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# Test answers for Statistics & Probability 2020

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Elance • Fin. & Mgt.

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`1. What is the median of: 5, 10, 15?`

• 5

• 9.5

• 10

• 15

`2. What is the most commonly used statistical measure of spread in a normally-distributed population?`

• covariance

• mean

• variance

• z-score

• standard deviation

`3. An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car buyers. The list includes 2,500 Ford buyers, 2,500 GM buyers, 2,500 Honda buyers, and 2,500 Toyota buyers. The analyst selects a sample of 400 car buyers, by randomly sampling 100 buyers of each brand.  Is this an example of a simple random sample?`

• Yes, because each buyer in the sample was randomly sampled.

• No, because every possible 400-buyer sample did not have an equal chance of being chosen.

• Yes, because car buyers of every brand were equally represented in the sample.

• Yes, because each buyer in the sample had an equal chance of being sampled.

`4. Which of the following statements are true? 1. Categorical variables are the same as qualitative variables. 2. Categorical variables are the same as quantitative variables. 3. Quantitative variables can be continuous variables.`

• 1 only

• 2 only

• 1 and 3 only

• 3 only

`5. Suppose c is a constant number. Calculate var(c).`

• c^2

• c

• c^2 - c

• c^2+c

• 0

`6. The variable X is the value of an uneven dice after one roll. It produced the following probability distribution P(X): P(1) = 0.05 P(2) = 0.28 P(3) = 0.12 P(4) = 0.23 P(5) = ? P(6) = ? What is the probability that X = 5 or X = 6?`

• 0.42

• 0.23

• 0.32

• 0.55

`7. Which of the following is a characteristic of an F-distribution?`

• Symmetric

• No no lower or upper bound

• Right Skewed

• Bimodal

`8. Symbolism: What does the x-bar represent (without any other symbols) in statistics?`

• Population standard deviation

• Sample standard deviation

• None of the other options

• Sample mean

• Population mean

`9. _____ are collections of observations.`

• Random variables

• Data

• Populations

• Expected values

`10. What is expected value?`

• All of the other choices, beside "no such thing"

• No such thing

• The maximum loss

• The probability of the next outcome

• Sum of all the possible outcomes * the probability of occurrence

`11. Experts rank athletic teams 1 through 10. This is an example of ______ data.`

• ordinal

• quantative

• discrete

• categorical

`12. What is the probability of rolling a fair dice and getting an even number and flipping a fair coin getting a head?`

• 0.25

• 0.75

• 0.5

• 0

`13. Symbolism: What does the small sigma represent (without any other symbols) in statistics?`

• Expected Value

• Mean

• Skewness

• Standard Deviation

• Variance

`14. What is true about these 5 numbers?  -10, -5, 0, 1, 2`

• The median and mean are equal to each other.

• Cannot compare means and medians.

• The mean is larger than the median.

• The median is larger than the mean.

`15. What is the skewness of a normal distribution?`

• 2

• 3

• 1

• 0

• 4

`16. You calculate the standard deviation of a data set and find that it is -1.23. From this you can determine which of the following is true?`

• Every value in the data set is the same.

• You made an arithmetic mistake because standard deviation cannot be negative.

• The mean must be negative.

• All of the values in the data set are negative.

`17. Where would the outliers be if a distribution had a skewness of +50?`

• Right

• Far right

• Far left

• Left

• No outliers

`18. What is the probability of rolling a fair dice and getting a 1 and flipping a fair coin getting a head?`

• 1/12

• 1/6

• 1/2

• 3/12

`19. How can you convert a variance to a standard deviation?`

• Variance = standard deviation

• Take the square root of the variance

• Square the variance

• Take the cubed root of the variance

• Take the log of the variance

`20. Suppose a fair die is tossed twice. What is the probability of rolling two fours?`

• 1/6/2013

• 2/6/2013

• 1/36

• 2/36

`21. What is the difference between the mean and the median?`

• Mean is not effected by skewness of the distribution

• Median is not affected by skewness of the distribution

• Both are always equal

• Mean is always greater than the Median

`22. Suppose E is an event in a sample space S with probability .3. What is the probability of the complement of E?`

• 1

• .7

• 0

• .3

`23. What is true about these 5 numbers?  -2, -1, 0, 5, 10`

• The median and mean are equal to each other.

• The median is larger than the mean.

• Cannot compare means and medians.

• The mean is larger than the median.

`24. Which of the following is not a measure of spread?`

• Upper Quartile

• Standard Deviation

• Variance

• Range

`25. The median grade on a midterm exam in a math class is 72. The teacher feels this is too low, so they award 10 extra points to every student in the class. What is the new median grade for the class?`

• 72

• 82

• Not enough information.

• 62

`26. The number of cars that went through a car wash during the noon hour over each of the past 8 days are the following: 5, 9, 2, 3, 3, 9, 8, 6 What is the range of this data?`

• 9

• 7

• 8

• 5.6

`27. A forestry researcher recorded many variables on the trees of a large forest. These variables include the height (in meters), the diameter (in centimeters), the species (pine, oak, etc.), and if the tree had Dutch Elm disease. In this study which variables that were recorded were quantitative?`

• Only species and height.

• Only height and diameter.

• All of the variables.

• Only height.

`28. Over the last 360 days of winter in Raleigh, NC (5 winters) we have had snow on 36 days. What is the probability that we will have snow on any random winter day this year?`

• 0.1

• 0.01

• 0.2

• 0.05

`29. Where would the outliers be if a distribution had a skewness of +1?`

• Left

• Right

• Far right

• No outliers

• Far left

`30. What power is used in the formula for variance?`

• 1

• 5

• 2

• 4

• 3

`31. Where would the outliers be if a distribution had a skewness of -50?`

• Far right

• No outliers

• Far left

• Right

• Left

`32. Your college professor standardizes everyone's test scores. Your standardized score is -1.35. Which of the following statements is true?`

• You scored within one standard deviation of the average test score.

• Your test score was above the average.

• Your test score was below the average.

`33. Discrete and continuous data are both forms of _______ data.`

• quantitative

• incomplete

• qualitative

• None of these

`34. Bob is a high school basketball player, who is a 72% free throw shooter. Bob has missed his first four free throws of the game. What is the probability that Bob makes his fifth free throw?`

• 90%

• 0%

• 72%

• 100%

`35. Using previous games to predict the score of a game is an example of ________ statistics.`

• inferential

• incomplete

• None of these

• descriptive

`36. What is the skewness of a normal distribution?`

• 3

• 1

• 2

• 0

• 4

`37. Two coins are tossed, what is the probability that two heads are obtained?`

• .5

• .75

• .25

• 0

• .125

`38. What is the probability of rolling a fair dice and getting an even number?`

• 1/6

• 1/3

• 4/6

• 1/2

`39. The average grade on a midterm exam in a math class is 72. The teacher feels this is too low, so they award 10 extra points to every student in the class. What is the new average grade for the class?`

• Not enough information.

• 72

• 82

• 62

`40. Let A be a normal distribution with a mean of 3 and B be a normal distribution with a mean of 17. What is the mean of A+B?`

• 17

• 51

• 3

• 20

• 14

`41. Which of the following is NOT a characteristic of a Normal distribution?`

• Unimodal

• Defined completely by mean and variance

• Symmetric

• Right Skewed

`42. You flip an unbiased coin 2 times - what is the probability of getting 2 heads?`

• 50%

• 25%

• Cannot determine

• 75%

• 100%

`43. The, "null hypothesis," refers to`

• that there is no relationship between two phenomena

• That there is a minor relationship between two phenomena

• That there is a significant relationship between two phenomena

• That the relationship depends on other factors

`44. True or false? Qualitative data is strictly numerical.`

• True

• False

`45. Which of the following is a measure of spread?`

• Mean

• Median

• Lower Quartile

• Range

`46. The Square of the standard deviation is called`

• Variance

• Covariance

• Mean

• Squared Distribution

`47. What is the median of the following 5 numbers?  1, 2, 3, 4, 10`

• 10

• 3

• 1

• 4

`48. A normal distribution generally takes the form of _______.`

• asymptote

• bell curve

• square ruit

• None of these

`49. Which of the following is quantitative data:`

• A list of song titles

• Test scores for English class

• A schedule of meetings

• A prescription written by a physician

`50. What is the average of the following 5 numbers?  1, 2, 3, 4, 10`

• 4

• 10

• 1

• 3

`51. What is the value of the middle observation in a ordered set of numbers`

• Mean

• Central Standard

• Mode

• Median

`52. A mean calculation is a part of _______ statistics.`

• Neither of these

• non-parametric

• parametric

`53. What is the mode of: 5, 10, 10, 15, 17?`

• 11.2

• 10

• 5

• 12

`54. The ______ describes the dispersion of a data set.`

• mean

• None of these

• median

• standard deviation

`55. Where would the outliers be if a distribution had a skewness of 0?`

• Right

• No outliers

• Left

• Far left

• Far right

`56. You flip an unbiased coin one time - what is the probability of getting tails?`

• 50%

• 100%

• 25%

• 75%

• Cannot determine

`57. The difference between the highest and lowest scores is called the ______.`

• sample

• mode

• range

• mean

`58. What is the mean of: 5, 10, 15?`

• 1

• 11

• 5

• 10

`59. How is P(A|B) interpreted?`

• The probability event A happens given that event B has happened

• The probability that event A or event B happens

• The probability event B happens given that event A has happened

• The probability event A happens given that event B did not happen

`60. If a data set follows a normal distribution, approximately ___% of data falls within 1 standard deviation of the mean.`

• 68%

• 25%

• 100%

• 0%

`61. Which plot is best use to display the relationship between a continuous dependent variable against a continuous independent variable`

• None of these

• Box Plot

• Bar Chart

• Scatter plot

• Histogram

`62. The variable X is the value of an uneven dice after one roll. It produced the following probability distribution P(X): P(1) = 0.05 P(2) = 0.28 P(3) = 0.12 P(4) = 0.23 P(5) = ? P(6) = ? What is the probability that X = 2 or X = 3?`

• 0.45

• 0.28

• 0.4

• 0.12

`63. The average price of a car in a used car lot is \$18,000. These prices are Normally distributed with a standard deviation of \$3,000. What is the probability that any random car is below \$18,000?`

• 95%

• 42%

• 68%

• 50%

`64. How do you calculate the Z-Score?`

• = standard error of the mean / standard deviation

• = observation + standard deviation / standard error of the mean

• = (observation - sample mean) / standard deviation

• = observation + standard deviation

• = observation - standard deviation

`65. A ______ is a numerical characteristic of a population`

• None of these

• constraint

• category

• parameter

`66. How can you convert a standard deviation to a variance?`

• Square the standard deviation

• Take the log of the standard deviation

• Take the square root of the standard deviation

• Take the cubed root of the standard deviation

• Variance = standard deviation

`67. What is the median of the following 5 numbers?  10, 2, 4, 3, 1`

• 1

• 3

• 4

• 10

`68. In a probability distribution, the second central moment can be another term for which of the following?`

• Variance

• Kurtosis

• Average

• Skewness

`69. Interpret an R-squared coefficient of .6 for a simple linear regression.`

• 60% of the variability in our dependent variable can be explained by our independent variable.

• This is an indicator that there must be a moderate positive correlation between both the dependent and independent variables.

• We can be 60% certain that there is a causal relationship between our dependent and independent variables.

• There is no interpretation for the R-squared value.

`70. Which one of these variables is a continuous random variable?`

• The number of correct guesses on a multiple choice test.

• The number of tattoos a randomly selected person has.

• The time it takes a randomly selected student to complete an exam.

• The number of women taller than 68 inches in a random sample of 5 women.

`71. What is the mean of a standard normal distribution?`

• 0

• 100

• 1

• 0.5

• 50

`72. Which of the following is an example of mutually exclusive events?`

• Being late to a meeting and being early to the same meeting

• Having one product off the assembly line be defective, but another product on that same assembly line work properly.

• Ordering a burger at a fast food restaurant and ordering fries at that same restaurant

• Having it rain on the same day that the sun comes out in the same city

`73. When does a Type I error occur?`

• There is no such term as a "Type I Error"

• You fail to reject the null hypothesis when it is false

• None of the other choices

• You reject the null hypothesis when it is true

• All of the other choices

`74. The probability of a discrete value in a continuous distribution is equal to __?`

• -1

• 0

• .99

• 0.5

• 1

`75. Which one of these variables is a binomial random variable?`

• number of women taller than 68 inches in a random sample of 5 women

• time it takes a randomly selected student to complete a multiple choice exam

• number of CDs a randomly selected person owns

• number of textbooks a randomly selected student bought this term

`76. _____ data is an example of nonmetric data.`

• Parametric

• Quantative

• Ordinal

• Sample

`77. What is derived from the second moment of distribution?`

• Pearson's Coefficient of Kurtosis

• Mean

• Skewness

• Variance

• Kurtosis

`78. What is the formula for the variance of a population?`

• SUM((( - sample mean)^3) / Number of observations)

• SQRT( SUM)((x - sample mean)^2) / Number of observations))

• SQRT( SUM(((x - sample mean)^3) / Number of observations))

• SUM(((observation - sample mean)^2) / Number of observations)

• SUM((observation - sample mean) / Number of observations)

`79. Suppose E and F are mutually exclusive events in a sample space S with probabilities .4 and .3 respectively. What is the probability of their union?`

• .7

• .1

• .4

• .3

`80. A bag contains 4 balls (2 red and 2 blue). You pull out one ball at a time without replacement.  What is the probability that the fourth ball chosen is a red ball?`

• 5/12

• 7/12

• 2/3

• 9/16

• 1/2

`81. Which of the following would be appropriate for a z-test?`

• Determining whether regular exercise decreases the number of new heart disease cases by more than 10% in a year

• Determining whether the life expectancy of women in a population is statistically different from that of men

• Determining if a small set of pieces of oak firewood burn longer than pine firewood

`82. Which of the following statements are true about confidence intervals for means? 1. The center of the confidence interval is always 0. 2. The bigger the confidence interval, the smaller the margin of error. 3. The bigger your sample, the smaller the margin of error.`

• 3 only

• 2 only

• 1 only

• 1 and 2 only

`83. The center line inside a box plot typically represents the _____ in any instance.`

• Inter-quartile Range

• Median of the distribution

• 2nd Percentile

• Average of the distribution

`84. Suppose you have generated this model to predict income: Income = 10 + .5(Years of Education), units are in thousands, ie 10.5 = \$10,500. Interpret Beta1.`

• At 5 years of education, income is expected to be \$25,000.

• For every additional year of education, income is expected to increase by \$10,500.

• At zero years of education, income is expected to be \$10,000.

• For every additional year of education, income is expected to increase by \$500.

`85. A manager of a large bank wants to compute the average interest rates across all bonds that the bank invests in. The manager randomly sampled 127 bonds that the bank invests in and calculated the average interest rate over the past year of the sample was 2.47%. What is the parameter of interest in this study?`

• The average interest rate of all bonds that the bank invests in.

• 2.47%

• All bonds that the bank invests in.

• The 127 bonds used in the calculation.

`86. What is the first moment of distribution?`

• Standard Deviation

• Mean

• Kurtosis

• Skewness

• Variance

`87. The preseason odds that the Hartford Whalers will win The Stanley Cup Championship are 1/4, and the odds are the same for the California Golden Seals.  What is the probability that BOTH will win the championship?`

• 1/4 = 0.25

• 0

• 1/16 = 0.0625

• 1/2 = 0.5

• 7/16 = 0.4375

`88. If you have a hypothesis test with a significance level of 0.05 and a p-value of 0.01, what is the result of your hypothesis test?`

• You fail to reject the null hypothesis

• You accept the null hypothesis

• Not enough information.

• You reject the null hypothesis

`89. Say 2 events satisfy the following equation: P(A intersect B) = P(A) x P(B). We say that events A and B are __.`

• Dependent

• Disjoint

• Independent

• Mutually exclusive

`90. C(n,r) is equal to...`

• n!r!

• n!/(r!(n-r)!)

• n!/r!

• n!/(n-r)!

`91. Which of the following examples involves paired data?`

• A group of 50 students had their blood pressures measured before and after watching a movie containing violence. The mean blood pressure before the movie was compared with the mean pressure after the movie.

• A study compared the average number of courses taken by a random sample of 100 freshmen at a university with the average number of courses taken by a separate random sample of 100 freshmen at a community college.

• None of the above.

• A group of 100 students were randomly assigned to receive vitamin C (50 students) or a placebo (50 students). The groups were followed for 2 weeks and the proportions with colds were compared.

`92. The median grade on a midterm exam in a math class of 60 students is 85. The teacher gives an additional 5 bonus points to the 3 students who scored the highest on the exam. What is the new median grade for the class?`

• 90

• 80

• 85

• Not enough information.

`93. P(n,r) is equal to...`

• n!r!

• n!/(r!(n-r)!)

• n!/(n-r)!

• n!/r!

`94. Symbolism: What does the Greek letter mu represent (without any other symbols) in statistics?`

• Sample standard deviation

• Sample mean

• Population mean

• Population standard deviation

• None of the other options

`95. In hypothesis testing, which of the following statements is always true?`

• The P-value is computed from the significance level.

• The P-value is the parameter in the null hypothesis.

• The P-value is a test statistic.

• The P-value is a probability.

`96. What is the cumulative probability at +1 standard deviation, for a random variable with normal distribution?`

• 50.00%

• 34.13%

• 2.28%

• 84.13%

• 15.87%

`97. A card is drawn randomly from an ordinary deck of playing cards. You win a prize if the card is a heart or the card is an ace. What is the probability that you will win the prize?`

• 1/13

• 16/52

• 13/52

• 17/52

`98. Which of the following is A test of normality?`

• Time Series Test of Normality

• Test of Data Normality

• Kolmogrov-Smirnov Test of Normality

• The Standard Test of Normality

• Marx's Test of Normality

`99. When do you fail to reject the null hypothesis?`

• P-Value is < alpha (level of significance)

• P-Value is > alpha (level of significance)

`100. Find the z-score: mean = 6, standard dev. = 2, observation = 7`

• -.5

• .5

• -1.5

• 1.5

`101. P(A)*P(B)=P(A and B) What can you conclude about A and B?`

• They are neither independent nor mutually exclusive.

• They are independent.

• They are mutually exclusive.

• They are independent and mutually exclusive.

`102. What is derived from the third moment of distribution?`

• Standard Deviation

• Variance

• Kurtosis

• Mean

• Skewness

`103. For a random variable X, E[X]=3 and E[X^2]=14. Var[X]=?`

• 0

• 17

• 5

• 23

• 11

`104. Suppose E and F are events in a sample space S. Suppose further that E has probability .2, F has probability .6, and the intersection of E and F has probability .1. What is the probability of the union of E and F?`

• .8

• .7

• .68

• .6

`105. The variance of X is 15. Y=X+5. What is the Variance of Y?`

• 20

• 17.5

• 15

• 40

• Not enough information to determine the Variance of Y.

`106. What power is used in the formula for skewness?`

• 4

• 3

• 5

• 2

• 1

`107. What are the characteristics of the f-distribution.`

• It is skewed to the right, and we can only use it to perform one-tailed tests.

• It is skewed to the left, and we can perform two-tailed tests.

• It is skewed to the right, and we can perform two-tailed tests.

• It is normally distributed, and we can perform two-tailed tests.

`108. Suppose A is always 3. Var(B)=4. What is Var(A+B)?`

• 13

• Not enough information.

• 7

• 0

• 4

`109. Which of the following is NOT a commonly used estimator in determining the parameters of an unknown probability density function?`

• Method of moments

• Cram??r???Rao bound

• Bayes least squared error

• Fourier transform

• Maximum likelihood

`110. Suppose E and F are mutually exclusive events in a sample space S. Suppose further that E has probability .3 and F has probability .4. What is the probability of the intersection of E and F?`

• .3

• .7

• 0

• .12

`111. What is the kurtosis of a normal distribution?`

• 2.5

• 3.5

• 3

• 4.5

• 4

`112. Where would the outliers be if a distribution had a skewness of -1?`

• Left

• Down

• Right

• No outliers

• Up

`113. Suppose E and F are events in a sample space S. Suppose further that E has probability .8 and F has probability .9. What is the largest possible value for the probability of the intersection of E and F?`

• .7

• .9

• .8

• .2

`114. For an airline, many times small cities have limited flights that go into their airports. To get a flight to Columbia, SC you must go through one of three cities: Raleigh, NC, Atlanta, GA, or Charlotte, NC. Two customers from Orlando, FL are trying to get to Columbia, SC with only one stop (one of the three above mentioned cities). Assume that they are equally likely to go through any of the above cities. What is the probability neither of the customers fly through Charlotte, NC?`

• 1/3

• 2/9

• 4/9

• 2/3

`115. C(n,0) = C(n,n)`

• False

• True

`116. Which of the following would be appropriate for ANOVA?`

• Determining whether an anti-cancer drug increases the number of patients who survive more than one year

• Determining whether the average food delivery time from restaurant A is shorter than restaurant B

• Determining whether the percentage of female voters is statistically different than the prior year.

• Determining which of several training programs yields the highest mean performance score on the exit exam

`117. What is the probability that two six-sided dice will roll the same number?`

• 1/12

• 1/6

• 1/10

• 1/36

• None of these

`118. What is the expected value of rolling an unbiased die (6 sided)?`

• 2.5

• 3.5

• 1.5

• 4.5

• 3.0

`119. If I tossed a fair coin 3 times, what is the probability of it landing on tails only once?`

• 1/8

• 1/2

• 3/8

• 1/4

`120. What is the probability of rolling a seven on two six-sided dice?`

• 1/10

• 1/6

• 1/7

• None of these

• 1/12

`121. Let X follow a Poisson distribution with a rate parameter of 7. What is Var(X)?`

• 1

• 1/49

• 7

• 1/7

• 49

`122. What is a Type II error?`

• Failure to reject the alternative hypothesis when it is true

• Rejecting the null hypothesis when it is true

• Rejecting the alternative hypothesis when it is true

• Failure to reject the null hypothesis when it is false

• Failure to reject the alternative hypothesis when it is false

`123. What is homoskedastic?`

• There is no adjustment factor (e.g. epsilon)

• The adjustment factor doesn't change (e.g. epsilon)

• I do not know

• The adjustment factor changes (e.g. epsilon)

`124. What is synonymous with the coefficient of determination?`

• CV

• R-Squared

• R

• Sigma

• Mu

`125. In a multiple regression model, what is the best way to test the joint significance of the independent variables?`

• Multiple T-tests

• Nested F-test

• Z-test

• Comparison of P-values in the model

`126. How do you calculate the standard error of the mean? (obs. = observations, sqrt = Square Root)`

• Variance / number of obs.

• Sqrt(Variance/sqrt(number obs.))

• Standard deviation/ sqrt(number of obs.)

• Sum(obs. - mean)^2 / (number of obs.)

`127. What is synonymous with the correlation coefficient?`

• Sigma

• R-Squared

• CV

• Mu

• R

`128. For an airline, many times small cities have limited flights that go into their airports. To get a flight to Columbia, SC you must go through one of three cities: Raleigh, NC, Atlanta, GA, or Charlotte, NC. Two customers from Orlando, FL are trying to get to Columbia, SC with only one stop (one of the three above mentioned cities). Assume that they are equally likely to go through any of the above cities. What is the probability one of the customers fly through Charlotte, NC, while the other does not fly through Charlotte, NC?`

• 4/9

• 1/3

• 2/3

• 2/9

`129. Chi-square is used predominantly in _______ statistics.`

• non-parametric

• parametric

• none of these

• descriptive

`130. The variance of X is 3. Y=3X. What is the variance of Y?`

• 3

• Not enough information.

• 27

• 9

• 1

`131. Which should you use to analyze a continuous dependent variable against a categorical independent variable?`

• Logistics Regression

• Linear Probability Model

• ANOVA

• Probit Regression

`132. Which statistic is not a measure of effect size?`

• F-statistic

• omega squared

• partial omega squared

• Eta squared

• R squared

`133. What formula is used to determine the probability of a series of outcomes WITH replacement?`

• Cumulative probability

• Hypergeometric

• Gamma distribution probability

• Gaussian or Cumulative probability

• Gaussian probability

`134. A survey was conducted to find the average weight of students living in the dorms or a university. To help improve the accuracy of the study, an equal number of students were randomly selected from each dorm for the sample. This sample is an example of what?`

• Simple Random Sample

• Stratified Random Sample

• Block Design

• Experiment

`135. What does R^2 (R-Squared) calculate?`

• The squared covariance

• The point where the regression crosses the Y axis

• The slope of the regression

• The closeness of a regression to the underlying data

• The coefficient of variation^2

`136. Which of the following numbers (measures of kurtosis of a distribution) would represent a platykurtic distribution?`

• 3.5

• 2

• 10

• 20

• 3

`137. What is the coefficient of variation?`

• Mean^2

• Kurtosis minus standard deviation

• Normalized measure of dispersion of a probability distribution

• Standard Deviation

• Skewness + Kurtosis

`138. A coin is tossed three times. What is the probability that it lands on heads exactly one time?`

• 0.125

• 0.500

• 0.250

• 0.375

• 0.333

`139. Suppose E and F are independent events in a sample space S. Suppose further that E has probability .3 and F has probability .4. What is the probability of the intersection of E and F?`

• .12

• 0

• .7

• 1

`140. The variance of X is 5 and the variance of Y is 8. What is the variance of X+Y?`

• 18

• 13

• 15

• Not enough information.

• 8

`141. Which of the assumptions is not one of the assumptions for creating a linear regression model (ie. Gauss-Markov Assumptions)?`

• The distribution of the residuals should have a mean of zero.

• The model estimating the dependent variable must have independent variables that are linear in parameters.

• The residuals must have a variance that depends on the values in the explanatory variable.

• There must exist a method of random sampling in order for our model to have any internal and external validity.

`142. P(X|Y)=.5 P(X)=.2 P(Y)=.4 What is P(X and Y),`

• .4

• .1

• .8

• .08

• .2

`143. What power is used in the formula for kurtosis?`

• 5

• 3

• 4

• 2

• 1

`144. A card is drawn randomly from a deck of ordinary playing cards. You win \$10 if the card is a spade or an ace. What is the probability that you will win money from playing the game once?`

• None of these.

• 1/13

• 4/13

• 17/52

• 13/52

`145. What is another form of expressing beta1 in a simple linear regression? y=dependent variable x=independent variable`

• cov(xy)/var(x)

• var(x)^2/var(x)var(y)

• cov(xy)/var(y)

• E(x)-E(x)^2

`146. Which of the following numbers (measures of kurtosis of a distribution) would represent a leptokurtic distribution?`

• 4

• 1

• 3

• 0

• 2

`147. Which of the following would be appropriate for a t-test?`

• Determining if a group of people who slept 4 hours before a test will score lower than a group of people who slept 8 hours before a test.

• Determining which of several medicines has the greatest effect on cell growth

• Determining whether the weight of all male golden eagles in a population is statistically different from that of female eagles

• Determining whether an anti-cancer drug increases the number of patients who survive more than one year

`148. Which of these linear regression models is quadratic?`

• Y = B0 + B1(X1)^2

• Y = B0 + B1X1 + B2(X1)^2

• Y = B0 + B1(X1*X2)^2

• Y = B0 + B1X1 + B2(X2)^2

`149. What is the probability that a coin will land on the same side when flipped twice?`

• .5

• .125

• .25

• .66

• .33

`150. Event A and Event B are independent and mutually exclusive.  True or False:  The probability of A must be 0 or the probability of B must be 0.`

• True

• False

`151. Suppose E and F are events in a sample space S. Suppose further that E has probability .3, F has probability .4, and the intersection of E and F has probability .2. Find the probability of the intersection of E and (the complement of F).`

• .1

• .2

• .3

• 0

`152. Suppose E and F are events in a sample space S. Suppose further that E has probability .8 and F has probability .9. What is the smallest possible value for the probability of the intersection of E and F?`

• .7

• .1

• .8

• .9

`153. Suppose X and Y are independent random variables. The variance of X is equal to 16; and the variance of Y is equal to 9. Let Z = X - Y.  What is the standard deviation of Z?`

• 7

• 5

• 25

• Not enough information to be able to answer the question.

• 2.65

`154. P(A|B)=.6 P(A)=.3 P(B)=.4 What is P(B|A)?`

• .8

• .60

• .75

• .90

• .45

`155. What is the probability of drawing an Ace from a deck of cards that includes the two Jokers?`

• 1/54

• 2/27

• 1/13

• 1/14

• None of these

`156. What is the cumulative probability at -1 standard deviation for a normal distribution?`

• 34.13%

• 84.13%

• 15.87%

• 2.28%

• 50.00%

`157. What is the formula for the Pearsonian Coefficient of Skewness?`

• 3*(population mean - population mode) / Variance

• 5*(population mean - population mode) / Standard deviation

• 5*(population mean - population mode) / Variance

• 2*(population mean - population mode) / Variance

• 3*(population mean - population mode) / Standard deviation

`158. Which of the following is NOT essential for multiple regression modeling?`

• There must be no perfect collinearity among independent variables.

• The model must be linear in parameters.

• The sample population must be derived from a normally distributed population.

• There must be more observations than independent variables to have enough degrees of freedom to make estimates.

`159. Suppose E and F are events in a sample space S. Suppose further that E has probability .5, F has probability .6, and the intersection of E and F has probability .2. Find the probability of the union of E and (the complement of F).`

• .3

• .8

• .6

• .5

`160. Suppose E and F are independent events in a sample space S. Suppose further that E has probability .3 and F has probability .4. What is the probability of the union of E and F?`

• .58

• .7

• .4

• .12

`161. Is it true that nCr = nC(n-r) ?`