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# AP Statistics Unit 2 Test With Answers

AP Statistics Unit 2 Practice Test

In a _________ only some members of a group are studied, but in a _________ all members of the group are studied.
In a sample only some members of a group are studied, but in a census all members of the group are studied.
The set of possible outcomes when rolling a standard six-sided number cube is {1, 2, 3, 4, 5, 6}. The average of this set is 3.5.
Nova rolls the cube 3 times and gets {1, 4, 4}. The average of this set is 3.0.
Which of these is/are true statements? Select all that applyThe population is {1, 4, 4}
The sample is {1, 4, 4}
3.5 is a population parameter.
3.5 is a statistic.
The sampling error for averages is 3.0.
The sample is {1, 4, 4}
3.5 is a population parameter.

The adult human brain weighs an average of about 3.1 lbs, and has a standard deviation of 0.3 lbs. A researcher takes a random sample of 48 brains from cadavers in medical schools across the nation within the past 5 years and measures a mean of weight of 3.22 lbs. Can the researcher conclude that adult brains are getting heavier? (Assume that the sample of brains came from cadavers who were representative of the U.S. adult population).

Yes, the difference between sample mean and population mean is statistically significant.

No, the sample size is too small to adequately represent the population of adult human brains.

No, the difference between sample mean and population mean is likely due to sampling error, or chance alone.

Yes, because the brains come from medical schools across the nation, the sample probably is representative of the population.

No, the difference between sample mean and population mean is likely due to sampling error, or chance alone.

Great! With such a large standard deviation, we can probably conclude that the difference between the sample mean and the population mean is due to chance alone. We would expect that any sample we select probably will not match the population mean exactly.

A scientist wants to find out how much exercise per week is enough to prevent cardiovascular disease in older women. To answer this question, he gathered a sample of volunteer women between the ages of 45 and 75 to participate in a study. Half of the women will walk on a treadmill three times a week for 25 minutes at a time. Half of the women were instructed to ride a stationary bike or treadmill at their discretion for three hours per week. Women were instructed to wear heart-rate monitors during workouts.

This is an example of a(n):

Experiment
The primary difference between an experiment and an observational study is that in a ___________some kind of treatment is imposed on the subjects. In a __________ , on the other hand, the researcher must not interfere with the data or the way it is collected for the study.
The primary difference between an experiment and an observational study is that in an Experiment some kind of treatment is imposed on the subjects. In a Observational Study , on the other hand, the researcher must not interfere with the data or the way it is collected for the study.
A group of researchers are examining which diets have the greatest impact on weight loss in human subjects. They decided to test three diets.
Low-Fat Diet: A 1500 kcal per day diet for women and a 1800 kcal per day diet for men, with 30% of calories from fat, 10% of calories from saturated fat, and an intake of 300 mg of cholesterol per day. Subjects were counseled to eat low-fat grains, vegetables, fruits, legumes, and to avoid fats, sweets, and high-fat snacks.
Mediterranean Diet: A 1500 kcal per day diet for women and a 1800 kcal per day diet for men, with no more than 35% of calories from fat (including 30-45 g of olive oil and a 20 g of nuts per day). Subjects were counseled to eat poultry and fish for protein, plenty of vegetables, and to avoid red meat.
Low-Carb Diet: No restriction was placed on calories, but subjects were instructed to consume no more than 20 g of carbohydrates per day with a gradual increase to 120 g per day to maintain weight loss. The ratio of protein to carbs to fat is not restricted.The study recruited 55 volunteers to participate in the 2-month study that were between the ages of 40 and 65 years, and had a body-mass index (BMI, or weight in kilograms divided by the square of their height in meters) of at least 27. The volunteers were randomly assigned to groups of between 17 and 19 participants.This is an example of an ________. The independent variable in this study is_________ and the dependent variable in this study is ______________
This is an example of an Experiment . The independent variable in this study is type of diet and the dependent variable in this study is weight loss .

Based on the information on the previous page, which of these describes one benefit to an observational study?

proves causation, not just association

sometimes are more ethical than experiments

are less expensive to conduct

sometimes are more ethical than experiments
A study found that Vietnam veterans who experienced Post Traumatic Stress Disorder (PTSD) were twice as likely to die from heart disease as veterans who did not suffer PTSD. The Senior Investigator examined the prevalence of heart disease, PTSD, and other problems in random samples of more than 4,000 Vietnam veterans. The study excluded patients with a prior history of heart disease and included a nation-wide sample of veterans. The study showed there was a positive relationship between the severity of the PTSD diagnosis, and the likelihood of death due to heart disease.
This is an example of an:
This is an example of an: Observational Study

From the results of the above study, can we conclude that PTSD causes heart disease in Vietnam Veterans?

Yes, the samples were randomly selected so we know they are representative of the whole population of Vietnam veterans.

No, heart disease could be caused by a number of other factors besides PTSD alone.

No, since this was an observational study we can only conclude that PTSD is associated with heart disease.

No, the only way to truly know if PTSD causes heart disease is to conduct a census of all Vietnam veterans.

No, since this was an observational study we can only conclude that PTSD is associated with heart disease.

A clinical researcher is conducting a study to determine the effectiveness of post-surgical care procedures. The researcher acquires databases of patient records from hospitals across the United States. From these databases, the researcher selects only those patients who underwent surgery. From this list of surgical patients, the researcher takes a random sample of 100 surgical patients. She then investigates whether the patient received the new post-surgery care procedure, the number of days the patient stayed in post-surgical care, and the patient’s status after recovery, among other variables.

Population:

Sampling frame:

Sample:

Sample Subject or Unit:

A clinical researcher is conducting a study to determine the effectiveness of post-surgical care procedures. The researcher acquires databases of patient records from hospitals across the United States. From these databases, the researcher selects only those patients who underwent surgery. From this list of surgical patients, the researcher takes a random sample of 100 surgical patients. She then investigates whether the patient received the new post-surgery care procedure, the number of days the patient stayed in post-surgical care, and the patient’s status after recovery, among other variables.

Population: surgical patients across the U.S.

Sampling frame: the list of patient records for patients who underwent surgery

Sample: the random sample of 100 surgical patients

Sample Subject or Unit: an individual surgery patient

Suppose the procedures of the survey will change in the following ways:
– The survey will be administered to groups of 1000 randomly selected incoming freshmen every year starting in 2016 and ending in 2021.
– The survey will be administered to the 1000 freshmen twice: during the first week of their first semester at UT, and during the first week of their 7th semester at UT.
Which of the following best describes the population of the new study:Incoming freshmen at 4-year UniversitiesAll students at 4-year Universities

The 1000 randomly selected freshmen

Students at the University of Texas at Austin

Incoming freshmen at the University of Texas at Austin

Students at the University of Texas at Austin

A survey will be given to 1000 randomly selected incoming freshmen at The University of Texas at Austin about their attitudes toward drinking. What is the population of this study?

Incoming freshmen at 4-year Universities

All students at 4-year Universities

The 1000 randomly selected freshman

Students at the University of Texas at Austin

Incoming Freshmen at the University of Texas at Austin

Incoming Freshmen at the University of Texas at Austin

A survey will be given to 1000 randomly selected incoming freshmen at The University of Texas at Austin about their attitudes toward drinking. What is the sample of this study?

incoming freshmen at 4-year Universities

All students at 4-year Universities

The 1000 randomly selected freshmen

Students at The University of Texas at Austin

Incoming freshmen at the University of Texas at Austin

The 1000 randomly selected freshmen

A major soft drink company advertises there are 20 ounces of soft drink in each bottle. A manager at their bottling plant wants to make sure the soft drink dispenser is putting the correct amount of soft drink in each bottle. He randomly selects 100 bottles from the production line, measures the contents of each bottle, and finds the sample has a mean 20.2 fluid ounces in each bottle. This mean can best be described as:

The sampling frame

The parameter

The population

The sample

The statistic

The statistic

If a mean is calculated from an entire population, it is known as the:

population

parameter

sample

sampling frame

statistic

parameter
The correct notation for a sample statistic mean and standard deviation are:
x-bar and s
The correct notation for a population parameter mean and standard deviation are:
µ and sigma
A parent conducted a survey to learn about the average grades of English Language Arts students at the local high school.
The parent randomly selected a sample that included 15 English I students, 16 English II students, 6 English III students, and 14 English IV students.
The most likely source of bias in this sample is:Incorrect Sampling FrameUndercoverage

Convenience Sampling

Judgment Sampling

Volunteer Sampling

Undercoverage

Greenpeace often enlists volunteers to conduct surveys on streets with high pedestrian traffic. These volunteers will wait in these high traffic areas, stopping pedestrians as often as they can to conduct surveys. Pedestrians that volunteers ask to survey have the option to walk away if they do not want to participate. What type(s) of bias are present in this type of sampling? (select all that apply).

Convenience Sampling

Judgment Sampling

Volunteer Sampling

Convenience Sampling

Volunteer Sampling

Deanne went to search for a new apartment to live in with her dog, Phillie. Rather than traveling to each location, Deanne decided to go online to make her decision based on ratings and reviews posted by the residents.
When searching online she discovered that there weren’t any apartment complexes in her area that had ratings above a 2.5 on a 5 point scale. Most of the comments mentioned things like bedbugs, leaking pipes, and trash around the buildings. The most likely source of bias in this sample is:Non-response biasUndercoverage

Convenience Sampling

Judgment Sampling

Voluntary Sampling

Voluntary Sampling

The commissioner of the NBA is asked to prepare a report on player satisfaction with team owners and the league’s management. The commissioner asks the executive director of the NBPA, the players union for the league, to name 10 to 20 players that she believes have a lot of influence in the league, and can accurately speak for the league as a whole. The most likely source of bias in this sample is:

Incorrect Sampling Frame

Undercoverage

Convenience Sampling

Judgment Sampling

Volunteer Sampling

Judgment Sampling

Which of the following is a characteristic of a correct sampling frame?

Each unit belongs to the population and appears only once in the sampling frame.

There are no identifiers, numerical or otherwise, attached to each unit.

Only some units have information enabling the researcher to make contact.

Other information is provided so that samples include demographic proportions similar to the population.

The frame contains as many units of the population as possible.

Each unit belongs to the population and appears only once in the sampling frame.

The frame contains as many units of the population as possible.

identify and explain the difference between populations, samples, and the role of random selection.

explain how and why random selection overcomes sampling bias

describe the characteristics of a Simple Random Sample

1. True or false: The random integer function of your calculator is not truly random.

True. Because calculators rely on algorithms they only simulate randomness.

True.. Because you can predict the next number it will give you.

False

True. Because calculators rely on algorithms they only simulate randomness.

Suppose a gym teacher wanted to use the random number table below to select students to be team captains. The teacher has 30 students and has numbered the students 01 to 30 on her roster.

2011 6754 1372 6590 7848 18618685 7966 1658 1087 9322 36871356 6007 9921 5371 6520 6580

What will be the number of the 3rd captain selected?

01

67

13

11

13

1. A early morning radio talk show invites callers to call in to share their opinion on a controversial new gun control law. Which of these is present in the sample?

I. Undercoverage

II. Voluntary response bias

III. Simple random sample

I only
II only
I and II only
I, II, and III

I and II only
A sociology graduate student is conducting a study on alcohol consumption and perceptions towards drinking and driving. She decides to go to a local bar in her area, and waits outside the bar on a Saturday night. She stops every 10th person who exits the bar, and asks them questions regarding how much alcohol they consumed and whether or not they plan to drive.
Which sampling method is being used?Random SamplingSystematic Sampling

Cluster Sampling

Stratified Random Sampling

Systematic Sampling

A researcher with the Office of Immigration Statistics is interested in studying how long it takes legal immigrants from Central and South America to obtain driver’s licenses after entering the country. Which of the following is the most effective plan for the study:

Conduct a door-to-door census in border states to ask when the residence dweller arrived in the U.S. and whether or not they have a driver’s license.

Using a database of legal immigrants from Central and South America, randomly select 1000 subjects and mail surveys out for them to complete and return.

Using a database of legal immigrants from Central and South America, randomly select 1000 subjects and conduct a telephone survey. Interviewers must speak the subject’s language.

Using a database of legal immigrants from Central and South America, randomly select 1000 subjects and compare the date of entry to DMV records for those subjects.

Using a database of legal immigrants from Central and South America, randomly select 1000 subjects and compare the date of entry to DMV records for those subjects.

A researcher is interested in how fast people walk in different parts of the country. He randomly selects 50 cities and towns from all over the U.S., and then finds a place with high pedestrian traffic in each city. He then measures the pace (in steps per minute) of every 20th person who walks by.

1.The method used to measure walking pace is:

2.Suppose the researcher discovers that there is a positive relationship between population and walking pace. Can the researcher claim that where you live causes you to walk faster or slower?

1. An observational study

2. No

According to the NFL, regulation footballs are inflated to an average 13 psi, with a 0.5 psi margin of error. An NFL analyst takes a random sample of 50 footballs used in NFL games and measures their inflation pressure at half time of the game in which they are used. The sample is found to have a mean inflation pressure of 12.7 psi. Can the analyst conclude that someone cheated by deflating the football below regulation inflation pressure?

Yes, since the sample was taken randomly the results are most likely valid.

Yes, the difference between the population mean and the sample mean is significant.

No, the analyst needs to sample footballs from every team to compare inflation pressures.

No, some footballs should be measured before the game and others should be measured at the end of the game.

No, the difference in population and sampling means is most likely due to sampling error.

No, the difference in population and sampling means is most likely due to sampling error.

An environmental nonprofit regularly has volunteers conduct surveys on streets and intersections with heavy pedestrian traffic. They are tasked with getting as many survey responses as they possibly can within a 4-hour shift.

Imagine that you are hearing about this survey on the news. You are concerned that the results may not be reliable because the nonprofit group used a fast and easy method that over-represented certain types of people.
Which type of sampling bias are you concerned about?
Correct! Convenience sampling
Judgment sampling
Nonresponse bias
Volunteer response bias

scatterplot
a graphical display that shows the relationship between two quantitative variables
explanatory variable
the independent variable that attempts to explain the relationship with the other variable. It becomes the x variable on the graph
response variable
the dependent variable that responses to the other variable being used. It becomes the y variable
correlation
the numerical measure r that measures the strength and direction of the linear relationship
outlier
a point that lies outside the overall pattern of the data
lurking variables
A variable other than x & y that simultaneously affects both variables and accounts for the correlation between the two
residual
the difference between the actual value of y and the predicted value of y for a specific x value
predicted value
the value y, found for a specific x from the regression equation
slope
the change in the predicted response variable for every unit increase in the explanatory variable
least squares regression line
also know as the regression line or line of best fit it is the line that minimizes the sums of the squares of the vertical distances from the actual points to the line
y-intercept
the value of the resonse variable when the explanatory variable is zero
coefficient of determination
the value of r-dquared which tells us what percent of the variability in y can be explained by the linear regression of y on x.
extrapolation
when we attempt to predict values for the reposnse variable that are outside the domain of the explanatory variable
leverage point
a point that has a strong effect on the regression line pulling the regression line toward it
influential point
a point that has a strong effect on the regression line if it is removed

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