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Test 3 Statistics
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1. One student drank 9 beers. You see from the scatterplot that his BAC was about
A)0.20. B)5. C)7. D)9. E)20.
A) 0.20
The scatterplot above shows
A) a moderately strong negative straight-line relationship between number of beers
and BAC.
B) a weak negative straight-line relationship between number of beers and BAC.
C) almost no relationship between number of beers and BAC.
D) a weak positive straight-line relationship between number of beers and BAC.
E) a moderately strong positive straight-line relationship between number of beers
and BAC.
E) a moderately strong positive straight-line relationship between number of beers
and BAC.
A plausible value of the correlation between number of beers and blood alcohol content, based on the scatterplot, is
A) r=-0.85. B) r=-0.3. C) rcloseto0. D) r=0.3. E) r=0.85.
E) r=0.85.
A study of grade school children finds that the correlation between hours of television watched per week during a school year and reading scores is r = -0.63. This tells us that
A) an arithmetic error was made because the correlation must be greater than 0.
B) children who watch more television tend to get higher reading scores.
C) children who watch more television tend to get lower reading scores.
D) there is almost no connection between television viewing and reading scores.
C) children who watch more television tend to get lower reading scores.
Just by looking at the data (don't do a calculation) you can see that the correlation between house size and heating cost is
A) close to zero.
B) clearly positive.
C) clearly negative.
D) not close to zero, but it could be either positive or negative.
E) makes no sense for these data.
B) clearly positive
The name for this kind of graph is a
A) histogram. B) bivariate plot. C) boxplot. D) scatterplot.
D) scatterplot
The IQ score of the student who has the lowest GPA is about A) 103. B) 0.6. C) 72. D) 7.2.
A) 103
The graph shows
A) a clear positive association.
B) very little association.
Ans: A
C) a clear negative association. D) a skewed distribution.
A) a clear positive association.
One of these numbers is the correlation r between IQ score and GPA. Which is it?
A) r=0.02 B) r=0.63 C) r=0.95 D) r=-0.63 E) r=-0.95
B) r=0.63
The correlation coefficient r is
A) 7.6. B) 0.0 C) 1.0. D) -0.6. E) -1.0.
C) 1.0.
Which of these statements is true of the correlation r?
A) r can only take values 0 or greater than 0.
B) r can only take values between -1 and 1, inclusive.
C) r describes only straight-line relationships.
D) Both A and C are correct.
E) Both B and C are correct.
E) Both B and C are correct.
There is a strong straight-line relationship between the outdoor temperature and the amount of energy used to heat a house. Lower temperatures require more energy to keep the house warm. Knowing this, a reasonable value for the correlation coefficient between temperature and home energy consumption is
A) r=1. B) r=0.8. C) r=0. D) r=-0.8. E) r=-1.
D) r=-0.8.
In a scatterplot of your data,
A) hours of TV news broadcast watching should be on the horizontal axis.
B) grade point average should be on the horizontal axis.
C) it makes no difference which is horizontal.
D) a scatterplot is not an appropriate type of graph for these data.
A) hours of TV news broadcast watching should be on the horizontal axis.
The plot of the data in the preceding question shows that students who watch more TV news broadcast watching tend to have higher grade indexes. You calculate the correlation r between hours of TV and grade point average. A plausible value is
A) r=-1. B) r=-0.4. C) r=0. D) r=0.4.
D) r=0.4.
Which of the following pairs of variables is most likely to show a negative correlation?
A) A person's income and her years of education
B) A car's weight and its gas mileage (miles per gallon)
C) A student's grade point average and his IQ score
D) A man's height and his income
B) A car's weight and its gas mileage (miles per gallon)
Which of the following pairs of variables is most likely to show a positive correlation?
A) Outside temperature and expense to heat home
B) Running speed and time to complete a race
C) Number of hours studying for a test and score on the test
D) Number of times a pencil is sharpened and its length
C) Number of hours studying for a test and score on the test
What can we say about the relationship between a correlation r and the slope b of the least-squares line for the same set of data?
A) r is always larger than b.
B) r and b always have the same sign (+ or -).
C) b is always larger than r.
D) b and r are measured in the same units.
E) Both C and D are correct.
B) r and b always have the same sign (+ or -).
The correlation between two variables x and y is 0.5. If we used a regression line to predict y using x, what percent of the variation in y would be explained?
A) 50% B) 25% C) 2.23% D) 75% E) 70.7%
B) 25%
If the least-squares regression line for predicting y from x is y = 500 - 20x, what is the predicted value of y when x = 10?
A) 300 B) 500 C) 4800 D) 700 E) 20
A) 300
One uses _________ to predict the value of a response variable for a given value of an explanatory variable.
A) correlation B) standard deviation C) association D) regression
D) regression
Suppose that the least-squares regression line for predicting y from x is y = 100 + 1.3x. Which of the following is a possible value for the correlation between x and y?
A) 1.3 B) -1.3 C) 0 D) -0.5 E) 0.5
E) 0.5
Deaths from highway accidents went down after the adoption of a national 55 mile-per- hour speed limit. Can we be confident that the lower speed limit caused the drop in deaths?
A) Yes, because the study was a randomized, comparative experiment.
B) No, because the effect of lower speed limits is confounded with the effect of better highways and safer cars.
C) Yes, because a drop in deaths over several years can't happen just by chance.
D) No, because of the placebo effect.
E) Yes, because correlation implies causation.
B) No, because the effect of lower speed limits is confounded with the effect of better highways and safer cars.
Suppose the textbook for your statistics course has 642 pages, how much would you predict it would cost new from the campus bookstore?
A) $24,498.72 D) $77.04
B) $24,421.80 E) None of the above
C) $115.08
C) $115.08
We can see from the equation of the line that, as the number of pages x goes up,
A) price y goes up, because the slope 38.04 is positive.
B) price y goes up, because the slope 0.12 is positive.
C) price y goes down because the slope 38.04 is less than 642.
D) price y goes down, because the slope 0.12 is less than 642.
B) price y goes up, because the slope 0.12 is positive.
You randomly choose one of them to attend a basketball game with you. What is the probability that you choose Quint?
A) 0.5(either he is chosen or he isn't). B) 5 C)0.2 D) 0 E) 1
C)0.2
You randomly choose one of them to attend a basketball game with you. What is the probability that you choose a friend whose name starts with the letter "M"?
A) 2 B) 1/2 C)2/3 D) 2/5 E) 3/5
D) 2/5
You randomly choose four of them to attend a basketball game with you. What is the probability that you choose at least one friend whose name starts with the letter "M"? A) 4 B) 1/4 C)1/5 D) 4/5 E) 1
E) 1
About 34% of people are expected to be infected by the flu this season. What is the risk that a randomly selected person will be infected by the flu?
A) 34 B) 0.34 C) 0.66 D) 66 E) 1 divided by the population size
B) 0.34
The probability that the sum is 7 when you roll two dice is 1/6; the probability that the sum is 11 is 1/18. Suppose you play a game where you win if the sum is 7 or 11. What is the probability that you win?
A) 2/6 B) 2/18 C) 7/6 D) 2/9 E) 2/24
D) 2/9
Only 20 of a sample of 275 students say they are vegetarians. Of these, nine eat both
fish and eggs, three eat eggs but not fish, and eight eat neither. If we choose one of those 275 students at random and the chosen student turns out to be a vegetarian, what is the probability that the chosen student eats neither fish nor eggs?
A) 8/275 B) 20/275 C) 8/20 D) 0.5 E) 1
C) 8/20
Suppose a sorority is selling 500 raffle tickets to raise money for a local charity. You
are going to be the first person to purchase any of the tickets. What is the smallest number of tickets you need to purchase to ensure that your probability of winning is greater than anyone else's probability of winning?
A) 251 B) 250 C) 500 D) 0.5 E) 2
A) 251
What is your expected net result, in dollars, per play?
A) -$8 B) -$1.78 C) $0 D) $1.78 E) $8
C) $0
This is a legitimate assignment of probabilities because it satisfies these rules:
A) all the probabilities are between 0 and 1.
B) all the probabilities are between -1 and 1.
C) the sum of all the probabilities is exactly 1.
D) Both (A) and (C).
E) Both (B) and (C).
D) Both (A) and (C).
What is the probability that a randomly chosen household owns fewer than two televisions?
A) 0.18 B) 0.28 C) 0.46 D) 0.54 E) 0.82
D) 0.54
Suppose a sorority sells 500 raffle tickets to raise money for a local charity. You
purchase 17 of the tickets. If the winning ticket is chosen at random, what is the probability that one of your tickets is chosen as the winning ticket?
A) 0.17 B) 0.017 C) 0.034 D) 0.500 E) 0.002
C) 0.034
Suppose Scott and Jennifer each rolls a sum of 9 on their first rolls. What is the probability that Quint will have a greater sum on his first roll?
A) 0 B) 1/6 C) 1/12 D) 5/18 E) 1
B) 1/6
An experiment has four possible outcomes: A, B, C, and D. Which of the following is a legitimate assignment of probabilities for these four events?
B) 0.3, 0.3, 0.3, 0.1
B) 0.3, 0.3, 0.3, 0.1
What is the expected value of the number of children a randomly chosen woman has had?
A) 1.00 B) 1.02 C) 1.42 D) 2.27 E) 2.5
B) 1.02
What is the expected sum when rolling two dice?
A) 6 B) 7 C) 6.5 D) 6/36 E) 42/36
B) 7
Suppose you pay $5 to roll the two dice, and you'll win a dollar amount equal to the sum of the two dice. What is your expected profit for this game?
A) $2 B) $5 C) $4 D) $6.50 E) $7
A) $2
Suppose that the sample space is S= {a, b, c, d, e, f, g, h, i, j} and outcomes are equally likely. Find the probability of the event A = "a vowel".
A. 0.2 B. 0.3 C. 0.22 D. 0.33
B) 0.3
If P (A) = 0.5, P(B) = 0.4, and P (A B) = 0.7, find P (A B).
A. 0.7 B. 0.1 C. 0.2 D. 0.9
C) 0.2
SupposethatAandBaretwoevents,P(A)=0.20,P(B)=0.05,P(A B)=0.02.Whatis P(A|B)?
A. 0.40 B. 0.10 C. 0.03 D. 0.02
A) 0.40
44. Find P (AB) given that P (A) = 0.3, P (B) = 0.5, and events A and B are mutually exclusive.
A. 0.8 B.0 C.0.15 D.0.2
A) 0.8
45. Find P (A B) given that P(A) = 0.5, P (B) = 0.4, and events A and B are independent.
A. 0.1 B.0 C.0.2 D.0.15
C) 0.2
A medical treatment has a success rate of 0.8. Two patients will be treated with this treatment. Assuming the results are independent for the two patients, what is the probability that neither one of them will be successfully cured?
A. 0.5 B. 0.36 C. 0.64 D. 0.04
D) 0.04
If P(B) = 0.3, P (AB) = 0.4, and P(AB) = 0.5, find P(A).
A. 0.5 B. 0.3 C. 0.6 D. 0.7
C) 0.6
What is your expected net result, in dollars, per play?
A) -$8 B) -$1.78 C) $0 D) $1.50 E) $8
D) $1.50
A six-sided die is made that has four Green sides and two Red sides, all equally likely to land face up when the die is tossed. The die is tossed two times. Which of these sequences (in the order shown) has the highest probability?
A. Green, Red B. Green, Green C. Red, Red D. all are equally likely
B) Green, Green
Suppose that the least-squares regression line for predicting y from x is y = 100 - 1.3x. Which of the following is a possible value for the correlation between x and y?
A) 1.3 B) -1.3 C) 0 D) -0.5 E) 0.5
D) -0.5
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