Statistics Final Exam Study Guide

In the following residual plot, consider the point that is indicated by the arrow. Which of the following statements must be true about the individual represented by that point? (a) The actual value of the response variable is larger than its predicted value. (b) The actual value of response variable is smaller than its predicted value. (c) The actual value of explanatory variable is larger than its predicted value. (d) The actual value of explanatory variable is larger than the observed value of the response variable.

(b) The actual value of response variable is smaller than its predicted value.

Consider the following probability model associated with the type of sneakers worn by high school basketball players in Massachusetts. What is the probability a randomly selected Massachusetts high school basketball player wears Adidas or Reebok sneakers? Adidas: 0.225 Reebok: 0.195 (a) 0.065 (b) 0.580 (c) 0.420 (d) 0.0225

(c) 0.420

The overall shape of this distribution is (a) skewed to the right (b) skewed to the left (c) roughly symmetric (d) uniform

(b) skewed to the left

If P(A)=.24 and P(B)=.52 and A and B are mutually exclusive, what is P(A or B)? (a) .1248 (b) .28 (c) .6352 (d) .76

(d) .76

In a large country in Central Pennsylvania, 42% of all registered voters are Democrats and 53% are Republicans. What is the probability a randomly selected voter is affiliated with some other party? (a) 0.95 (b) 0.05 (c) 1.00 (d) 0.21

(b) 0.05

In a class of 100 students, the grades on a statistics test are summarized in the following frequency table: grade frequency 91-100 11 81-90 31 71-80 42 61-70 16 The median grade is in which of the following intervals? (a) 61-70 (b) 71-80 (c) 81-90 (d) Since the individual grades are not known, the median cannot be determined.

(b) 71-80

Suppose 70% of all adults drink coffee. If you were to conduct a simulation involving coffee- drinkers and non-coffee drinkers, which of the following is a valid assignment of digits to represent coffee drinkers? (a) 0,1,2= coffee drinker; 3,4,5,6,7,8,9= not a coffee drinker (b) 0,1,2,3= coffee drinker; 4,5,6,7,8,9= not a coffee drinker (c) 0,1,2,3,4= coffee drinker; 5,6,7,8,9= not a coffee drinker (d) 0,1,2,3,4,5,6= coffee drinker; 7,8,9= not a coffee drinker

(d) 0,1,2,3,4,5,6= coffee drinker; 7,8,9= not a coffee drinker.

The pie chart above describes the distribution of favorite school subject for 300 high-school students. The number of students whose favorite subject is math is: (a) 26 (b) 45 (c) 60 (d) 78

(d) 78

At the beginning of the school year, a high school teacher asks every student in her classes to fill out a survey that asks for their age, gender, their number of years they have lived at their current address, their favorite school subject, and whether they plan to go to college after high school. Which of the following best describes the types of variables that are being measured? (a) five quantitative variables (b) two categorical variables and two quantitative variables (c) two categorical variables and three quantitative variables (d) three categorical variables and two quantitative variables

(d) three categorical variables and two quantitative variables

You play tennis regularly with a friend, and from past experience, you believe that the outcome of each match is independent. For any given match you have a probability of 0.6 of winning. The probability that you lose the next two matches is (a) 0.16 (b) 0.40 (c) 0.80 (d) 0.36

(a) 0.16

Based on the shape of this distribution, what numerical measures would best describe it? (a) The median and the IQR (b) The mean and standard deviation (c) The mean and the quartiles (d) The median and the standard deviation

(a) The median and the IQR

Consider a large number of countries around the world. There is a positive correlation between the number of laptops per 1000 people (x) and the average life expectancy y. Does this mean that we could increase the life expectancy in Rwanda by shipping laptops to that country? (a) No: if the correlation were negative we could accept that conclusion, but this correlation is positive. (b) No: the positive correlation just shows that richer countries have both more laptops and higher life expectancies. We don't know if there is causation. (c) Yes: the positive correlation means that if we ship do more laptops we can expect an increase in life expectancy. (d) Yes: the correlation says that as laptops go up, it causes life expectancy to go up.

(b) No: the positive correlation just shows that richer countries have both more laptops and higher life expectancies. We don't know if there is causation.

A scatterplot of a set of data is shown below. Which statement is true? (a) The least square regression line has a positive slope (b) The least square regression line has a slope of zero. (c) There is no relationship between X and Y. (d) A line is not an appropriate model for this data.

(b) The least square regression line has a slope of zero.

Which of the following statements is false? (a) All possible outcomes together must have probabilities that add up to 1. (b) A phenomenon is random if individual outcomes are uncertain. (c) The probability of any outcome must be a number between 0 and 1. (d) A probability can be a number greater than 1.

(d) A probability can be a number greater than 1.

One group recieved a placebo. Why not just give this group no treatment at all? (a) It is not ethical to give no treatment at all in this setting. (b) You can't do an experiment without a placebo. (c) Subjects would be disappointed if not given a pill. (d) Just thinking you are getting a treatment may have an effect on whether or not you stop smoking.

(d) Just thinking you are getting a treatment may have an effect on whether or not you stop smoking.

Suppose a high school guidance counselor wants to find out the proportion of students at his high school who have tried alcohol. He sends out an email to 200 randomly chosen students asking them if they have tried alcohol. Of the 92 that responded, 6% said they had tried alcohol. Describe how nonresponse might lead to bias in this study.

A nonresponse might lead to a bias in the study because the counselor may assume that those who did not reply might've had tried alcohol and they wouldn't want to tell the counselor.

Suppose a high school guidance counselor wants to find out the proportion of students at his high school who have tried alcohol. He sends out an email to 200 randomly chosen students asking them if they have tried alcohol. Of the 92 that responded, 6% said they had tried alcohol. Describe how response bias might lead to bias in this study.

The counselor would have a negative bias towards those who said they have tried alcohol.

You would draw a segmented bar graph (a) to show the distribution of heights of students in this course. (b) to determine if gender and favorite toy as a child are associated (c) to show the five-number summary for the heights of female students (d) to show the relationship between the height of female students and the heights of their mothers.

(b) to determine if gender and favorite toy as a child are associated

The five-number summary of the distribution of scores on the final exam in Psych 001 last semester was min=18 Q1=39 Med=62 Q3=76 Max=100. A total of 416 students took the exam. About how many students had scores about 39? (a) 104 (b) 208 (c) 312 (d) 400

(c) 312

Which of the following is a valid statistical question? (a) How many people voted in the last school board election? (b) How many points were scored by the New England Patriots during the 2014-15 regular NFL season? (c) How long will you be in line when you get lunch from the cafeteria? (d) How tall is Mount Everest?

(c) How long will you be in line when you get lunch from the cafeteria?

Which of the following are resistant to outliers? (a) The mean and standard deviation (b) The median and standard deviation (c) The median and the IQR (d) The range and the IQR

(c) The median and the IQR

The correlation between the heights (feet) of fathers (x) and the heights (feet) of their adult sons (y) is r=0.89. If the sons' heights were instead measured in inches, the correlation between heights of fathers and heights of sons would be (a) much smaller than 0.89 (b) slightly smaller than 0.89 (c) unchanged; equal to 0.89 (d) slightly larger than 0.89

(c) unchanged; equal to 0.89

What is the purpose of the random assignment of treatments to subjects in an experiment? (a) To create roughly equivalent groups before treatments are administered. (b) To prevent certain groups in the population from being systematically excluded in the experiment. (c) To reduce bias in the selection of the subjects to be included in the experiment. (d) To eliminate the need for blinding in an experiment.

(a) To create roughly equivalent groups before treatments are administered.

Two events are said to be mutually exclusive if: (a) They both contain the same outcomes (b) They do not contain any outcomes in common (c) They both have at least one outcome in common (d) One event contains all of the outcomes that are not contained in the other event.

(b) They do not contain any outcomes in common.

Consider the following probability model associated with the number of raffle tickets purchased by each customer: 0.15 0.15 ___________ 0.25 0.25 What is the probability a randomly selected customer buys 3 raffle tickets? (a) 0.15 (b) 0.25 (c) 0.35 (d) 0.20

(d) 0.20

During his NBA career, Larry Bird made approximately 89% of all free throws. Suppose Larry makes 10 free throws in a row. What is the probability he will make the next free throw? (a) 0.11 (b) 0.50 (c) 0.01 (d) 0.89

(d) 0.89

A statistics teacher states the probability of a surprise quiz on any given day is 0.30. If quizzes are given independently of the day, what is the probability there will be a surprise quiz on the next two consecutive days? (a) 0.09 (b) 0.21 (c) 0.42 (d) 0.60

(a) 0.09

Which of the distributions below has the larger standard deviation? (a) Distribution A (b) Distribution B (c) The standard deviations are equal since the ranges are equal (d) The standard deviations are equal since both distributions are symmetric.

(a) Distribution A

Steve's boss told him that he did not deserve a raise and that Steve was making an amount similar to other managers with his experience. Steve gathered some data and found that the z-score for his salary as composed to other managers with the same level of experience is -1.35. Which of the following is the best interpretation of this z-score? (a) Steve makes 1.35% less than other managers with his experience level. (b) Steve makes $1.35 less per play period than the average for managers with his experience level. (c) Steve makes $1.35 less per hour than the average for managers with his experience level. (d) Steve's salary is 1.35 standard deviation below the mean salary of all managers with his experience level.

(d) Steve's salary is 1.35 standard deviation below the mean salary of all managers with his experience level.

The United Nations has data on the percent of adult males and females who are illiterate in 142 countries. The correlation between male illiteracy rate and female illiteracy rate is r=0.945. This tells us that (a) countries with high male illiteracy tend to also have high female illiteracy, and the relationship is very strong. (b) countries with high male illiteracy tend to also have high female illiteracy, but the two are only weakly related. (c) countries with high male illiteracy tend to have low female illiteracy, and the relationship is very strong. (d) countries with high male illiteracy tend to have low female illiteracy, but the two are only weakly related.

(a) countries with high male illiteracy tend to also have high female illiteracy, and the relationship is very strong.

The experiment was "double-blind." This means that (a) neither the subjects nor the people who worked with them knew whether they were taking bupropion, the nicotine patch, the combination of the two, or the placebo. (b) the subjects did not know that the treatments were intended to reduce their smoking. (c) the subjects did not know whether they were taking bupropion or placebo. (d) the bupropion pills looked just like the placebo pills.

(a) neither the subjects nor the people who worked with them knew whether they were taking bupropion, the nicotine patch, the combination of the two, or the placebo.

The correlation between the heights of fathers (x) and the heights of their adult sons (y) is r= 0.89. This tells us that (a) taller than average fathers tend to have taller than average sons. (b) taller than average fathers tend to have shorter than average sons. (c) 89% of all sons are taller than their fathers. (d) there is almost no connection between heights of fathers and sons.

(a) taller than average fathers tend to have taller than average sons.

A study of the effects of television measured how many hours of television each of 125 grade school children watched per week during a school year and their reading scores. Which variable would you put on the horizontal axis of a scatterplot of the data? (a) Hours of television, because it is the response variable (b) Hours of television, because it is the explanatory variable. (c) Reading score, because it is the response variable. (d) Reading score, because it is the explanatory variable.

(b) Hours of television, because it is the explanatory variable.

A scatterplot and a least regression line are shown in the figure below. If the point (20,25) that is labeled A is removed from the data set, which one of the statements below is TRUE? (a) The slope will decrease and the y-intercept will decrease. (b) The slope will decrease and the y-intercept will increase. (c) The slope will increase and the y-intercept will increase. (d) The slope will increase and the y-intercept will decrease.

(b) The slope will decrease and the y-intercept will increase.

A random number generator is used to select 12 students from a large statistics class to rate a statistics video. The 12 students selected are (a) the population (b) a simple random sample of the class (c) a census (d) a voluntary response sample

(b) a simple random sample of the class

A random sample survey interviewed 3,800 U.S. adults nationwide by telephone. One question asked was whether they agreed with this statement: "Some people say we should have a third major political party in this country in addition to the Democrats and Republicans." In this sample, 53% of the people asked responded, "Yes we should have a third political party." The population for this sample survey appears to be (a) all registered voters. (b) all adult residents of the U.S. (c) the 3,800 people who were interviewed. (d) people who think we should have a third political party.

(b) all adult residents of the U.S.

The mean of the distribution (don't try to find it) is (a) very close to the median (b) clearly less than the median (c) clearly greater than the median (d) you can't say because the mean is random

(b) clearly less than the median

The most important advantage of experiments over observational studies is that (a) experiments are usually easier to carry out. (b) experiments can give better evidence of causation. (c) confounding cannot happen in experiments. (d) an observational study cannot have a response variable.

(b) experiments can give better evidence of causation.

A recent study showed that teenagers who had night lights in their rooms as babies are more likely to suffer from myopia (near sightedness) than teenagers who had not used night lights. But genetic factors are known to play a role, and near-sighted parents are more likely to install a night light in their children's room. This makes it hard to tell if the night light caused the myopia. This is an example of (a) double-blinding (b) the placebo effect (c) a confounding variable (d) an explanatory variable

(c) a confounding variable

A random sample survey interviewed 3,800 U.S. adults nationwide by telephone. One question asked was whether they agreed with this statement: "Some people say we should have a third major political party in this country in addition to the Democrats and Republicans." In this sample, 53% of the people asked responded, "Yes we should have a third political party." The news article that reports the poll results says, "The margin of error is plus or minus two percentage points." This means that (a) we can be absolutely certain that between 51% and 55% of all adult Americans think we should have a third party. (b) we expect that exactly 53% of all adult Americans think we should have a third party. (c) we expect that between 51% and 55% of all adult Americans think we should have a third party. (d) we expect that between 51% and 55% of the 3,800 people interviewed think we should have a third party.

(c) we expect that between 51% and 55% of all adult Americans think we should have a third party.

A local community organizer is considering running for city council. She wants to measure her name recognition by doing a survey in the council district in which she intends to run. Which of the following survey methods would produce unbiased results? (a) Place pollsters in front of every grocery store in her district on Saturday morning and asking each person entering the store if he or she recognizes the organizer's name. (b) Sending a survey card to all registered voters in her district asking them to call a number to state whether or not they recognize the organizer's name. (c) Calling people from her district listed in the phone book and asking each if he or she recognizes the organizer's name. (d) Gathering a random sample of eligible voters in her district, a pollster visits each of the voter's homes, and asks the voter if he or she recognizes the organizer's name..

(d) Gathering a random sample of eligible voters in her district, a pollster visits each of the voter's homes, and asks the voter if he or she recognizes the organizer's name..