in the survey who do not respond might have opinions different from those who do respond
Random variable X is normally distributed with mean 10 and standard deviation 3, and random variable Y is normally distributed with mean 9 and standard deviation 4. If X and Y are independent, describe the distribution of Y - X.
normal with mean -1 and standard deviation 5
On a standardized test, the student's z-score was near zero. What does this tell us about the student's test score?
was near average
A delivery service places packages into large containers before flying them across the country. These filled containers vary greatly in their weight. Suppose the delivery service's airplanes always transport two such containers on each flight. The two containers are chosen so their combined weight is close to, but does not exceed, a specified weight limit. A random sample of flights with these containers is taken, and the weight of each of the two containers on each selected flight is recorded. What is the correlation of the weights of the two containers on the same flight?
will have a negative correlation
Twenty types of beef hot dogs were tested for calories and sodium (mg). The hot dogs averaged 156.85 calories with a standard deviation of 22.64, and the sodium level averaged 401.15 mg with a standard deviation of 102.43 mg. The correlation was given as r = 0.887. Calculate the equation of the LSRL predicting sodium level from number of calories.
y(hat)=- 228.30 +4.01x
Students in a large psychology class measured the time, in seconds, it took each of them to perform a certain task. The times were later converted to minutes. If a student had a standardized score of z = 1.72 before the conversion, what is the standardized score for the student after the conversion?
z=1.72
The histogram displays the frequencies of waiting times, in minutes, for 175 patients in a dentists office. Which of the following could be the median of the waiting times, in minutes?
7.25
Which of the following statistics is defined as the 50th percentile?
the median
The number of sweatshirts a vendor sells daily has the following probability distribution. If each sweatshirt sells for $25, what is the expected daily total dollar amount taken in by the vendor from the sale of sweatshirts?
$38.00
At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. For those surveyed, there was no association between age and preferred method of eating ice cream. Create a two-way table that shows the distribution of responses.
(fill in)
The faces of a four-sided fair die are numbered 1 through 4, respectively. For a certain game, the die is tossed and the number that lands facedown is recorded. The table below summarizes the points a player earns for the number that lands facedown. Consider two independent tosses of the die. Let the random variable S represent the sum of the points earned from the two tosses. Make the probability distribution of S.
(fill in)
The histogram below displays the times, in minutes, needed for each chimpanzee in a sample of 26 to complete a simple navigational task. It was determined that the largest observation, 93, is an outlier since Q3+ 1.5(Q3-Q1 )= 87.125. Sketch a boxplot that could represent the information in the histogram.
(fill in)
draw a dot plot which represents a set of data that has a very large standard deviation
(fill in)
A least squares regression line was fitted to the weekly cost of groceries in dollars (cost) versus the number of household members (number) for a group of families. The resulting equation is predicted cost = -33.22 + 44.77(number) A randomly selected family of four spends $135 on groceries in an average week. What is the difference between this family's actual cost and the predicted average family cost?
-$10.86
The prices, in thousands of dollars, of 304 homes recently sold in a city are summarized in the histogram below. Based on the histogram, where does the median fall?
The median price is not greater than $750,000
In the design of a survey, which of the following best explains how to minimize response bias?
carefully word and field test survey questions
A researcher wishes to test a new drug developed to treat hypertension (high blood pressure). A group of 40 hypertensive men and 60 hypertensive women is to be used. The experimenter randomly assigns 20 of the men and 30 of the women to the placebo and assigns the rest to the treatment. The major reason for separate assignment for men and women is that:
the new drug may affect men and women differently