### QNT561 Final Exam Complete Solution 400+ answers

**QNT561 Final Exam Complete Solution 400+ answers**

1. The expected value of the a probability distribution

A. Is the same as the random variable

B. Is another term for the mean

C. Is also called the variance

D. Cannot be greater than 1

2. Which of the following is a correct statement about a probability?

A. It may range from 0 to 1

B. It may assume negative values

C. It may be greater than 1

D. It cannot be reported to more than 1 decimal place

3. An experiment is a

A. Collection of events

B. Collection of outcomes

C. Always greater than 1

D. The act of taking a measurement or the observation of some activity

4. Which level of measurement is required for the median?

A. Nominal

B. Ordinal

C. Interval

D. Ratio

5. Which level of measurement is required for the mode?

A. Nominal

B. Ordinal

C. Interval

D. Ratio

6. In a set of observations, which measure of central tendency reports the value that occurs most often?

A. Mean

B. Median

C. Mode

D. Geometric mean

7. The weighted mean is a special case of the

A. Mean

B. Median

C. Mode

D. Geometric mean

8. The relationship between the geometric mean and the arithmetic mean is

A. They will always be the same

B. The geometric mean will always be larger

C. The geometric mean will be equal to or less than the mean

D. The mean will always be larger than the geometric mean

9. Suppose you compare the mean of raw data and the mean of the same raw data grouped into a frequency distribution. These two means will be

A. Exactly equal

B. The same as the median

C. The same as the geometric mean

D. Approximately equal

10. In a set of 10 observations the mean is 20 and the median is 15. There are 2 values that are 6, and all other values are different. What is the mode?

A. 15

B. 20

C. 6

D. None of the above

11. Which of the measures of central tendency is the largest in a positively skewed distribution?

A. Mean

B. Median

C. Mode

D. Cannot tell from the information given

12. Which of the following is not a measure of dispersion?

A. Range

B. Variance

C. Standard deviation

D. All of the above are measures of dispersion

13. A disadvantage of the range is

A. Only two values are used in its calculation

B. It is in different units than the mean

C. It does not exist for some data sets

D. All of the above

14. The mean deviation is

A. Based on squared deviations from the mean

B. Also called the variance

C. Based on absolute values

D. Always reported in squared units

15. The standard deviation is

A. Based on squared deviations from the mean

B. In the same units as the mean

C. Uses all the observations in its calculation

D. All of the above

16. The variance is

A. Found by dividing by N by the mean

B. In the same units as the original data

C. Found by squaring the standard deviation

D. All of the above

17. In a positively skewed distribution

A. The mean, median, and mode are all equal

B. The mean is larger than the median

C. The median is larger than the mean

D. The standard deviation must be larger than the mean or the median

18. Which of the following statements is true regarding the standard deviation?

A. It cannot assume a negative value

B. If it is zero, then all the data values are the same

C. t is in the same units as the mean

D. All the above are all correct

19. A uniform distribution is defined by

A. Its largest and smallest value

B. Largest value

C. Smallest value

D. None of the above

20. The normal approximation to the binomial is used when

A. The sample size is at least 30

B. Both *np* and *n* (1 - p) are at least 5

C. The mean and the variance are the same

D. The *z* value is greater than 0

21. A sample

A. Is a part of the population

B. Has more than 30 observations

C. Is usually identified as *N*

D. All of the above

22. Which of the following is not a reason for sampling?

A. The destructive nature of certain tests

B. The physical impossibility of checking all the items in the population

C. The adequacy of sample results

D. All of the above are reasons for sampling

23. Which of the following is not a method of probability sampling?

A. Random sampling

B. Systematic sampling

C. Stratified sampling

D. All of the above are methods of probability sampling

24. In a simple random sample

A. Every *k*^{th} item is selected to be in the sample

B. Every item has a chance to be in the sample

C. Every item has the same chance to be in the sample

D. All of the above

25. Suppose a population consisted of 20 items. How many different sample of *n* = 3 are possible?

A. 6840

B. 1140

C. 20

D. 120

26. The difference between the sample mean and the population mean is called the

A. Population mean

B. Population standard deviation

C. Standard error of the mean

D. Sampling error

27. The mean of the all the sample means and the population mean will

A. Always be equal

B. Always be normally distributed

C. Characterized by the standard error of the mean

D. None of the above

28. We wish to develop a confidence interval for the population mean. The shape of the population is not known, but we have a sample of 40 observations. We decide to use the 92 percent level of confidence. The appropriate value of z is:

A. 1.96

B. 1.65

C. 2.58

D. 1.75

29. Which of the following statements is not a characteristic of the *t* distribution.

A. It is a continuous distribution

B. It has a mean of 0

C. It is symmetrical

D. Like *z* there is only one *t* distribution

30. We wish to develop a confidence interval for the population mean. The population follows the normal distribution and we have a sample of 10 observations. We decide to use the 90 percent level of confidence. The appropriate value of to represent the level of confidence is

A. *z* =1.65

B. *z* = 1.96

C. *t* = 1.833

D. *t* = 1.812

37. The fraction or ratio of a sample possessing a certain trait is called

A. Population

B. Mean

C. Confidence interval

D. Proportion

32. To develop a confidence interval for a proportion

A. We need to meet the binomial conditions

B. The sample should be at least 100

C. p should be less than .05

D. None of the above

33. The finite population correction factor is used when

A. *n* is more than 30

B. *N* is more than 1000

C. *n* is greater than 5

D. *n*/*N* is more than .05

34. We wish to estimate the population proportion. We want to be 95 percent confident of our results and we want the estimate to be with .01 of the population parameter. No estimate of the population proportion is available. What value should we use for *p*?

A. 1.96

B. .01

C. .50

D. We cannot complete the problem, we need more information.

35. The null hypothesis

A. Is a statement about the value of the population parameter

B. Will always contain the equal sign

C. Cannot include values less than 0

D. Both a and b are correct

36. The alternate hypothesis

A. Is accepted if the null hypothesis is rejected

B. Will always contain the equal sign

C. Tells the value of the sample mean

D. None of the above

37. The level of significance

A. Is frequently .05 or .01

B. Can be any value between 0 and 1.

C. Is the likelihood of rejecting the null hypothesis when it is true.

D. All of the above.

38. A Type I error is

A. The correct decision

B. A value determined from the test statistic

C. Rejecting the null hypothesis when it is true

D. Accepting the null hypothesis when it is false.

39. The critical value is

A. Calculated from sample information

B. Cannot be negative

C. The point that divides the acceptance region from the rejection region

D. A value determined from the test statistic

40. In a one-tailed test

A. The rejection region is in one of the tails

B. The rejection region is split between the tails

C. The *p*-value is always less than the significance level

D. The *p*-value is always more than the significance level

41Which of the following is not a requirement for the two-sample test of means for independent samples when both samples contain less than 30 observations?

A. Normal populations

B. Equal population standard deviations

C. Equal sample sizes

D. All of the above are required.

42To conduct a test of hypothesis for dependent samples we assume that

A. The distribution of the difference between the paired observations follows the normal distribution

B. Both samples are at least 30

C. The samples are unrelated

D. All of the above

43When conducting a test of hypothesis for the dependent samples

A. We should have at least 30 pairs.

B. The significance level is more than .05.

C. The *p*-value is more than .10.

D. None of the above

44Which of the following is not necessary to determine a *p*-value?

A. Knowledge of whether the test is one-tailed or two-tailed

B. The value of the test statistic

C. The level of significance

D. All of the above are needed

45In a two-way ANOVA the second source of variation is due to

A. Random error

B. Blocks

C. Total variation

D. None of the above

46uppose we conduct an ANOVA test of four treatment means and reject the null hypothesis. Construction of a confidence interval for the difference between the first and second sample mean revealed the interval to be 10 plus or minus 12. We conclude

A. This pair of means differ

B. This pair of means does not differ

C. Because we do not know the units involved, we cannot draw any conclusion

D. Because we do not know the degrees of freedom, we cannot draw any conclusion

47Which of the following is not an assumption required for ANOVA?

A. The populations are normally distributed

B. The populations have equal standard deviations

C. The samples are independent.

D. All of the above.

48Which of the following is *not* a characteristic of the *F* distribution?

A. It is a discrete distribution

B. In cannot be negative

C. It is based on two sets of degrees of freedom

D. All of the above

47In a multiple regression equation there

A. Are two or more independent variables

B. Is only one dependent variable

C. Is one intercept value

D. All of the above

50A dummy variable or indicator variable

A. May assume only a value of 0 or 1

B. Is another term for the dependent variable

C. Is found by (*Y* - *Y'*)

D. Is equal to *Y'*

* *

51 In the ANOVA table the value of k is

A. The number of independent variables

B. The total number of observations

C. The number of degrees of freedom

D. The sum of squares total

52. Multicollinearity occurs when

A. The residuals are correlated

B. Time is involved in the analysis

C. The independent variables are correlated

D. The residuals are not constant for all *Y'* values

53. A correlation matrix

A. Shows all simple coefficients of correlation

B. Shows all possible net regression coefficients

C. Shows the correlations that are positive

D. Reports the multiple regression equation

54. To conduct a nonparametric test the

A. Population must follow the normal distribution

B. The standard deviation must be known

C. It is not necessary to make any assumption about the shape of the population

D. The data must be at least interval scale

55. In a goodness-of-fit test where the sample size is 200, there are 5 categories, and the significance level is .05. The critical value of *X*^{2} is

A. 9.488

B. 11.070

C. 43.773

D. None of the above

56. In a goodness-of-fit test

A. All the cell frequencies must be the same

B. There must be at least 30 observations

C. Forty percent of the cells must contain at least 10 observations

D. None of the above

57. In a contingency table

A. The number of rows must be the same as the number of columns

B. A variable is classified according to two criteria

C. There must be at least 10 observations in each cell

D. All of the above

58. In a contingency table a sample of 400 people is classified by gender and hair color (4 groups: blond, brown, black, and red). How many degrees of freedom are there?

A. 3

B. 8

C. 399

D. None of the above

59. To find the expected frequency in a contingency table

A. Take the square root of the degrees of freedom

B. Multiple the row total by the column total and divide the result by the grand total

C. Use the total number of observations minus one

D. None of these

60. Suppose we select a sample of 100 observations and organize them into 6 categories. We wish to investigate whether the number of observations could be the same in each of the categories in the population. How many degrees of freedom are there?

A. 5

B. 97

C. 3

D. None of these

61. To conduct the sign test, we assume

A. The population is normally distributed

B. The scale of measurement is interval

C. The samples are dependent

D. There are at least 20 observations in the sample

62. An index

A. Shows a percent change from one period to another

B. Must be larger than 100

C. Can employ qualitative data

D. Cannot assume negative values

63 The role of statistics is business research is to capture a population’s characteristics by using inferential statistics from a sample’s characteristics – True

64. To conduct a one sample test of means and use the *z* distribution as the test statistic

A. We need to know the population mean

B. We can use the sample standard deviation provided *np* is at least 30

C. We need *np* to be at least 5

D. Both a and b are correct

65. A *p*-value is

A. The same as the population proportion

B. The same as the significance level

C. The fraction of the population that has a particular characteristic

D. The probability of finding a value of the test statistic this extreme when the null hypothesis is true

66. A Type II error occurs when

A. We accept a false null hypothesis

B. We reject a true alternate hypothesis

C. We reject a false null hypothesis

D. None of the above

67. Which of the following statements are correct when deciding whether to use the *z* or the *t* distribution?

A. Use *z* when the sample size is 30 or more

B. Use *z* when we have a normal population and we know the standard deviation

C. Use *t* when the population is normal, the population standard deviation is not known, and *n* is less than 30

D. All of the above statements are correct

68. In a two-sample test of means for independent samples, the equal sign always appears in

A. The null hypothesis

B. The alternate hypothesis

C. The upper tail of the test statistic

D. None of the above

69. In a two-sample test of means for independent samples, we use the *z* distribution when

A. The population standard deviations are equal

B. Both populations are positively skewed

C. Both samples are at least 30

D. *n* and *n*(1-) are both greater than 5

70. Which of the following is a requirement for a two-sample test of proportions

A. The population standard deviations are equal.

B. Both populations are positively skewed

C. Both samples are at least 30.

D. *n* and *n*(1-) are both greater than 5

71 Which of the following measures of central location is affected most by extreme values?

A. Mean

B. Median

C. Geometric mean

D. Mode

72 Which level of measurement is required for the mode?

A.Ordinal

B.Nominal

C.Ratio

D.Interval

73 A difference between calculating the sample mean and the population mean is:

A.We divide the sum of the observations by n - 1 instead of n

B.Only in the symbols, we use instead of µ and n instead of N.

C.There are no differences.

D.The observations are ranked and select the middle value for the population mean.

74 In which of the following distributions is the probability of a success usually small?

A. Poisson

B. Binomial

C. All distribution

D. Hypergeometric

75 The difference between a random variable and a probability distribution is:

A.A random variable does not include the probability of an event.

B.A random variable can only assume whole numbers.

C.A probability distribution can only assume whole numbers.

D.None of the above.

76 The mean and the variance are equal in

A.The hypergeometric distribution.

B.The binomial distribution.

C.All probability distributions.

D. The Poisson distribution.

77 In a simple random sample

A. Every Kth item is selected to be in the sample.

B. Every item has a chance to be in the sample.

C. Every item has the same chance to be in the sample.

D. All of these

78 A sample

A. Is part of the population.

B. Has more than 30 observations.

C. Is usually identified as N.

D. All of these

79 The difference between the sample mean and the population mean is called the

A. Sampling error.

B. Population standard deviation.

C. Population mean.

D. Standard error of the mean.

80 We wish to develop a confidence interval for the population mean. The shape of the population is not known, but we have a sample of 40 observations. We decide to use the 92% level of confidence. The appropriate value of z is:

A. 1.75

B. 1.65

C. 1.96

D. 2.58

81 We wish to develop a confidence interval for the population mean. The population follows the normal distribution, the standard deviation of the population is 3, and we have a sample of 10 observations. We decide to use the 90% level of confidence. The appropriate value of to represent the level of confidence is

A. t=1.812

B. z=1.96

C. z =1.65

D. t=1.833

82 A point estimate is

A. Always an estimate of the population mean.

B. Always equal to the population value.

C. An estimate of the population parameter.

D. None of these

83 We use the General Rule of Multiplication to combine

A. Events based on subjective probabilities

B. Mutually exclusive events.

C. Events that are not independent.

D. Events that total more than 1.00.

84. If the two samples are not independent, their population means can still be compared using the ____________ statistic.

A. . paired t

B. . Z

C. . F

D. . chi-square

85 Which of the following is/are an appropriate null hypothesis for a two-sided test of the difference between two population means? 1. H0: ?1 = ?2 2. H0: ?1 ? ?2 3. H0: ?1 – ?2 = 0

A. . 1

B. . 2

C. . 3

D. . both 1 and 3

86 An experiment is a:

A.The act of taking a measurement or the observation of some activity.

B.Collection of outcomes.

C.Collection of events

D. Always greater than 1.

87 Which of the following is a correct statement about a probability?

A. It cannot be reported to more than 1 decimal place.

B. It may assume negative values.

C. It may range from 0 to 1.

D. It may be greater than 1.

88 Which of the following statements is true regarding a population?

A. It must be a large number of values.

B. It must refer to people.

C. It is a collection of individuals, objects, or measurements.

D None of these

89 Which of the following statements is true regarding a sample?

A. It is a part of population.

B. It must contain at least five observations.

C. It refers to descriptive statistics

D. All of these are correct

90 A discrete variable is

A. Cannot be negative.

B. Can assume only whole number values.

C. An example of a qualitative variable.

D. Can assume only certain clearly separated values

91 In a two-sample test of means for independent samples, the equal sign always appears in

A. The null hypothesis.

B. The alternate hypothesis.

C. The upper tail of the test statistic.

D. None of these

92 In a two-sample test of means for independent samples, we use the z distribution when

A. nB and n(1-B) are both greater than 5.

B. Both populations have at least 4,000 observations.

C The population standard deviations are equal.

D. Both population standard deviations are known.

93) A Type I error is

A. Accepting the null hypothesis when it is false.

B. A value determined from the test statistic

C. The correct decision

D. Rejecting the null hypothesis when it is true

94 To conduct a nonparametric test the.

A. The data must be at least interval scale.

B. The standard deviation must be known.

C. Population must follow the normal distribution.

D. It is not necessary to make any assumption about the shape of the population.

95 In a contingency table a sample of 400 people is classified by gender and hair color (4 groups: blond, brown, black, and red). How many degrees of freedom are there?

A. 3

B. 8

C. 399

D. None of these

96 In a contingency table

A. The number of rows must be the same as the number of columns.

B. A variable is classified according to two criteria.

C. There must be at least 10 observations in each cell.

D. All of these

97 The multiple standard error of estimate is

A. Is based on the (Y - Y)2.

B. Is negative when one of the net regression coefficients is 0.

C.Is found by taking the square root of SSR/SS total.

D.All of these

98 In the ANOVA table the value of k is

A.The sum of squares total.

B.The total number of observations

C.The number of independent variables.

D.The number of degrees of freedom.

99 A dummy variable or indicator variable

A. Is equal to Y

B. Is another term for the dependent variable.

C. May assume only a value of 0 or 1.

D. Is found by (Y - Y).

100 Suppose we have a population that follows the normal distribution. Which of the following statements is correct regarding the distribution of sample means?

A. The population standard deviation is always unknown

B. The distribution of samples means will follow the uniform distribution

C. The distribution of the sample means will also follow the normal distribution

D. None of the above is correct

101 Suppose we have a population that does not follow the normal distribution. If we select sample of what size will the distribution approximate the normal distribution?

A. 2

B. 5

C. 20

D. 30

102 The standard error of the mean is

A. The standard deviation of the sampling distribution of sample means

B. Always normally distributed

C. Sometimes less than 0

D. None of the above

103 A point estimate is

A. Always an estimate of the population mean

B. Always equal to the population value

C. An estimate of the population parameter

D. None of the above

104 A confidence interval

A. Always includes the population parameter

B. Decreases in width as the sample size is increased

C. Cannot include a value of 0

D. None of the above

105 If we wished to decrease the width of a confidence interval, we would *not* do which of the following

A. Increase the size of the sample

B. Reduce the size of the population

C. Decrease the level of confidence

D. None of the above

106 Under which of the following conditions would the standard deviation assume of negative value

A. When all the data values were negative

B. When more than half of the data values were negative

C. If all the data values were the same

D. The standard deviation cannot be negative

107 The difference between a histogram and a bar chart is:

A. The midpoints are connected with a histogram but not with a bar chart

B. The bars must be next to each other on a histogram and separated in a bar chart

C. Cumulative frequencies are required in a bar chart

D. None of the above

108 The appropriate alternative hypothesis for a lower tail test to determine if mean body weight of all the men who have joined a health club is less than 185 pounds would be

A. HA: μ ≥ 185 lb

B. HA: μ < 185 lb

C. HA: μ = 185 lb

D. HA: μ ≠ 185 lb

109 The normal distribution is a

A. Discrete distribution

B. Continuous distribution

C. Positively skewed distribution

D. None of the above

110Which of the following are characteristics of the normal distribution?

A. It is a symmetric distribution

B. It is bell-shaped

C. It is asymptotic

D. All of the above

111Which of the following are correct statements about a normal distribution?

A. It cannot assume negative numbers

B. It is defined by its mean and standard deviation

C. All normal distributions have a variance of at least 1

D. All of the above are correct

112 Which of the following statements is correct regarding the standard normal distribution

A. It is also called the *z* distribution

B. Any normal distribution can be converted to the standard normal distribution

C. The mean is 0 and the standard deviation is 1

D. All of the above are correct

113 The area under a normal curve between 0 and -1.75 is

A. .0401

B. .9599

C. .4599

D. None of the above.

114 The continuity correction factor is used when

A. The sample size is at least 5

B. Both *np* and *n* (1 - p) are at least 30

C. A continuous distribution is used to approximate a discrete distribution

D. The standard normal distribution is applied

115 The difference between the sample mean and the population mean is called the:

A. Sampling error.

B. Population standard deviation.

C. Population mean.

D. Sandard error of the mean.

116 A confidence interval:

A. Always includes the population parameter.

B. Decreases in width as the sample size is increased

C. Cannot include a value of 0

D. None of these

117 The alternate hypothesis

A. None of these

B. Will always contain the equal sign.

C. Is accepted if the null hypothesis is rejected

D. Tells the value of the sample mean.

118 To conduct a nonparametric test the.

A. The data must be at least interval scale.

B. The standard deviation must be known.

C. Population must follow the normal distribution.

D. It is not necessary to make any assumption about the shape of the population

119 In the ANOVA table the value of k is

A. The sum of squares total.

B. The total number of observations

C. The number of independent variables.

D. The number of degrees of freedom.

120 The difference between a random variable and a probability distribution is

A. A random variable does not include the probability of an event

B. A random variable can only assume whole numbers

C. A probability distribution can only assume whole numbers

D. None of the above

121. Which of the following is not a requirement of a binomial distribution?

A. A constant probability of success

B. Only two possible outcomes

C. A fixed number of trails

D. Equally likely outcomes

122 The mean and the variance are equal in

A. All probability distributions

B. The binomial distribution

C. The Poisson distribution

D. The hypergeometric distribution

123. Bayes' Theorem

A. Is an example of subjective probability

B. Can assume of value less than 0

C. Is used to revise a probability based on new or additional information

D. Is found by applying the complement rule

124. The difference between a permutation and a combination is

A. In a permutation order is important and in a combination it is not

B. In a permutation order is not important and in a combination it is important

C. A combination is based on the classical definition of probability

D. A permutation is based on the classical definition of probability

125. A difference between calculating the sample mean and the population mean is

A. Only in the symbols, we use instead of µ and n instead of N

B. We divide the sum of the observations by n - 1 instead of n

C. The observations are ranked and select the middle value for the population mean

D. There are no differences

126. Which of the following measures of central location is affected most by extreme values?

A. Median

B. Mean

C. Mode

D. Geometric mean

127. In which of the following distributions is the probability of a success usually small?

A. Binomial

B. Poisson

C. Hypergeometric

D. All distribution

128. Which of the following is not a requirement of a probability distribution?

A. Equally likely probability of a success

B. Sum of the possible outcomes is 1.00

C. The outcomes are mutually exclusive

D. The probability of each outcome is between 0 and 1

129 For a binomial distribution

A. *n* must assume a number between 1 and 20 or 25

B. p must be a multiple of .10

C. There must be at least 3 possible outcomes

D. None of the above

130. Events are independent if

A. By virtue of one event happening another cannot.

B. The probability of their occurrence is greater than 1.

C. We can count the possible outcomes.

D. The probability of one event happening does not affect the probability of another event happening.

E. None of the above.

131 . The Special Rule of Addition is used to combine

A. Independent events.

B. Mutually exclusive events

C. Events that total more than one.

D. Events based on subjective probabilities

E. Found by using joint probabilities.

132. We use the General Rule of Multiplication to combine

A. Events that is not independent.

B. Mutually exclusive events.

C. Events that total more than 1.00.

D. Events based on subjective probabilities

E. Found by using joint probabilities.

133 A nominal scale variable is

A. Cannot have more than two categories.

B. Has a meaningful zero point.

C. Usually the result of counting something

D. May assume negative values.

134. We wish to develop a confidence interval for the population mean. The shape of the population is not known, but we have a sample of 40 observations. We decide to use 92% level of confidence. The appropriate values of Z is:

A. 1.65

B. 1.96

C. 2.58

D. 1.75

135. Which of the following is a correct statement about a probability?

A. It may range from 0 to 1.

B. It may assume negative values.

C. It may be greater than 1.

D. It cannot be reported to more than 1 decimal place.

E. All the above are correct.

136. An experiment is a

A. Collection of events.

B. Collection of outcomes.

C. Always greater than 1.

D. The act of taking a measurement or the observation of some activity.

E. None of the above is correct.

137. Which of the following is not a type of probability?

A. Subjective

B. Independent

C. Relative frequency

D. Classical

138. We use the General Rule of Multiplication to combine

A. Mutually exclusive events

B. Events that is not independent

C. Events that total more than 1.00

D. Events based on subjective probabilities

139. Which of the following is not a type of probability?

A. Independent

B. Subjective

C. Relative frequency

D. Classical

140. Which of the following is a correct statement about probability?

A. It may assume negative values

B. It may range from 0 to 1

C. It may be greater than 1

D. It cannot be reported to more than 1 decimal place

141. The ratio scale of measurement

A. Is usually based on counting

B. Usually involves ranking

C. Has a meaningful zero point

D. Cannot assume negative values

1421. Which of the following statements is true regarding a population?

A. It must be a large number of values

B. It must refer to people

C. It is a collection of

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