# 商务统计习题

Practice Test 1 Business Statistics:

Multiple Choice: Each is worth two points

Identify the letter of the choice that best completes the statement or answers the question.

**Skip 15-17,18,20 Ch10-12,13 Material

____ 1. The sum of the relative frequencies for all classes will always equal

a. the sample size

b. the number of classes

c. one

d. any value larger than one

____ 2. The interquartile range is

a. the 50th percentile

b. another name for the variance

c. the difference between the largest and smallest values

d. the difference between the third quartile and the first quartile

____ 3. The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals

a. 8

b. 10

c. 6400

d. 4,096

____ 4. The numerical value of the standard deviation can never be

a. larger than the variance

b. zero

c. negative

d. smaller than the variance

____ 5. The set of all possible sample points (experimental outcomes) is called

a. a sample

b. an event

c. the sample space

d. a population

____ 6. A random variable that can assume only a finite number of values is referred to as a(n)

a. infinite sequence

b. finite sequence

c. discrete random variable

d. discrete probability function

Exhibit 5-11

A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown

below:

Number of

Breakdowns Probability

0 0.12

1 0.38

2 0.25

3 0.18

4 0.07

____ 7. Refer to Exhibit 5-11. The probability of at least 3 breakdowns in a month is

a. 0.5

b. 0.10

c. 0.30

d. 0.90

____ 8. A normal probability distribution

a. is a continuous probability distribution

b. is a discrete probability distribution

c. can be either continuous or discrete

d. must have a standard deviation of 1

Exhibit 6-6

The starting salaries of individuals with an MBA degree are normally distributed with a mean of \$40,000 and a standard deviat ion

of \$5,000.

____ 9. Refer to Exhibit 6-6. What percentage of MBA's will have starting salaries of \$34,000 to \$46,000?

a. 38.49%

b. 38.59%

c. 50%

d. 76.98%

____ 10. Given that Z is a standard normal random variable, what is the value of Z if the area between -Z and Z is 0.901?

a. 1.96

b. -1.96

c. 0.4505

d. ±1.65

____ 11. Which of the following is not a measure of central location?

a. mean

b. median

c. variance

d. mode

____ 12. The descriptive measure of dispersion that is based on the concept of a deviation about the mean is

a. the range

b. the interquartile range

c. the absolute value of the range

d. the standard deviation

____ 13. Which of the following symbols represents the mean of the population?

a. σ2

b. σ

c. μ

d. ____ 14. Which of the following symbols represents the size of the sample

a. σ2

b. σ

c. N

d. n

____ 15. If two events are independent, then

a. they must be mutually exclusive

b. the sum of their probabilities must be equal to one

c. their intersection must be zero

d. None of these alternatives is correct..

____ 16. Which of the following statements is(are) always true?

a. -1 ≤ P(E i) ≤1

b. P(A) = 1 - P(A c)

c. P(A) + P(B) = 1

d. ∑P ≥ 1

____ 17. A measure of the average value of a random variable is called a(n)

a. variance

b. standard deviation

c. expected value

d. coefficient of variation

____ 18. Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

a. 0.2592

b. 0.0142

c. 0.9588

d. 0.7408

____ 19. The expected value of a discrete random variable

a. is the most likely or highest probability value for the random variable

b. will always be one of the values x can take on, although it may not be the highest probability value for

the random variable

c. is the average value for the random variable over many repeats of the experiment

d. None of these alternatives is correct.

____ 20. Which of the following is not a property of a binomial experiment?

a. the experiment consists of a sequence of n identical trials

b. each outcome can be referred to as a success or a failure

c. the probabilities of the two outcomes can change from one trial to the next

d. the trials are independent

Exhibit 5-9

The probability distribution for the daily sales at Michael's Co. is given below.

Daily Sales

(In \$1,000s) Probability

40 0.1

50 0.4

60 0.3

70 0.2

____ 21. Refer to Exhibit 5-9. The expected daily sales are

a. \$55,000

b. \$56,000

c. \$50,000

d. \$70,000

____ 22. For a standard normal distribution, the probability of z 0 is

a. zero

b. -0.5

c. 0.5

d. one

Exhibit 6-2

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.

____ 23. Refer to Exhibit 6-2. What percent of players weigh between 180 and 220 pounds?

a. 28.81%

b. 0.5762%

c. 0.281%

d. 57.62%

Exhibit 6-6

The starting salaries of individuals with an MBA degree are normally distributed with a mean of \$40,000 and a standard deviat ion

of \$5,000.

____ 24. Refer to Exhibit 6-6. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least \$47,500?

a. 0.4332

b. 0.9332

c. 0.0668

d. 0.5000

Short Answer/Problems

1.The following data represent the daily demand (y in thousands of units) and the unit price (x in dollars) for a product.

Daily Demand (y) Unit Price (x)

47 1

39 3

35 5

44 3

34 6

20 8

15 16

30 6

a. Compute and interpret the sample covariance for the above data.

b. Compute and interpret the sample correlation coefficient.

2.The daily dinner bills in a local restaurant are normally distributed with a mean of \$28 and a standard deviation of \$6.

a. What is the probability that a randomly selected bill will be at least \$39.10?

b. What percentage of the bills will be less than \$16.90?

c. What are the minimum and maximum of the middle 95% of the bills?

d. If twelve of one day's bills had a value of at least \$43.06, how many bills did the restaurant collect on that day?

3.Below you are given a partial computer output based on a sample of 7 observations, relating an independent variable (x) and a dependent

variable (y).

Predictor Coefficient Standard Error

Constant 24.112 8.376

x -0.252 0.253

Analysis of Variance

SOURCE SS

Regression 196.893

Error 94.822

a. Develop the estimated regression line.

b. If you are given that x = 50, find the estimate of y based on your regression equation.

c. Determine the coefficient of determination and interpret your answer.

Solutions to MC

1. ANS:C

2.ANS:D

3.ANS:D

4.ANS:C

5.ANS:C

6.ANS:C

7.ANS:D

8.ANS:A

9. ANS:D10.ANS:D

11. ANS: C12.ANS:D13.ANS: C14.ANS:D15.ANS: D16.ANS:B17.ANS: C18. ANS: B

19. ANS: C20.ANS:C21.ANS: B22.ANS:C23.ANS: D24.ANS:C25.ANS: C26. ANS: A

27. ANS: B28. ANS: D29. ANS: C

Solutions to Short Answer

1. ANS:

a. -47 (rounded). Since the covariance is negative, it indicates a negative relationship between x and y.

b. -0.922. There is a strong negative relationship between x and y.

2. ANS:

a. 0.0322

b. 0.0322

c. minimum = \$16.24 maximum = \$39.06

d. 2,000

3. ANS:

a.

= 24.112 + 0.816x

b.

If x = 50 then = 24.112 + 0.816x 24.1 + 0.82 ( 50 ) = 65.1

c. 0.675 So there is a fairly strong positive relationship between x and y.

Practice Test 2 Business Statistics:

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. μ

b. σ

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

____ 8. Which of the following is(are) point estimator(s)?

a. σ

b. μ

c. s

d. α

____ 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. a sample point

c.an experiment

d. 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. 20

b. 7

c. 5!

d. 10

_____ 16. The “Top Three” at a race track 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?

a. 302,400

b. 720

c. 1,814,400

d. 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. can have any value between zero and one

c. must be 0.75

d. is 0.25

_____ 18. The symbol ? shows the

a.union of events

b. 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. 1.21

b. 0.64

c. 0.78

d. 1.78

_____ 20. If P(A) = 0.62, P(B) = 0.47, and P(A ? B) = 0.88; then P(A ? B) =

a. 0.2914

b. 1.9700

c. 0.6700

d. 0.2100

_____ 21. If P(A) = 0.85, P(A ? B) = 0.72, and P(A ? B) = 0.66, then P(B) =

a. 0.15

b. 0.53

c. 0.28

d. 0.15

_____ 22. Two events are mutually exclusive if

a. the probability of their intersection is 1

b. they have no sample points in common

c. the probability of their intersection is 0.5

d. 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. 0.30

b. 0.15

c. 0.00

d. 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) =

a. 0.00

b. 0.15

c. 0.8

d. 0.2

_____ 25. A subset of a population selected to represent the population is a

a.subset

b.sample

c.small population

d. 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. E ach possible sample should have

a. the same probability of being selected

b. a probability of 1/n of being selected

c. 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.sample statistic

b.parameter

c.simple random sample

d.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 error of the mean is

a. 3

b. 2

c. greater than 2

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. 1.1022

b. 2

c. 30

d. 1.4847

Short Ans wer/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: b. Assign probabilities to the sample points and show their values.

c. What is the probability that the agency will not sell any houses in a given day?

d. What is the probability of selling at least 2 houses?

e. What is the probability of selling 1 or 2 houses?

f. What is the probability of selling less than 3 houses?

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).

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. Compute P(D).

b. Compute P(A ? B).

c. Compute P(A?C).

d. Compute the probability of the complement of C.

e. Are A and B mutually exclusive? Explain your answer.

f. Are A and B independent? Explain your answer.

g. Are A and C mutually exclusive? Explain your answer.

h. Are A and C independent? Explain your answer.

4. Consider a population of five weights identical in appearance but weighing 1, 3, 5, 7, and 9

ounces.

a. Determine the mean and the variance of the population.

b. 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.

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? Solutions to MC Problems

1. ANS: B2ANS:C3.ANS:C4. ANS:A5. ANS:C6. ANS:B7.ANS:D 8.ANS:C9.ANS:B10. ANS:A

11. ANS: A12.ANS:C13.ANS: A14.ANS:A15.ANS: D16.ANS:B17.ANS: C18.ANS:A

19. ANS: B20.ANS:D21.ANS: B22.ANS:B23.ANS:C24.ANS:C25. ANS: B26. ANS: A

27. ANS: D28.ANS: D29. ANS: D

Short Ans wer/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. A NSW ERS: 2. A NSW ERS:a. 0.0 b. 0.6 c. 0.0

3ANSW ERS:

a. 0.23

b. 0.06

c. 0.4

d. 0.9

e. No, P(A?B) ≠ 0

f. No, P(A?B) ≠ P(A)

g. No, P(A ? C) ≠ 0h. Y es, P(A?C) = P(A)

4. ANSW ERS:a. 5 and 8b. 5 and 3c. 1.732

5. A NSW ERS:a. 10.5 0.363 normalb.0.0314c. 0.0794

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