Stats
1. What is the probability that a randomly selected attendee graduated in 1998 and went into the military?
College Job Military Other
1968 56 73 85 7
1998 173 62 37 20
(A) 0.072
(B) 0.127
(C) 0.303
(D) 0.596
(E) 0.669
On the SAT, there are five answer choices (A, B, C, D, and E). The probability of randomly
guessing the correct answer is .2.
a) What is the probability that on a 25-question section of the SAT by complete random
guessing that exactly 8 questions will be answered correctly?
Answer is Binompdf(25,.2,8)=.0623
Suppose there is a correlation of r = 0.9 between number of hours per day
students study and GPAs. Which of the following is a reasonable conclusion?
(A) 90% of students who study receive high grades.
(B) 90% of students who receive high grades study a lot.
(C) 90% of the variation in GPAs can be explained by variation in number of
study hours.
(D) 10% of the variation in GPAs cannot be explained by variation in number
of study hours per day.
(E) 81% of the variation in GPAs can be explained by variation in number of
study hours per day.
(E) 81% of the variation in GPAs can be explained by variation in number of study hours per day.
A fair die is rolled 3 times. The first 2 rolls resulted in 2 fives. What is the probability of not rolling 5 on the next roll?
(A) 1
(B) 5/6
(C) (3C1) (1/6)^2 (5/6)^2
(D) (1/6)^2 (5/6)
(E) 0
Major universities claim that 72% of their senior athletes graduate that year. Fifty senior athletic
students attending major universities are randomly selected and recorded in order of selection.
What is the standard deviation of senior athletics students graduating that year?
Answer is Radical (50)(.72)(.28)= 3.174
The American Medical Association (AMA) wishes to determine the percentage
of obstetricians who are considering leaving the profession because of the rapidly
increasing number of lawsuits against obstetricians. How large a sample should
be taken to find the answer to within ±3% at the 95% confidence level?
(A) 6
(B) 33
(C) 534
(D) 752
(E) 1068
(E) 1068
A plumbing contractor obtains 60% of her boiler circulators from a company whose defect rate is 0.005 and the rest from a company whose defect rate is 0.010. What proportion of the circulators can be expected to be defective? If a circulator is defective, what is the probability that it came from the first company?
A) .0070, .429
B) .0070, .600
C) .0075, .500
D) .0075, .600
E) .0150, .571
A) .0070, .429
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
A. 1/2
B. 2/5
C. 8/15
D. 9/20
P(E) = n(E)/n(S) = 9/20.
D. 9/20
Which of the following statements about the correlation coefficient are true?
I. The correlation coefficient and the slope of the regression line may have
opposite signs.
II. A correlation of 1 indicates a perfect cause-and-effect relationship between
the variables.
III. Correlations of +.87 and −.87 indicate the same degree of clustering around
the regression line.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
(C) III only
Suppose 4% of the population have a certain disease. A laboratory blood test gives a positive reading for 95% of people who have the disease and for 5% of people who do not have the disease. What is the probability of testing positive? If a person tests positive, what is the probability the person has the disease?
A) .086, .442
B) .086, .500
C) .086, .914
D) .500, .950
E) .914, .950
A) .086, .442
In one state, 52% of the voters are Republicans, and 48% are Democrats. In a second state, 47% of the voters are Republicans, and 53% are Democrats. Suppose a simple random sample of 100 voters are surveyed from each state.
What is the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state
(A) 0.04
(B) 0.05
(C) 0.24
(D) 0.71
(E) 0.76
(C) 0.24
A plumbing contractor obtains 60% of her boiler circulators from a company
whose defect rate is 0.005, and the rest from a company whose defect rate is
0.010. What proportion of the circulators can be expected to be defective?
If a circulator is defective, what is the probability that it came from the first
company?
(A) .0070, .429
(B) .0070, .600
(C) .0075, .500
(D) .0075, .600
(E) .0150, .571
(A) .0070, .429
In a litter of eight puppies, 5 are female. 2 of the puppies are picked at random.
Which of the following is true?
(A) The probability that both puppies are female is (2/5)^2
(B) The probability that both puppies are female is (5/8)^2
(C) The probability that both puppies are female is (5/8)(4/7)
(D) The expected number of female puppies is 1.25
(E) The situation can be described by a binomial model.
(C) The probability that both puppies are female is (5/8)(4/7)
Which of the following statements are true?
I. A completely randomized design offers no control for lurking variables.
II. A randomized block design controls for the placebo effect.
III. In a matched pairs design, participants within each pair receive the same treatment.
(A) I only
(B) II only
(C) III only
(D) All of the above.
(E) None of the above.
(E) None of the above.
Both over-the-counter niacin and the prescription drug Lipitor are known to
lower blood cholesterol levels. In one double-blind study Lipitor outperformed
niacin. The 95% confidence interval estimate of the difference in mean cholesterol
level lowering was (18, 41). Which of the following is a reasonable conclusion?
(A) Niacin lowers cholesterol an average of 18 points, while Lipitor lowers cholesterol
an average of 41 points.
(B) There is a .95 probability that Lipitor will outperform niacin in lowering
the cholesterol level of any given individual.
(C) There is a .95 probability that Lipitor will outperform niacin by at least 23
points in lowering the cholesterol level of any given individual.
(D) We should be 95% confident that Lipitor will outperform niacin as a
cholesterol-lowering drug.
(E) None of the above.
(E) None of the above.