AP Stats Midterm

The box plots above summarize two data sets, A and B. Which of the following must be true?

I. Set A contains more data than Set B
II. The box of Set A contains more data than the box of Set B
III. The data in Set A have a larger range than the data in Set B.

I and II only

Suppose a new regulation requires businesses to pay all employees a minimum wage of $15.00 per hour. A small coffee shop currently has 9 employees— 5 employees whose wages are less then $15.00 and 4 employees whose wages are more than $15.00 per hour. To meet the new regulation, the coffee shop plans to increase the wages of the 5 employees whose wages are less than $15.00 per hour to $15.00 per hour. The other 4 employees will not receive a wage increase at this time.

Which of the following must be true about the median wage of the 9 employees after the wage increase occurs?

The median wage will be $15.00 per hour.

The distribution of housing prices in a city includes several outliers at the upper end of the distribution and no outliers at the lower end of the distribution.

Which of the following is the most resistant, or robust, measure of center of the distribution of housing prices?

The median, because it is not greatly affected by the outliers.

A company conducted a charity drive and recorded the donations made by the employees of two departments, A and B. The back-to-back stemplot below shows the amounts given by the employees from department A and the amounts given by employees from department B.

Based on the back-to-back stemplot, which of the following is correct?

The median donation for the employees from department A is greater than the median donation for the employees from department B.

A random sample of middle school students from District 1 and a random sample of middle school students from District 2 were selected with an even number of students in each sample. The number of minutes each student spent playing a certain mobile game application in a typical day was recorded. The data are summarized in the following table.

If no two students within each district spent the same amount of time playing the mobile game application, which statement must be true?

The percentage of students in both samples who spent less than 130 minutes playing the game is equal.

The boxplot shown summarizes the 100 highest salaries for municipal employees in a large city.

The new municipal employee was hired and was told that the salary would be within the middle 50 percent of the current 100 highest salaries.

Based on the boxplot, which of the following is closest to the width of the interval in which the new employee’s salary will fall?

$7,000

A botanist is studying the weights, measured in pounds, of pumpkins grown at two different farms. The box plots show the distrbution of pumpkin weight for two samples of equal size, one from farm A and the other from farm B.

Based on the boxplots, which of the following is a correct conclusion about the distribution of pumpkin weight for the samples from the two farms?

There are more pumpkin weights that are less than 100 pounds from farm B than there are from farm A.

The number of new projects started each month at an advertising agency for the last six months is:

2 5 3 3 6 3

The interquartile range (IQR) for the above data is

2

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.

Based on the graph, which statement must be true?

For students in grade 7, the number who chose activity C was greater than the number who chose activity B.

The prices, in thousands of dollars, of 304 homes recently sold in a city are summarized in the histogram below. Based on the histogram, which of the following statements must be true?

The median price is not greater than $750,000.

The average apple weighs 100 grams with a SD of 5 grams and is approximately normally distributed. The average grapefruit weighs 250 grams with a SD of 10 grams and is approximately normally distributed. Which pair of weights for an apple and a grapefruit would have the same z-score?

apple: 107 grams, grapefruit: 265 grams

The weights of adult male Labrador Retrievers are approximately Normally distributed with a mean of 87 pounds and a standard deviation of 8 pounds. Which of the following statements is true?

The proportion of adult male Labrador Retrievers that weigh less than 80 pounds is approximately equal to the proportion that weigh more than 94 pounds.

Sadie is a math teacher. She gives her students a test and calculates that the mean score is 64.7, the median is 72 and the SD is 7.15. She decides to add 6 points to each student’s score. What are the new mean, median, and SD after she adds the points?

70.7, 78, 7.15

Tara’s test grade was a 60%. The class average was a 75%, and the SD was 5.1%. What statement best describes her z-score and her test grade?

z= -2.94. Compared to the rest of the class, Tara’s grade is low.

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. What percent of travel times take more than 35 minutes?

16%

For a certain population of penguins, the distribution of weight is approximately normal with mean 15.1 kilograms (kg) and standard deviation 2.2 kg. Approximately what percent of the penguins from the population have a weight between 11.0 kg and 17.5 kg?

83%

The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachael is at the 99th percentile in height for adult women, then her height, in inches, is closest to

70

For which of the following distributions is the mean greater than the median?

A

Use Figure 1-1. For this density curve, which of the following is true?

A) It is symmetric
B) The total area under the curve is 1
C) The median is 2.5
D) The mean is 2.5)
E) All of the above

E) All of the above

Use Figure 1-1. For this density curve, what percent of the observations lie above 3?

40%

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 collection 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 separably. The two scatter plots show the data from the 10 female lions and the 10 male lions.

Based on the scatter plots, for which gender does there appear to be evidence theat the more time a lion cub spends playing, the sooner the cub is likely to begin hunting?

For female cubs only

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 scatter plot below shows the number of defective parts produced by each machine on the selected days.

Which statement gives the best comparison between the number of defective parts produced by the machines during the first hour of operation on the 19 days?

Machine A usually, but not always, produced fewer defective parts than machine B.

For which of the following scatter plots is the correlation between x and y closest to 0?

E

A data scientist had 5 different sets of data. For each data set the scientist fit a least-squares regression line, then graphed the residuals versus the predicted values for each. Which residual plot indicates that the least-squares regression model was the most appropriate model to fit the data?

D

An engineering student collected data on the maximum height, in feet, and the maximum speed, in miles per hour, of thirteen roller coasters. A scatter plot of the data and the least-squares regression line are shown. The maximum heights of five of the roller coasters are 60, 105, 150, 200, and 215 feet.

If the least-squares regression line is used to predict the maximum speed for the five roller coasters, for which maximum height, in feet, would the absolute value of the residual be largest?

105

There is an approximate linear relationship between the heights of females and their age (from 5 to 18 years) described by the predicted height = 50.3 + 6.01(age), where height is measured in cm and age in years. Which of the following is NOT correct?

The estimated intercept is 50.3 cm. We can conclude from this that the typical height of female children at birth is 50.3 cm.

Children between the ages of 18 months and 29 months, there is an approximate linear relationship between height (cm) and age. The relationship can be represented by

predicted height = 64.93 ÷ 0.63(age in months)

Loretta is 20 months old and 80 cm tall. What is her residual?

2.47

Exercise physiologists are investigating the relationship between lea nobody mass (in kilograms) and the resting metabolic rate (in calories per day) in sedentary males.

Based on the computer output above, which of the following is the best interpretation of the value of the slope of the regression line?

For reach additional kilogram of lean body mass, the resting metabolic rate increases on average by 22.563 calories per day.

On-base percentage plus slugging (OPS) is a statistic used in baseball to measure a team’s batting success. The number of runs score and OPS for 30 baseball teams was used to conduct a linear regression analysis. The scatter plot and computer output for the regression analysis is shown.

Which of the following is the most appropriate interpretation of the statistics 93.47% in the regression output?

93.47% of the variation in number of runs scored can be explained by the linear regression with OPS.

A sample of 15 golfers who played a golf course on a certain day was selected. For each golfer, the average driving distance (x), in yards, and the percent of fairways hit on the drive (y) were recorded.

The scatter plot displays the percent of fairways hit versus the average driving distance. Also shown is the least-squares regression line, y=66.228+0.0002x.

The point circled on the scatter plot is considered an influential point. A new least-squares regression line will be calculated with the influential point removed. How will the removal of the influential point affect the new least-squares regression line for the remaining 14 points?

The y-intercept will increase, and the slope will be negative.

Researchers conducted a study to investigate whether watching an outdoor scene while exercising improves health more than exercise alone. Fourteen fifth-grade students participate in two trials of the study. For one trial, the students rode a stationary bicycle for 15 minutes while watching a video of someone cycling through a forest. For the other trial, the students rode a stationary bicycle for 15 minutes without watching a video. Each student completed both trials in a randomized order. The researchers recorded the students heart rates after each trial.

Which of the following is the best description of the study?

A randomized matched-pairs experiment

The recreation committee of a certain town is interested in creating a new nature trail for walkers, runners, and bikers. A random sample of 100 town residents were asked whether they are in favor of creating the new trail. Of those sampled, 78 said yes.

What is the population of interest for which the committee can generalize its conclusions?

All town residents

A total of 13 distinct groups, but with each group similar to the other groups, participate in a craft fair. To investigate how satisfied the participants were with the fair, the fair director conducted a survey. The director randomly selected 5 of the groups participating in the fair and surveyed all members of the selected groups.

Which statement best describes the sampling method used by the director?

It was cluster sampling, because the sample consisted of all members of the 5 randomly selected groups.

An experiment was conducted to investigate whether submerison in cold water causes a lower heart rate. The experiment used 50 volunteers. The 25 youngest volunteers had their heart rate measured while holding their breath for 30th seconds with their face submerged in cold water. The 26 oldest volunteers had theirheart rate measured while holding their breath for 30 seconds with their face not submerged in cold water. The mean heart rate for volunteers who had their face submerged in cold water was lower than the mean heart rate for volunteers who did not have their face submerged in cold water.

Which of the following elements of a well-designed experiment is missing?

I. Comparison of at least two treatment groups
II. The random assignment of treatments to experimental units
III. Replication

II only

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 then 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 medical researcher is interested in assessing the effectiveness of a new medication for pain relief. Three hundred volunteers will be randomly assigned to groups. One group will receive the new medication at a low dose, one group will receive the new medication at a high dose, and one group will receive a placebo that looks like the new medication but does not contain any active ingredients. Each person will be asked to rate his or her level of pain at the beginning of the experiment and again two hours after taking the medication or placebo.

What is the number of treatments for this experiment?

3

Researchers will conduct an experiment to compare the effective of two brands of shampoo—Brand X and Brand Y. They will use a matched-pairs design in which each participant will use one brand for one week and then the other brand for one week. For each participant, the researchers will randomly assigned with shampoo, Brand X or Brand Y, will be used first, and 15 milliliters of shampoo will be used for each hair wash. Because the temperature of the water is known to have an effect, a water temperature less than 100F will be used for the first week and a water temperature greater than 100F will be used for the second week. At the end of each week, the effectiveness of the shampoo being used will be measured.

Which of the following would improve this matched-pairs experiment?

Let each participant decide for themselves what water temperature to use, but each participant must keep the water temperature the same for both brands.

A medical researcher conducted a study to investigate the effectiveness of two drugs, L and M, designed to reduce the number of seizures that people with epilepsy might have. Each person in a group of 120 adult volunteers who had epilepsy was randomly assigned to one of two groups. Those assigned to one group took drug L for one year, and those assigned to the other group took drug M for one year. Each participant recorded the number of seizures that occurred during the year.

To which group is it most reasonable to generalize the results of this study?

All adults with epilepsy who are similar to those who volunteered for the study.

The Physicians Health study, a large medical experiment involving 22,000 male physicians, attempted to determine whether aspirin could help prevent heart attacks. In this study, one group of about 11,000 physicians took an aspirin every other day, while a control group took a placebo. After several years, it was determined that the physicians in the group that took aspirin had significantly fewer heart attacks than the physicians in the control group. Which of the following statements explains why it would not be appropriate to say that everyone should take aspirin every other day?

I. The study included only physicians, and different results may occur in individuals in other occupations.
II. The study included only males and there may be different results for females.
II. Although taking aspirin may be helpful in preventing heart attacks, it may be harmful to some other aspects of health.

I, II, and III

A paint manufacturer conducted an experiment to investigate whether a new formula produces paint that lasts longer on the exterior of a building than paint produced using an older formula. A grid of 20 squares was drawn on one side of an exterior wall of a building. The new formula was randomly assigned to 10 squares, and the older formula was assigned to the remaining 10 squares. Each square was painted with the assigned formula. One year later, each square was rated on how well the paint had lasted, using a numerical scale for which larger values indicated longer-lasting paint.

Which of the following best describes the design of the experiment?

A completely randomized design, because each formula was randomly assigned to 10 squares.

At a small company, 40% of the employees are classified as junior level, and 32% of the employees work in department A. Of those classified as junior level, 55% work in department A. One employee will be selected at random.

What is the probability that the selected employee works in department A and is classified as junior level.?

0.22

A randomly selected student is asked to respond Yes, No, or Maybe to the question “Do you intend to vote in the next presidential election?” The sample space is {Yes, No, Maybe}. Which of the following represents a legitimate assignment of the probability for this sample space?

0.5, 0.3, 0.2

You play tennis regularly with a friend, and from experience, you believe that the outcome of each match is independent. For any given match you have probability of 0.7 of winning. The probability that you win the next two matches is:

0.49

People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 9.4% of the American population has 0-negative blood. If 12 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor?

0.694

Forrest has determined that if he gets to the bus stop at 7:30 AM, there is a 0.15 probability that he misses the bus. If he arrives at the bus stop four consecutive days at 7:30, what is the approximate probability that he catches the bus all four days? Assume each day is independent.

0.522

The probability that a new microwave oven will stop working in less than 2 years is 0.05. The probability 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 of 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

In a certain town 60% of the households own a cellular phone, 40% own a page, and 20% own both a cellular phone and pager. The proportion of households that own a cellular phone but not a page is

40%

Karmen and Sophia are on a swim team and race in different events at a swim meet. The probability that Karmen will win her race at the swim meet is 0.1. The probability that Sophia will win her race at the swim meet is 0.3. If the events of Karmen winning her race and Sophia winning her race are independent, what is the probability that either Karmen or Sophia will win her race at the swim meet?

0.37

100 randomly selected adult Americans were asked if they thought that young adults (18-21) should be allowed to go into combat situations. Here are the results, classified by age of the subject.

Which of the following is the probability of a “yes” answer, given that the person was 18-21?

0.32

100 randomly selected adult Americans were asked if they thought that young adults (18-21) should be allowed to go into combat situations. Here are the results, classified by age of the subject.

What is the probability that a randomly selected subject in the study is 22+ or answered “No”?

0.84