Multiple Choice: Each is worth two points
Identify the letter of the choice that best completes the statement or answers the question.
____ 1. The sample statistic s is the point estimator of a.
 b.
 c. d.
____ 2. A sample statistic is an unbiased estimator of the population parameter if a. the expected value of the sample statistic is equal to zero b. the expected value of the sample statistic is equal to one c. the expected value of the sample statistic is equal to the population parameter d. it is equal to zero
____ 3. A property of a point estimator that occurs whenever larger sample sizes tend to provide point estimates closer to the population parameter is known as a. efficiency b. unbiased sampling c. consistency d. relative estimation
____ 4. A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. In this problem the 0.22 is a. a parameter b. a statistic c. the standard error of the mean d. the average content of colognes in the long run
____ 5. A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately a. normal because is always approximately normally distributed b. normal because the sample size is small in comparison to the population size c. normal because of the central limit theorem d. None of these alternatives is correct.
____ 6. As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution a. becomes larger b. becomes smaller c. stays the same d. None of these alternatives is correct.
____ 7. From a population of 200 elements, a sample of 49 elements is selected. It is determined that the sample mean is 56 and the sample standard deviation is 14. The standard error of the mean is a. 3 b. 2 c. greater than 2 d. less than 2
1

____ 8. Which of the following is(are) point estimator(s)? a.
 b.
 c. s d.

____ 9. A population characteristic, such as a population mean, is called a. a statistic b. a parameter c. a sample d. the mean deviation
____ 10. The sample statistic, such as , s, or , that provides the point estimate of the population parameter is known as a. a point estimator b. a parameter c. a population parameter d. a population statistic
____ 11. The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on the a. central limit theorem b. fact that we have tables of areas for the normal distribution c. assumption that the population has a normal distribution d. None of these alternatives is correct.
____ 12. Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The mean and the standard deviation of the sampling distribution of the sample means are a. 8.7 and 1.94 b. 36 and 1.94 c. 36 and 1.86 d. 36 and 8
____ 13. When constructing a confidence interval for the population mean and a small sample is used, the degrees of freedom for the t distribution equals a. n-1 b. n c. 29 d. 30
_____ 14. The collection of all possible sample points in an experiment is a. the sample space b. c. d. a sample point an experiment the population
_____ 15. Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there? a. b.
20
7 c. d.
5!
10
_____ 16. The “Top Three” at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many “Top Three” outcomes are there?
2

a. b. c. d.
302,400
720
1,814,400
10
_____ 17. Given that event E has a probability of 0.25, the probability of the complement of event E a. cannot be determined with the above information b. c. can have any value between zero and one must be 0.75 d. is 0.25
_____ 18. The symbol

shows the a. b. union of events intersection of events c. sum of the probabilities of events d. sample space
_____ 19. If P(A) = 0.38, P(B) = 0.83, and P(A

B) = 0.57; then P(A

B) = a. b. c. d.
1.21
0.64
0.78
1.78
_____ 20. If P(A) = 0.62, P(B) = 0.47, and P(A

B) = 0.88; then P(A

B) = a. b. c. d.
0.2914
1.9700
0.6700
0.2100
_____ 21. If P(A) = 0.85, P(A

B) = 0.72, and P(A

B) = 0.66, then P(B) = a. b. c. d.
0.15
0.53
0.28
0.15
_____ 22. Two events are mutually exclusive if a. b. the probability of their intersection is 1 they have no sample points in common c.
d. the probability of their intersection is 0.5 the probability of their intersection is 1 and they have no sample points in common
_____ 23. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then
P(A

B) = a. b. c. d.
0.30
0.15
0.00
0.20
_____ 24. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then
P(A

B) =
3

a. b. c. d.
0.00
0.15
0.8
0.2
_____ 25. A subset of a population selected to represent the population is a a. b. c. d. subset sample small population
None of the alternative answers is correct.
_____ 26. A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have a. the same probability of being selected b. c. a probability of 1/ n of being selected a probability of 1/ N of being selected d. a probability of N / n of being selected
_____ 27. A probability distribution for all possible values of a sample statistic is known as a a. b. c. d. sample statistic parameter simple random sample sampling distribution
_____ 28. From a population of 200 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard a. 3 b. c.
2 greater than 2 error of the mean is d. less than 2
_____ 29. From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately a. b. c. d.
1.1022
2
30
1.4847
Solutions to MC Problems
1. ANS: B
2. ANS: C
3. ANS: C
4. ANS: A
5. ANS: C
6. ANS: B
7. ANS: D
8. ANS: C
9. ANS: B
10. ANS: A
11. ANS: A
4

12. ANS: C
13. ANS: A
14. ANS: A
15. ANS: D
16. ANS: B
17. ANS: C
18. ANS: A
19. ANS: B
20. ANS: D
21. ANS: B
22. ANS: B
23. ANS: C
24. ANS: C
25. ANS: B
26. ANS: A
27. ANS: D
28. ANS: D
29. ANS: D
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Short Answer/Problems
Directions : Clearly designate your solution to each portion of the questions asked and show your entire work and method for arriving at the solution.
1. The sales records of a real estate agency show the following sales over the past 200 days:
# Houses
Sold
0
1
Number of
Days
60
80
2
3
40
16
4 a. b. c.
4
How many sample points are there?
Assign probabilities to the sample points and show their values.
What is the probability that the agency will not sell any houses in a given day? d. e.
What is the probability of selling at least 2 houses?
What is the probability of selling 1 or 2 houses? f. What is the probability of selling less than 3 houses?
ANSWERS: a. b.
5
Houses Sold Probability
0
1
2
3
0.30
0.40
0.20
0.08
4 c. d. e. f.
0.3
0.3
0.6
0.9
0.02
2. Assume two events A and B are mutually exclusive and, furthermore, P(A) = 0.2 and P(B) = 0.4. a. Find P(A

B).
b. Find P(A

B).
c. Find P(A

B).
ANSWERS: a. b. c.
0.0
0.6
0.0
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3.You are given the following information on Events A, B, C, and D. P(A) = .4, P(B) = .2, P(C) = .1,
P(A

D) = .6, P(A

B) = .3, P(A

C) = .04, P(A

D) = .03
a. b. c.
Compute P(D).
Compute P(A

B).
Compute P(A

C).
d. e. f.
Compute the probability of the complement of C.
Are A and B mutually exclusive? Explain your answer.
Are A and B independent? Explain your answer. g. h.
Are A and C mutually exclusive? Explain your answer.
Are A and C independent? Explain your answer.
ANSWERS: a. b. c. d. e. f. g. h.
0.23
0.06
0.4
0.9
No, P(A

B)

0
No, P(A

No, P(A

B)

C)
P(A)

0
Yes, P(A

C) = P(A)
4. Consider a population of five weights identical in appearance but weighing 1, 3, 5, 7, and 9 ounces. a. b.
Determine the mean and the variance of the population.
Sampling without replacement from the above population with a sample size of 2 produces ten possible samples. Using the ten sample mean values, determine the mean of the population and the variance of . c. Compute the standard error of the mean.
ANSWERS: a. b. c.
5 and 8
5 and 3
1.732
5. A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? b. What is the probability that these 64 students will spend a combined total of more than $715.21? c. What is the probability that these 64 students will spend a combined total between
$703.59 and $728.45?
ANSWERS: a. 10.5 0.363 normal b. c.
0.0314
0.0794
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