Business Statistics 1 Revision

1. The complete collection of all entities under study is called the __________.

A. sample

B. parameter

C. statistic

D. population

2. A portion (subset) of the entities under study is called the __________.

A. parameter

B. sample

C. population

D. statistic

3. Claudia Taylor, Director of Global Industrial Sales in Melbourne, is concerned by a deteriorating sales trend. Specifically, the number of customers is stable at 1500 but they are purchasing less each year. She orders her staff to search for causes of the downward trend by surveying all 1500 industrial customers. For this study, the set of 1500 industrial customers is a

________________.

A. statistic

B. sample

C. population

D. parameter

4. When a person collects information from the entire population, this is called a _____________.

A. sample

B. census

C. statistic

D. parameter

5. Claudia Taylor, Director of Global Industrial Sales in Melbourne, is concerned by a deteriorating sales trend. Specifically, the number of customers is stable at 1500 but they are purchasing less each year. She orders her staff to search for causes of the downward trend by selecting a focus group of 40 industrial customers. Sue is ordering a ___________________.

A. statistic from the industrial customers

B. census of the industrial customers

C. sorting of the industrial customers

D. sample of the industrial customers

6. Claudia Taylor, Director of Global Industrial Sales in Melbourne, is concerned by a deteriorating sales trend. Specifically, the number of customers is stable at 1500 but they are purchasing less each year. She orders her staff to search for causes of the downward trend by surveying all 1500 industrial customers. One question on the survey asked the customers to rate ‘Merchandise is delivered on time’ on a scale of 1 to 5, with 1 meaning ‘never’ and 5 meaning ‘always’. The average response of the 1500 customers to this question is a ________________.

A. parameter

B. population

C. sample

D. statistic

7. Claudia Taylor, Director of Global Industrial Sales in Melbourne, is concerned by a deteriorating sales trend. Specifically, the number of customers is stable at 1500 but they are purchasing less each year. She orders her staff to search for causes of the downward trend by selecting a focus group of 40 industrial customers. One question asked the focus group customers to rate ‘Merchandise is delivered on time’ on a scale of 1 to 5, with 1 meaning ‘never’ and 5 meaning ‘always’. The average response of the 40 customers to this question is a

________________.

A. parameter

B. population

C. sample

D. statistic

29. Which of the following operations is meaningful for processing nominal data?

A. addition

B. multiplication

C. ranking

D. counting

8. Claudia Taylor, Director of Global Industrial Sales in Melbourne, is concerned by a deteriorating sales trend. Specifically, the number of customers is stable at 1500 but they are purchasing less each year. She orders her staff to search for causes of the downward trend by surveying all 1500 industrial customers. One question on the survey asked the customers, ‘Which of the following best describes your primary business: (a) manufacturing, (b) wholesaler, (c) retail, (d) service’. The measurement level for this question is

___________________.

A. nominal level

B. ordinal level

C. interval level

D. ratio level

9. Which of the following operations is meaningful for processing ordinal data, but is meaningless for processing nominal data?

A. addition

B. multiplication

C. ranking

D. counting

10. A consumer has been asked to rank five cars based upon their desirability. This level of measurement is ___________________.

A. nominal

B. ratio

C. ordinal

D. interval

11. A level of data measurement that has an absolute zero is called ____________.

A. nominal

B. ordinal

C. interval

D. ratio

12. Upon discovering an improperly adjusted drill press, Jack Joyner, Director of Quality Control, ordered an inspection of ‘every fifth casting drilled on the evening shift’. Less than 1% of the castings were defective, so Jack released the evening shift’s production to assembly. This is an example of ___________________.

A. nonparametric statistics

B. nominal data

C. descriptive statistics

D. inferential statistics

13. The unemployment rate is often used as an indicator of a community’s economic vitality. An unemployment rate is best described as what level of measurement?

A. nominal

B. ordinal

C. interval

D. ratio

14. A graphical representation of a frequency distribution is called a ___________.

A. stem and leaf plot

B. ogive

C. histogram

D. pie chart

15. Which of the following is best to show the percentage of a total budget that is spent on each category of items?

A. histogram

B. ogive

C. stem and leaf chart

D. pie chart

16. Consider the following frequency distribution:

  

Class Interval

Frequency

 

10-under 20

15

 

20-under 30

25

 

30-under 40

10

What is the cumulative frequency of the second class interval?

A. 25

B. 40

C. 15

D. 50

17. The number of phone calls arriving at a switchboard each hour has been recorded and the following frequency distribution has been developed.

  

Class Interval

Frequency

 

20-under 40

30

 

40-under 60

45

 

60-under 80

80

 

80-under 100

45

What is the approximate range of this data?

A. 0.45

B. 0.90

C. 0.225

18. The cumulative frequency for a class is 27. The cumulative frequency for the nest (non-empty) class will be __________.

A. less than 27

B. equal to 27

C. greater than 27

D. 27 minus the next calss frequency

19. Consider the following frequency distribution given below:

  

Class Interval

Frequency

 

20-under 40

0.2

 

40-under 60

0.3

 

60-under 80

0.4

 

80-under 100

0.1

There were 60- numbers in the data set. How many numbers were in the interval 40-under 60?

A. 30

B. 50

C. 18

D. 12

20. The lowest appropriate level of measurement for the mean is _________.

A. nominal

B. ordinal

C. interval

D. ratio

21. The average of the squared deviations from the arithmetic mean is called the _________.

A. standard deviation

B. mean absolute deviation

C. variance

D. coefficient of variation

22. The empirical rule says that approximately what percentage of the values would be within 2 standard deviations of the mean in a bell shaped set of data?

A. 95%

B. 68%

C. 50%

D. almost all

23. A statistics student made the following grades on 5 tests: 84, 78, 88, 78 and 72. What is the mean grade?

A. 78

B. 80

C. 72

D. 84

24. A commuter travels many kilometres to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 34, 39, 41, 35 and

41. The mean time required for this trip was __________.

A. 35

B. 41

C. 37.5

D. 38

25. The following frequency distribution was constructed for the age of accounts receivable.

The frequency distribution reveals that the accounts receivable ages are _______.

A. skewed to the left

B. skewed to the right

C. not skewed

D. normally distributed

26. If the occurrence of one event does not affect the occurrence of another event, then the two events are _______.

A. mutually exclusive

B. complements

C. independent

D. elementary events

27. The joint probability of X and Y is also referred to as _______.

A. the intersection of X and Y

B. the union of X and Y

C. the marginal probability of X and Y

D. the probability of X given Y

28. Given P(A) = 0.40, P(B) = 0.50, P(A Ç B) = 0.15. Find P(A È B).

A. 0.90

B. 1.05

C. 0.75

D. 0.65

29. Given P(A) = 0.40, P(B) = 0.50, P(A Ç B) = 0.15. Find P(B|A).

A. 0.20

B. 0.80

C. 0.30

D. 0.375

31. Meagan Davies manages a portfolio of 200 common stocks. Her staff classified the portfolio stocks by ‘industry sector’ and ‘investment objective’.

  

Investment

Industry Sector

Total

 

objective

Electronics

Airlines

Healthcare

 

Growth

100

10

40

150

 

Income

20

20

10

50

 

Total

120

30

50

200

If a stock is selected randomly from Meagan’s portfolio, P(Healthcare È Electronics) = _______.

A. 0.25

B. 0.85

C. 0.60

D. 0.75

32. If a stock is selected randomly from Meagan’s portfolio, P(Growth Healthcare) =

___________.

A. 0.25

B. 0.40

C. 0.20

D. 0.80

33. Are ‘Healthcare’ and ‘Income’ independent, why or why not?

A. Yes, because P(Healthcare Income) = P(Healthcare)

B. No, because P(Healthcare) = P(Income)

C. No, because P(Income Ç Healthcare) = P(Healthcare) P(Income)

D. Yes, because P(Income Ç Healthcare) ≠ 0

35. Given P(A) = 0.6, P(B) = 0.4, P(A Ç B)=0.24. Which of the following statements is true?

A. P(A|B) = 0.60

B. P(A|B) = 0.40

C. P(B|A) = 0.60

D. A and B are mutually exclusive

36. You are offered an investment opportunity. Its outcomes and probabilities are presented in the 

X P(X)

  

–$1000

.40

 

$0

.20

 

+$1000

.40

The mean of this distribution is _____________.

A. –$400

B. $0

C. $200

D. $400

37. You are offered an investment opportunity. Its outcomes and probabilities are presented in the following table.

X P(X)

  

–$1000

.40

 

$0

.20

 

+$1000

.40

Which of the following statements is true?

A. This distribution is skewed to the right.

B. This is a binomial distribution.

C. This distribution is symmetric.

D. This distribution is skewed to the left.

38. You are offered an investment opportunity. Its outcomes and probabilities are presented in the following table.

X P(X)

  

–$1000

.40

 

$0

.20

 

+$1000

.40

Which of the following statements is true?

A. This distribution is skewed to the right.

B. This is a binomial distribution.

C. This distribution is symmetric.

D. This distribution is skewed to the left.

39. A student randomly guesses the answers to a five question true/false test. If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses no question?

A. 0.000

B. 0.200

C. 0.500

D. 0.031

40. If X is a binomial random variable with n = 8 and p = 0.6, the standard deviation of X is

______.

A. 4.8

B. 3.2

C. 1.92

D. 1.39

41. If X is a binomial random with n = 10 and p = 0.4, what is the probability that X is equal to 3?

A. 0.215

B. 0.057

C. 0.300

D. 0.120

42. If X is uniformly distributed over the interval 8 to 12, inclusively (8 £ X £ 12), then the mean ( ) of this distribution is __________________.

A. 10

B. 20

C. 5

D. incalculable

43. If X is uniformly distributed over the interval 8 to 12, inclusively (8 £ X £ 12), then the standard deviation ( ) of this distribution is __________________.

A. 4

B. 1.33

C. 1.15

D. 2

45. If X is a normal random variable with mean 60 and standard deviation 2, calculate the z-score if X = 57.

A. 1.5

B. 2.5

C. -1.6

D. -0.5

46. Let Z be a normal random variable with mean 0 and standard deviation 1. Use the normal tables to find P(Z > –1.1).

A. 0.3643

B. 0.8643

C. 0.1357

D. -0.1357

47. A z-score is the number of __________ that a value is from the mean.

A. variances

B. standard deviation

C. units

D. miles

48. The z-value associated with a two-sided 95% confidence interval is _______.

A. 1.28

B. 1.645

C. 1.96

D. 2.575

49. Sam Gates, Marketing Director of Mansfield Motors’ Electrical Division, is leading a study to assess the relative importance of product features. An item on survey questionnaire distributed to 121 of Mansfield’s customers asked them to rate the importance of ‘ease of maintenance’ on a scale of 1 to 10 (with 1 meaning ‘not important’ and 10 meaning ‘highly important’). His staff assembled the following statistics.

  

Ease of Maintenance

 

Mean

7.5

 

Population Standard Deviation

1.1

The 95% confidence interval for the population mean rating of ‘ease of maintenance’ is ______.

A. 5.34 to 9.66

B. 7.34 to 7.66

C. 5.69 to 9.31

D. 7.30 to 7.70

50. The t-distribution is similar to a normal distribution. However the t-distribution is _______.

A. not symmetric

B. bimodal

C. flatter

D. discrete

51. James Weepu, Human Resources Manager with Auckland First Bank (AFB), is reviewing the employee training programs of AFB branches. His staff randomly selected personnel files for 100 tellers in the Southern Region and determined that their mean training time was 25 hours. Assume that the population standard deviation is 5 hours. The 92% confidence interval for the population mean of training times is ________.

A. 16.25 to 33.75

B. 24.30 to 25.71

C. 17.95 to 32.05

D. 24.13 to 25.99

52. Consider the following null and alternative hypotheses. Ho: µ £ 7

Ha: µ > 6

These hypotheses _______________.

A. are not mutually exclusive

B. are not collectively exhaustive

C. do not reference a population parameter

D. are established correctly

53. Consider the following null and alternative hypotheses. Ho: s ³ 558

Ha: s < 558

These hypotheses _______________.

A. are not mutually exclusive

B. are not collectively exhaustive

C. do not reference a population parameter

D. are established correctly

54. The rejection and not rejectance regions are divided by a point called the _______.

A. dividing point

B. critical value

C. rejection value

D. not rejectance value

55. The probability of committing a Type I error is called _______.

A. α

B. β

C. x

D. σ

56. In statistical hypothesis testing, another name for is _______.

A. level of significance

B. power

C. beta

D. Type II error probability

57. The probability of committing a Type II error is represented by _______.

A. α

B. β

C. 1 – α

D. α / 2

58. A researcher is testing a hypothesis of a single mean. The critical z-value for = .05 and a two-tailed test is +1.96. The observed z-value from sample data is 2.85. The decision made by the researcher based on this information is to _____ the null hypothesis.

A. reject

B. not reject

C. redefine

D. change the alternate hypothesis into

59. Restaurateur Daniel Valentine is evaluating the feasibility of opening a restaurant in Richmond. The Chamber of Commerce estimates that ‘Richmond families, on the average, dine out at least 3 evenings per week’. Daniel plans to test this hypothesis using a random sample of 81 Richmond families. His null hypothesis is __________.

A. μ ³ 3

B. s ³ 3

C. n = 81

D. μ < 3

60. When the rod shearing process at Newcastle Steel is ‘in control’ it produces rods with a mean length of 120 cm. Periodically, quality control inspectors select a random sample of 36 rods. If the mean length of sampled rods is too long or too short, the shearing process is shut down. The alternative hypothesis is _________.

A. n = 36

B. μ = 120

C. μ ≠ 120

D. n ≠ 36

61. The diameter of DVDs is normally distributed. Periodically, quality control inspectors at Dandenong DVDs randomly select a sample of 16 DVDs. If the mean diameter of the DVD is too large or too small the DVD punch is shut down for adjustment; otherwise, the punching process continues. The null hypothesis is _______.

A. n ≠ 16

B. n = 16

C. m = 3.5

D. m ≠ 3.5

63. A measure of the degree of relatedness of two variables is _______.

A. regression

B. correlation

C. residual

D. least squares analysis

64. In the regression equation y = 75.65 + 0.50x, the slope is _______.

A. 0.5

B. 75.65

C. 1.00

D. indeterminable

66. The difference between the actual y-value and the predicted y-value found using a regression equation is called the _______.

A. slope

B. residual

C. outlier

D. scatter plot

67. A standard deviation of the error of the regression model is called the _______.

A. coefficient of determination

B. sum of squares of error

C. standard error of the estimate

D. r-squared

68. The total of the squared residuals is called the _______.

A. coefficient of determination

B. sum of squares of error

C. standard error of the estimate

D. r-squared

69. The coefficient of determination must be _______.

A. between –1 and +1

B. between –1 and 0

C. between 0 and 1

D. equal to SSE / (n – 2)

70. For a data set the regression equation is y = 21 – 3x. The correlation coefficient for this data

_______.

A. must be 0

B. is negative

C. must be 1

D. is positive

71. If there is perfect negative correlation between two sets of numbers, then _______.

A. r = 0

B. r = –1

C. r = +1

D. SSE = 1

72. The following data is to be used to construct a regression model:

  

x

5

7

4

15

12

9

 

y

8

9

12

26

16

13

Using α = 0.05 to test the null hypothesis H0:β1 = 0, the critical values are _________.

A. -1.943 and 1.943

B. -2.447 and 2.447

C. -2.132 and 2.132

D. -2.776 and 2.776

73. The following data is to be used to construct a regression model:

  

x

1

9

5

4

8

9

 

0

 

y

2

4

9

9

3

3

The value of intercept is _________.

A. -2.67

B. -1.25

C. 1.36

D. 14.41

75. In the model y = β0 + β1x1 + β2x2 + β3x3 + ε , ε is _________________.

A. a partial regression coefficient

B. the regression constant

C. the error of prediction

D. the response variable

76. Multiple regression analysis produced the following tables.

  

Coefficients

Standard   Error

t Statistic

p-value

 

Intercept

752.0833

336.3158

2.236241

0.042132

 

x1

11.87375

5.32047

2.231711

0.042493

 

x2

1.908183

0.662742

2.879226

0.01213

 

 

df

SS

MS

F

p-value

 

Regression

2

203693.3

101846.7

6.745406

0.010884

 

Residual

12

181184.1

15098.67

 

Total

14

384877.4

A. ŷ = 752.0833 + 11.87375x1 + 1.908183x2

B. ŷ = 752.0833 + 336.3158 x1 + 2.236241 x2

C. ŷ = 336.3158 + 5.32047 x1 + 0.662742 x2

D. ŷ = 2.236241 + 2.231711 x1 + 2.879226 x2