AP STATS Final

The distribution of lengths of salmon from a certain river is approximately normal with standard deviation 3.5 inches. If 10 percent of salmon are longer than 30 inches, which of the following is closest to the mean of the distribution?

26 inches

In a parking lot with 200 cars, 50 cars are white, 30 are red, and 20 cars are silver. One car will be selected at random from the parking lot. If each car in the parking lot has only one color, which of the following cannot be the probability that the selected car will be green?

0.6

Which of the following is the best description of a positive association between two variables?

As the value of one of the variables increases, the value of the other variable tends to increase.

Which of the following statements about a least-squares regression analysis is true?

III only

In driving a car, the events of driving over the speed limit and getting a speeding ticket are

Neither

Events D and E are indpendent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true?

P(D or E) = 0.72

Ninety percent of the people who have a particular disease will have a positive result on a given diagnostic test. Ninety percent of the people who do not have the disease will have a negative result on this test. If 5 percent of a certain population has the disease, what percent of that population would test positive for the disease?

14%

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. Which of the following tables show the distribution responses?

Adults: 50, 20, 70 Children: 100, 40, 140

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.

In a certain school district, students from grade 6 through grade 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. Which of the following is supported by the bar chart?

Grade 12 had the least relative frequency of participating students.

For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays?

0.335

A fair coin has come up 'heads' 10 times in a row. The probability that the coin will come up heads on the next flip is...

50%

Some descriptive statistics for a set of scores are shown below. For this test, a certain student has a standardized score of z=-1.2. What score did this student receive on the test?

779.42

Dairy farmers are aware there is often a linear relationship between the age, in years, of a dairy cow and the amount of milk produced, in gallons per week. The least-squares regression line produced from a random sample is Milk = 40.8 - 1.1(Age). Based on the model, what is the difference in predicted amounts of milk produced between a cow of 5 years and a cow of 10 years?

A cow of 5 years is predicted to produce 5.5 more gallons per week.

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?

Negative, linear, and strong

To check the effect of cold temperature on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a freezer for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before breakage is measured on each rubber band, and the mean for the cold bands is compared to the mean for the others. Is this a good experimental design?

No, because temperature is confounded with brand.

A veterinarian collected data on the weights of 1,000 cats and dogs treated in a veterinary clinic. The weight of each animal was classified as either healthy, underweight, or overweight. The data are summarized in the table. Based on the data in the table, which of the following is the most appropriate type of graph to visually show whether a relationship exists between the type of animal and the weight classification?

Segmented bar chart

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.

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.

A school is having a contest in which students guess the number of candies in a jar. The student whose guess is closest to the correct number of candles in the jar wins a prize. The number of candies guessed by male and female students is shown in the back-to-back templet below.

The distribution of guesses for male and female students are both skewed to the left.

A scatterplot of student heights, in inches, versus corresponding arm span length, in inches, is shown below. One of the points in the graph is labeled A. If the point labeled A is removed, which of the following statements would be true?

The slope of the least squares regression line increases and the correlation coefficient increases.

List the sample space and tell whether the outcomes are equally likely. Toss a coin three times; record the number of heads.

{0,1,2,3}, not equally likely

A marketing firm obtained random samples of 20 people in five regions of the country to investigate the level of interest in a new product. People in the sample were asked to rate their level of interest on a scale from 1 to 10, with 1 being the least amount of interest and 10 being the greatest. The histograms show the results for each region. The graph for which region displays data for level of interest with the least standard deviation?

(ITS A PICTURE of a graph off to the right side)

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?

-0.87

Opinion-polling organizations contact their respondents by sampling random telephone numbers. Assume that interviewers can now reach about 71% of U.S. households, while the percentage of those contacted who agree to cooperate with the survey is 31%. Each household, it can be safely assumed, is independent of the others. What is the probability of failing to contact a household or of contacting the household but not getting them to agree to the interview?

0.78

At a sporting event, cheerleaders will throw 50 bundled T-shirts into the crowd. The T-shirt sizes consist of 10 small, 15 medium, and the remainder either large or extra large. Suppose Ana catches a T-shirt. What is the probability that she will catch a T-shirt that is not a size small?

0.80

The table shows several values of x and their corresponding values of y. Which of the following is closest to the correlation between x and y?

0.98

A random sample of 374 United States pennies was collected, and the age of each penny was determined. According to the boxplot below, what is the approximate interquartile range (IQR) of the ages?

16

Each value in a sample has been transformed by multiplying by 3 and then adding 10. If the original sample had a variance of 4, what is the variance of the transformed sample?

36

The buyer for an electronics store wants to estimate the proportion of defective wireless game controllers in a shipment of 5,000 controllers from the store's primary supplier. The shipment consists of 200 boxes each containing 25 controllers. The buyer numbers the boxes from 1 to 200 and randomly selects six numbers in that range. She then opens the six boxes with the corresponding numbers, examines all 25 controllers in each of these boxes, and determines the proportion of the 150 controllers that are defective. What type of sample is this?

Cluster random sample

A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area?

Even with a correlation value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.

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.

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. Which of the following is the best 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.

Which of the following distinguishes an observational study from a randomized experiment?

In an observational study treatments are not randomly assigned, whereas in a randomized experiment treatments are randomly assigned.

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?

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.

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. Which of the following statements 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.

As part of a study on facility needs, the administrators of a university wanted to estimate the percent of students who use the exercise facilities on a regular basis. From the 34,000 students who attend the university, a random sample of 370 male students and 400 female students was selected. Of the 770 students selected, 493 students indicated that they use the exercise facilities on a regular basis. What are the population and the sample of the study?

The population is the 34,000 students who attend the university, and the sample if the 770 students who were selected.

Two sections of a class took the same test. Section A had 15 students who had a mean score of 80, and Section B had 20 students who had a mean score of 90. Overall, what was the mean score for all of the students on the quiz?

is 85.7

Which two events are most likely to be independent?

registering to vote; being left-handed

The number of tickets purchased by a customer for a musical performance at certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the umber 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

In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language or both. What is the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course?

0.13

A researcher in Alaska measured in age (in months) and the weight (in pounds) of a random sample of adolescent moose. When the least-squares regression analysis was performed, the correlation was 0.59. Which of the following is the correct way to label the correlation?

0.59

An exponential relationship exists between the explanatory variable and the responsible variable in a set of data. The common logarithm of each value of the response variable is taken, and the least-squares regression line has an equation of log (y) = 7.3 - 1.5x. Which of the following is closest to the predicted value of the response variable for x = 4.8?

1.26

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 B represent the number if books a student buys at the next book fair. What is the expected value of B?

1.79

A friend of yours plans to toss a fair coin 200 times. You watch the first 20 tosses and are surprised that she got 15 heads. But then you get bored and leave. How many heads do you expect her to have when she has finished all 200 tosses?

105

For a recent season in college football, the total number of rushing yards for that season is recorded for each running back. The mean number of rushing yards for the running backs that season is 790 yards. One running back had 1,637 rushing yards for the season, which is 2.42 standard deviations above the mean number of rushing yards. What is the standard deviation of the number of rushing yards for the running backs that season?

350 yards

A random sample of 25 households from the Mountainview School District was surveyed. In this survey, data were collected on the age of the youngest child living in each household. The histogram below displays the data collected in the survey. In which of the following intervals in the median of these data located?

8 years old to less than 10 years old

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

A manufacturer makes lightbulbs and claims that their reliability is 98 percent. Reliability is defined to be the proportion of nondefective items that are produced over the long term. If the company's claim is correct, what is the expected number of non defective lightbulbs in random sample of 1,000 bulbs?

980

A company determines the mean and standard deviation of the number of sick days taken by its employees in one year. Which of the following is the best description of the standard deviation?

Approximately the mean distance between the number of sick days taken by individual employees and the mean number of sick days taken by all employees.

A dog food company wishes to test a new high-protein formula for puppy food to determine whether it promotes faster weight gain than the existing formula for that puppy food. Which of the following strategies is most appropriate for accomplishing this?

Block on dog breed and randomly assign puppies to existing and new formula groups within each breed.

A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than 3?

For many rolls of die, the long-run relative frequency of a number less than 3 landing face up is 1/3.

List the sample space and tell whether the outcomes are equally likely. Toss a coin three times; record the order of heads and tails.

{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}, equally likely

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. 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

A local employer asked for help selecting a new type of desk chair. Thirty employees volunteered, and each employee used the new desk chair for two weeks and the current desk chair for two weeks. To determine which chair was used first, acorn was flipped for each employee. Heads represented using the new chair first, and tails represented using the current chair first. At the end of each two-week period, the employees were asked to rate their satisfaction with the new chair. Which of the following best describes this study?

It is a well-designed experiment because there is random assignment, replication, and comparison of at least two treatment groups.

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.

The number of siblings was recorded for each student of a group of 80 students. Some summary statistics and histogram displaying the results are shown. 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, which of the following can be concluded?

The median is less than the mean, and the distribution has two outliers.

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 nonprofit organization plans to hold a raffle to raise funds for its operation. 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?

The ticket owners lose an average of $0.95 per raffle ticket.

A new restaurant is interested in determining the best time-temperature combination for roasting a five-pound cut of lamb. The times to be tested are 45 minutes, 60 minutes, and 90 minutes at the temperatures of 350 degrees Fahrenheit and 425 degrees Fahrenheit for each time, with the exception of the 90 minute-425 degree combination.

The two cuts that are being roasted for each time-temperature combination are an example of replication.

A graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph?

The value of maximum minus third quartile is less than the value of first quartile minus minimum.

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.

In a large set of data that are approximately normally distributed, r is the value in the data set that has a z-score of -1.00 s is the value of the first quartile, and t is the value of the 20th percentile Which of the following is the correct order from least to greatest for the values of r, s, and t?

r, t, s