Download STAT31 Final Exam Fall 2005 December 17, 2005

STAT31 Final Exam
Fall 2005
December 17, 2005
Name:
PID:
Section #:
Instructions:
Fill in the above information. Bubble-in your name, correct PID and sign the honor pledge on the
bubble sheet. Both of the bubble sheet and the question set will be collected.
Each question has only one correct choice (decimals may need rounding). Use "number 2" pencil
only - do not use ink - fill bubble completely. No notes or remarks are accepted - do not tear or fold
the bubble sheet. Choice #5 is NEVER a correct answer.
A grade of zero will be assigned for the entire exam if the bubble sheet is not filled out according to
the above instructions.
There are 35 questions. Each question is worth 1 point.
The exam time is from 8:00AM to 10:00AM.
1. A soft-drink machine can be regulated so that it discharges an average of µ ounces per
cup. If the ounces of fill are normally distributed with a standard deviation of 0.4 oz. what
value should µ be set at so that 6-oz. cups will overflow only 1.5% of the time?
A) 5.13
B) 6.87
C) 5.18
D) 6.00
2. The following quantities are available from a dataset with two variables X and Y:
X = 15, S X = 2, SY = 3. In addition, the intercept and slope of the regression line are
a = 10, b = −.6. What are the correlation r and Y ?
A) -0.4; 1.
B) -0.9; 19
C) -0.4; 19
D) -0.9; 1
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3. If a student got A in Midterm I, she has 0.8 chance of getting A as the final grade; if she
didn't get A in Midterm I, the chance of getting A as the final grade is 0.2. Suppose 1/5 of
the students got A in Midterm I. If Sam did not get A as his final grade in this class, what's
the probability that he got A in Midterm I?
A) 4/5
B) 1/2
C) 1/17
D) 1/5
4. We roll a pair of standard fair dice and observe the total number of dots on the top faces.
Our sample space is S={2,3,4,5,6,7,8,9,10,11,12}. What's the probability that the total
number of dots is more than 8?
A) 11/12
B) 5/18
C) 1/3
D) 5/12
5. A Tar Heel basketball player makes 80% of all his free throw attempts. During each
practice he is going to shot 4 free throws. As a student of STAT 31, you are interested in
finding out the probability for him to hit more than half free throws during the practice.
k
P(X=k)
Entry is P(X=k) where X is binomial with n=4 and p=0.2
0
1
2
3
4
0.4096
0.4096
0.1536
0.0256
0.0016
Utilizing the above binomial table, that probability is
A) 0.9728
B) 0.8192
C) 0.4096
D) 0.0272
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6. A study tries to understand how children grow. The data were obtained by measuring the
heights of 161 children and their corresponding ages. Their average age is 23.5 months,
average height is 79.85 centimeters and the correlation between height and age is 0.9. One
can obtain a least-squares regression line as
Height=64.932+0.6348*Age.
What will be the slope of the regression line if we try to infer a child's age from her height
by setting Height to be the explanatory variable?
A) 1.2760.
B) -0.6348.
C) 1.5577.
D) 1.5753.
7. A stack of four cards contains two red cards and two black cards. I select two cards, one at
a time, and do not replace the first card selected before selecting the second card.
Consider the events
A = the first card selected is black.
B = the second card selected is red.
The events A and B are
A) mutually exclusive.
B) complements.
C) independent.
D) none of the above.
8. X and Y are random variables with σ X2 = 4, σ Y2 = 5, and the correlation between X and Y
is -0.2. Then σ X2 + 2Y is
A) 24
B) 20
C) 9
D) 14
9. Event A occurs with probability 0.4. The conditional probability that A occurs given that
B occurs is 0.7, while the conditional probability that A occurs given that B does not
occur is 0.2. What is P(B|A)?
A) 4/7.
B) 7/10.
C) 0.
D) 5/6.
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10. A college basketball player makes 80% of his free throws. At the end of a game, his team
is losing by two points. He is fouled attempting a three-point shot and is awarded three
free throws. Assuming each free throw is independent, what is the probability that he
loses the game?
A) 0.64
B) 0.104
C) 0.006
D) 0.896
11. "Let’s Make A Deal" is a very popular game show back in the 90’s. A player is given the
choice of three doors. Behind one door is the Grand Prize (a car and a cruise); behind the
other two doors are booby prizes (stinking pigs). The player picks a door, and the host
opens one of the remaining doors. There is a booby prize behind the open door. The host
then offers the player two choices, either to stay with the door that was chosen at the
beginning, or to switch to the remaining closed door.
Susan went to the game show for the first time, and guess what? She was invited to play it
on stage. Her lucky number is 3, so she chose Door 3 to begin with. The host opens Door
1, which contains a REALLY stinking pig.
Since Door 1 is the farthest one away from the host, the lazy host does not open Door 1 as
frequently as Door 2 when Door 3 is selected by the player. A STAT31 student did an
observational study and observed that the probability for the host to open Door 1 is only
1/3 when Door 3 is selected.
Now, given that Door 1 was opened and Susan selected Door 3, what is the probability
that Susan is going to win if she sticks with her choice?
A) ¼
B) ¾
C) 3/8
D) 1/3
12. A television station is interested in predicting whether or not voters in its broadcasting
area are in favor of federal funding for abortions. It asks its viewers to phone in and
indicate whether they are in favor or disfavor of this. Of the 2241 viewers who phoned in,
1574 (70.24%) were opposed to federal funding for abortions. The number 70.24% is
A) a sample.
B) a statistic.
C) a population.
D) a parameter.
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13. Which of the following is not a major principle of experimental design?
A) Replication
B) Randomization
C) Segmentation
D) Controlled experiment
14. Researchers wish to determine if a new experimental medication will reduce the
symptoms of allergy sufferers without the side effect of drowsiness. To investigate this
question, the researchers give the new medication to 50 adult volunteers who suffer from
allergies. Forty four of these volunteers report a significant reduction in their allergy
symptoms without any drowsiness.
This study could be improved by
A) repeating the study with only the 44 volunteers who reported a significant reduction
in their allergy symptoms without any drowsiness, and giving them a higher dosage
this time.
B) using a control group.
C) including people who do not suffer from allergies in the study in order to represent a
more diverse population.
D) all of the above.
15. The six people listed below are enrolled in an on-line statistics course.
1. Castellan 2. Gael 3. Jones 4. Klein 5. Moore 6. Saunter
This class list is to be randomly divided into two groups of three students each for a group
project. Use the list of random digits below to randomly select the names of the three
students who will form the first group. The remaining students will comprise group 2.
Start at the beginning of the list and use the numerical labels attached to the names.
27102 56027 55892 33063 41842 81868 71035 09001 43367 49497 54580 81507
How are the two groups made up?
A) Group 1: Gael, Castellan, Gael.
B) Group 1: 2, 7, 1.
C) Group 1: Gael, Moore, Saunter.
D) Group 1: Gael, Castellan, Moore.
Group 2: Moore, Jones, Klein.
Group 2: 5, 6, 8.
Group 2: Castellan, Jones, Klein.
Group 2: Jones, Klein, Saunter.
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16. On a chilly spring afternoon, 10 lab sections of a statistics class all have full attendance.
The 10 lab sections each have the same number of students enrolled in it. A class
evaluation is about to be administered to some of the students. It has been decided to first
randomly select 3 of the 10 lab sections and then give the evaluation to a simple random
sample of one-fourth of the students in those sections.
A) Convenience sampling.
B) Multistage sampling.
C) Simple random sampling.
D) Stratified random sampling.
17. Suppose that you are a student worker in the Statistics department and they agree to pay
you using the Random Pay system. Each week the Chair flips a fair coin. If it comes up
head, your pay for the week is $80; if it comes up tail, your pay for the week is $40. Your
friend is working for the Engineering department and makes a flat pay of $60.5 per week.
What is the standard deviation of your weekly pay?
A) 28
B) 784
C) 20
D) 400
18. Use the same information from the previous question. What is the probability that your
total earning in 100 weeks is more than hers?
A) 0.4013
B) 0.5000
C) 0.5987
D) 0.3741
19. An agricultural researcher plants 25 plots with a new variety of corn. A 90% confidence
interval for the average yield for these plots is found to be 162.72 ± 4.47 bushels per acre.
Which of the following would produce a confidence interval with a smaller margin of
error than this 90% confidence interval?
A) Compute a 99% confidence interval rather than a 90% confidence interval. The
increase in confidence indicates that we have a better interval.
B) Plant only five plots rather than 25, because five are easier to manage and control.
C) Plant 100 plots rather than 25.
D) None of the above.
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20. A 90% confidence interval for the mean µ of a population is computed from a random
sample and found to be 9 ± 3. Which of the following could be the 95% confidence
interval based on the same data?
A) 9 ± 4.
B) 9 ± 2.
C) 9 ± 3.
D) Without knowing the sample size, any of the above answers could be the 95%
confidence interval.
21. The time needed for college students to complete a certain paper-and-pencil maze follows
a normal distribution with a mean of 30 seconds and a standard deviation of 3 seconds.
You wish to see if the mean time µ is changed by vigorous exercise, so you have a group
of nine college students exercise vigorously for 30 minutes and then complete the maze.
You compute the average time X that it takes these students to complete the maze and
test the hypotheses
H0: µ = 30, Ha: µ ≠ 30.
You find that the results are significant at the 5% level. You may also conclude
A) the test would also be significant at the 1% level.
B) the test would also be significant at the 10% level.
C) both of the above.
D) none of the above.
22. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures
the motivation, attitude, and study habits of college students Scores range from 0 to 200
and follow (approximately) a normal distribution with mean 115 and standard deviation σ
= 25. You suspect that incoming freshmen have a mean µ, which is different from 115
because they are often excited yet anxious about entering college. To test your suspicion,
you test the hypotheses
H0: µ = 115, Ha: µ ≠ 115.
You give the SSHA to 25 students who are incoming freshmen and find their mean score
is 116.2. The p-value of your test is
A) 0.8104
B) 0.1151
C) 0.2302
D) 0.4052
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23. The larger the level of confidence used in constructing a confidence interval of the
population mean,
A) the wider the confidence interval
B) the narrower the confidence interval
C) the smaller the value of zα / 2
D) the smaller the probability that the confidence interval will contain the population
mean
24. In a one-sided test, the p-value is found to be equal to .068. If the test had been two-sided,
the p-value would have been
A) 0.466
B) unknown based on the information given.
C) 0.136
D) 0.034
25. Researchers are studying yield of a crop in two locations. The researchers are going to
compute independent 90% confidence intervals for the mean yield at each location. The
probability that at least one of the intervals will cover the true mean yield at the
corresponding location is
A) 0.19
B) 0.99
C) 0.95
D) 0.81
26. A college basketball player makes 80% of his free throws. Over the course of the season,
he will attempt 100 free throws. Assuming free-throw attempts are independent, what is
the probability that he makes at least 90 of these attempts? (use normal approximation
with no continuity correction)
A) 0.0122
B) 0.0043
C) 0.0062
D) 0.0087
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27. Which of the following statements is true about confidence interval and accuracy?
A) The bigger the confidence level, the less confident you are with a confidence interval
and the less accurate the interval is.
B) The smaller the confidence level, the more confident you are with a confidence
interval and the more accurate the interval is.
C) The bigger the confidence level, the more confident you are with a confidence
interval but the less accurate the interval is.
D) The smaller the confidence level, the more confident you are with a confidence
interval but the less accurate the interval is.
28. A fair coin (one for which both the probability of heads and the probability of tails are 0.5)
is tossed six times. The probability that less than 1/3 of the tosses are heads is
A) 0.0043
B) 0.09
C) 0.33
D) 0.109
29. A multiple choice exam has 100 questions, each with five possible answers. If a student is
just guessing at all the answers, the probability that he gets more than 30 correct is (use
the continuity correction)
A) 0.0043
B) 0.1020
C) 0.3100
D) 0.0087
30. In a test of statistical hypotheses, the p-value tells us
A) the largest level of significance at which the null hypothesis can be rejected.
B) the smallest level of significance at which the null hypothesis can be rejected.
C) if the alternative hypothesis is true.
D) if the null hypothesis is true.
31. In order to determine the p-value, which of the following is not needed?
A) The value of the test statistic
B) The level of significance
C) Whether the test is one or two sided
D) All of the above are needed
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32. A certain population follows a normal distribution with mean µ and standard deviation σ
= 2.5. You collect data and test the hypotheses
H0: µ = 1, Ha: µ ≠1.
You obtain a P-value of 0.022. Which of the following is true?
A) A 99% confidence interval for µ will include the value 1.
B) A 95% confidence interval for µ will include the value 1.
C) A 99% confidence interval for µ will include the value 0.
D) A 95% confidence interval for µ will include the value 0.
33. Two peasants plant two different varieties of corn. Peasant A plants 25 plots with Corn A
and Peasant B plants 16 plots with Corn B. In general, the yield per plot (in bushels) for
Corn A has an N(150, 50) distribution while the yield per plot for Corn B has an N(140,
40) distribution. They have agreed to enter a competition based on the average yield per
plot at the end of the year. What is the probability that Peasant A wins?
A) Close to 0.2611
B) Close to 0.2389
C) About 0.7611
D) About 0.7389
34. A random sample of size 25 is to be taken from a population that is normally distributed
with mean 60 and standard deviation 10. The number X of the observations in our sample
that are larger than 70 is to be computed. The sampling distribution of X is
A) binomial with n=25 and p=0.16.
B) normal with mean 60 and standard deviation 10.
C) binomial with n=25 and p=0.5.
D) normal with mean 60 and standard deviation 2.
35. The weights of extra large eggs have a normal distribution with a mean of 1 oz. and a
standard deviation of 0.1 oz. The probability that a dozen eggs weighs more than 13 oz. is
approximately
A) 0.2033
B) 0.0000
C) 0.0020
D) 0.1814
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Answer Key
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35.
A
A
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B
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D
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B
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B
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A
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B
A
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B
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C
D
A
B
B
A
C
A
C
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