Stats Final Exam
Which of the following is not true?
If two events are independent, then they must be mutually exclusive.
Scenario 3-7 One cup of dried soybeans contains 846 calories. Which of the following statements is appropriate?
It would be inappropriate to predict the protein content of soybeans with this regression model, since their calorie content is well beyond the range of these data.
When drawing a histogram it is important to
Label the vertical axis, so the reader can determine the counts or percent in each class interval
There are three children in a room, ages three, four, and five. If a four year old child enters the room, the
Mean age will stay the same but the variance will decrease
There is a positive correlation between the size of a hospital (measured by number of beds) and the median number of days that patients remain in the hospital. Does this mean that you can shorten a hospital stay by choosing to go to a small hospital?
No - the positive correlation is probably explained by the fact that seriously ill people go to larger hospitals
Scenario 3-2 Do these data provide strong evidence that drinking wine actually causes a reduction in heart disease deaths?
No, countries that drink lots of wine differ in other ways from countries that drink little wine. We can't be sure the wine accounts for the difference in heart disease deaths.
Based on this box plot, which of the following statements is true?
The interquartile range is about $20,000.
You are playing a board game with some friends that involves rolling two six-sided dice. For eight consecutive rolls, the sum on the dice is 6. Which of the following statements is true?
The probability of rolling a 6 on the ninth roll is the same as it was on the first roll.
A researcher reports that, on average, the participants in his study lost 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report must be a fraud. Which of the following statements is correct?
The report only gives the average. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend's experience does not necessarily contradict the study results.
Based on pie chart about Patel: Which of the following statements is true about these results?
The results of the survey are unreliable because response to the survey was voluntary.
Scenario 3-7 Which of the following best describes what the number S= 3.37648 represents?
The standard deviation of the residuals is 3.37648
Suppose we fit the least-squares regression to a set of data. If a plot of the residuals shows a curved pattern,
a straight line is not a good model for the data
Scenario 4-2 The population is
all American school teachers
Based on this box plot, which of the following statements is true?
all of the above
Question about National League and American League: Which of the following is a correct statement?
all of the above
The density curve for a continuous random variable X has which of the following properties?
all of the above
When controlled experiments are impractical or unethical, which of the following would be necessary to establish a cause-and-effect relation between two variables
all of the above
Event A occurs with probability 0.3, and event B occurs with probability 0.4. If A and B are independent, we may conclude that
all of the abpve
If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, we say the phenomenon is
random
The principle reason for replication in designing experiments is that it
reduces sample variability
The Bradley effect is a theory proposed to explain observed discrepancies between voter opinion polls and election outcomes in some elections where a white candidate and a non-white candidate run against each other. The theory proposes that some voters tend to tell pollsters that they are undecided or likely to vote for a non-white candidate, and yet, on election day, vote for the white opponent. This is an example of
response bias
You would draw a scatterplot to
show the relationship between the height of female students and the heights of their mothers
The fraction of the variation in the values of a response y that is explained by the least-squares regression of y on x is the
square of the correlation coefficient
A marketing research firm wishes to determine if the adult men in Laramie, Wyoming, would be interested in a new upscale men's clothing store. From a list of all residential addresses in Laramie, firm selects a simple random sample of 100 and mails a brief a questionnaire to each. The chance of the 100 homes in a particular neighborhood in Laramie end up being the sample of residential addresses selected is
the same as for any other set of 100 residential addresses.
A market company wishes to find out whether the population of students at a university prefers brand A or brand B of instant coffee. A random sample of students is selected, and each one is asked to try brand A first and then brand B (or vice versa, with the order determined at random). They then indicate which brand they prefer. The response variable is
which brand they prefer
Scenario 3-4 Based on the scatterplot, the least-squares line would predict that a car that emits 10 grams of CO per mile driven would emit approximately how many grams of NOX per mile driven?
1.1
Students at University X must have one of four class ranks - freshman, sophomore, junior, or senior. At University X, 35% of the students are freshman and 30% are sophomores. If a university X student is selected at random, the probability that he or she is either a junior or senior is
35%
Scenario 3-6 The y-intercept of the least squares line is
4.65
Scenario 5-11 Which of the following statements supports the conclusion that the event "right-handed" and the event "online" are not independent?
51/60 doesn't equal 166/200
You want to use a simulation to estimate the probability of getting exactly one head and one tail in two tosses of a fair coin. You assign the digits 0, 1, 2, 3, 4 to heads and 5, 6, 7, 8, 9 to tails. Using the following random digits to execute as many simulations as possible, what is your estimate of the probability?
6/10
A set of data has a median that is much larger than the mean. Which of the following statements is most consistent with this information?
A stem plot of the data is skewed left.
Scenario 3-7 The circled point on the scatter plot represents lima beans, which have 621 calories and 37 grams of protein. The residual for lima beans is:
-4.18
Scenario 5-2 The probability that you draw either a brown or green candy is
.4
Scenario 5-2 The probability that you do not draw a red candy is
.8
Scenario 6-6 The probability that X = 1.5 is
0
This is a standard deviation contest. Which of the following sets of four numbers has the largest possible standard deviation?
0, 0, 10, 10
Based on this dotplot, which of the following is the best estimate of the probability of drawing 3 or fewer white marbles (out of 15) from the jar?
0.035
Event A has probability 0.4. Event B has probability 0.5. If A and B are independent, then the probability that both events occur is
0.2
Scenario 5-9 What is the probability that the person said "yes", given that she is a woman?
0.20
Scenario 5-8 Find P(B | F) and write in words what this expression represents.
0.30; The probability the student ate breakfast, given she is female.
Scenario 5-8 What is the probability that the student had breakfast?
0.50
Suppose that A and B are independent events with P(A) = 0.2 and P(B) = 0.4. P(A U B) is:
0.52
Scenario 6-3 Which of the following is the standard deviation of X?
0.6325
Scenario 5-10 Find the value of P(A U B) and describe it in words.
0.6; The probability that the student takes either chemistry or Spanish, or both.
Scenario 6-3 Which of the following is the mean of X?
1
Let X be the outcome of rolling a fair six-sided die. P(2 < X < 5)
1/2
Scenario 5-4 The probability that you score 4 points both times is
1/36
Scenario 6-6 The probability that X is at least 1.5 is
1/4
Section 4-8 The experimental units are
100 adult volunteers
Question about the stem plot: To which of the following data sets does the stem plot correspond?
116, 118, 121, 124, 128, 133, 137, 142, 146, 179
Question about the stem plot: The median point for this class is
130.5
About acceptance rate: What percent of the schools have an acceptance rate of less than 20%?
16%
Based on this box plot, the five-number summary is
28, 39, 48, 60.5, 77
The standard deviation of 16 measurements of people's weights (in pounds) is computed to be 5.4. The variance of these measurements is
29.16
In a certain town, 60% of the households have fiber optic internet access, 30% have at least one high-definition television, and 20% have both. The proportion of households that have neither fiber optic internet or high-definition television is:
30%
About acceptance rate: What interval contains fewer than half of all the observations?
30% _<acceptance rate< 45%
Scenario 5-11 What is the probability that the student chosen is left-handed or prefers to communicate with friends in person?
34/200 + 85/200 - 13/200 = 0.53
A description of different houses on the market includes the following variables. Which of these variables is quantitative?
All of the above
Graph about amount of money: The histogram
All of the above
Scenario 4-3 The simple random sample is
Bechhofer, Taylor, Weiss
Scenario 3-2 Which country is represented by the clear triangle in the scatterplot?
Canada
A survey records many variables of interest to the researchers conducting the survey. Which of the following variables, from a survey conducted by the U.S. Postal Service, is categorical?
County of residence
Scenario 3-7 Which of the following statements is a correct interpretation of the slope of the regression line?
For each 1-unit increase in the calorie content, the predicted protein content increases by 0.063 gram.
A basketball player makes 2/3 of his free throws. To simulate a single free throw, which of the following assignments of digits to making a free throw are appropriate? I. 0 and 1 correspond to making the free throw and 2 corresponds to missing the free throw. II. 01, 02, 03, 04, 05, 06, 07, and 08, correspond to making the free throw and 09, 10, 11, and 12 correspond to missing the free throw. III. Use a die and let 1, 2, 3, and 4 correspond to making a free throw while 5 and 6 correspond to missing a free throw.
I, II, III
Scenario 3-1 Which of the following statements are supported by the scatterplot? I. There is a positive association between height and volume. II. There is an outlier in the plot. III. As the height of a cherry tree increases, the volume of useable lumber it yields increases.
I, II, and III
Which of the following is true about the least-squares regression line? I. The slope is the predicted change in the response variable associated with a unit increase in the explanatory variable. II. The line always passes through the point, (x,y), the means of the explanatory and response variables, respectively. III. It is the line that minimizes the sum of the squared residuals.
I, II, and III are all true
Which of the following statements about influential points and outliers are true? I. An influential point always has a high residual. II. Outliers are always influential points. III. Removing an influential point always causes a marked change in either the correlation, the regression equation, or both.
III only
Scenario 4-2 The sample is
The 1347 teachers who mail back the questionnaire.
Which of the following random variables should be considered continuous?
The time it takes for a randomly chosen woman to run 100 meters
A study of child development measures the age (in months) at which a child begins to talk and also the child's score on an ability test given several years later. The study asks whether the age at which a child talks helps predict the later test score. The lease-squares regression line of test score y on age x is y= 110-1.3x. According to this regression line, what happens (on the average) to children who talk one month later than other children?
Their predicted test scores go down 1.3 points.
A stratified random sample addresses the same issues as which of the following experimental designs?
a block design
Scenario 4-7 If the farmer had fed Kent pellets to an SRS of 5 pigs from litter A and an SRS of five pigs from litter B, with the remaining 10 pigs getting Moormans pellets, then he would have been using
a block design
In order to assess the opinion of students at the University of Minnesota on campus snow removal, a reporter for the student newspaper interviews the first 12 students he meets. The method of sampling used is
a convenience sample
The essential difference between an experiment and an observational study is that
an experiment imposes treatments on the subjects, but an observational study does not
Which of the following is not a major principle of good design for all experiments?
blocking
A marine biologist wants to estimate the mean size of the barnacle Semibalanus balnoides on a stretch of rocky shoreline. To do so, he randomly selected twenty 10-cm square plots and measured the size of each barnacle in each plot. This is an example of
cluster sampling
Scenario 4-7 The feed they get is not the only factor affecting the rate at which pigs gain weight. Genetic differences also affect weight gain. It is likely that the pigs in litter A are genetically different from the pigs in litter B, since the two litters have different mothers. Since the farmer is only interested in determining which brand of pellets is better, the study suffers from
confounding
Scenario 3-2 The scatterplot shows that
countries that drink more wine have lower death rates from heart disease
Scenario 4-7 The farmer has conducted a(n)
experiment; but not a completely randomized experiment
The most important advantage of experiments over observational studies is that
experiments can give better evidence of causation
Scenario 3-4 In the scatterplot, the point indicated by the open circle is an outlier.
has a negative value for the residual
Event A occurs with occurs with probability 0.8. The conditional probability that event B occurs, given that A occurs, is 0.5. The probability that both A and B occur
is 0.4
The mean age of five people in a room is 30 years. One of the people, whose age is 50 years, leaves the room. The mean age of the remaining four people in the room
is 25
Two variables are said to be negatively associated if
larger values of one variable are associated with smaller values of the other
Are dogs better at tracking the movement of white objects or red objects? Fifteen experienced "disk dogs" who have been trained to catch flying disks in mid-air are given the chance to catch a bright red disk or a plain white disk. Each disk is thrown 10 times for each dog, with the sequence of disks (red or white) determined randomly. The proportion of red disks caught to the proportion of white disks caught is compared for each dog. This is an example of
matched pairs design
Based on this pie chart, we may conclude that
more than half of the cars in the study were from the United States
Simple Random Sampling
none of the above
Which of these statements about the table of random digits is true?
none of these is true
Scenario 3-2 The correlation between wine consumption and heart disease deaths is one of the following values. From the scatterplot, which must it be?
r = -0.84
Scenario 3-1 If the data point (65,70) were removed from this study, how would the value of the correlation (r) change?
r would be larger, since this point does not fall in the pattern of the rest of the data
Scenario 3-3 If the stopping distance were measured in meters rather than feet ( 1 meter = approx. 3.28 feet), how would the correlation (r) change?
r would not change, since the calculation of r does not depend on the units used.
A reporter wishes to portray baseball players as overpaid. Which measure of center should he report as the average salary of major league players?
the mean
The least-squares regression line is fit to a set of data. If one of the data points has a positive residual, then
the point must lie above the least-squares regression line
If I toss a coin 5000 times
the proportions of heads will be close to 0.5
A 1992 Roper poll found that 22% of Americans say that the Holocaust may not have happened. The actual question asked in the poll was "Does it seem possible to you that the Nazi extermination of the Jews never happened?" and 22% responded possible. The results of this poll cannot be trusted because
the question is worded in a confusing manner