OPRE 6301 - 3

If two events are independent, what is the probability that they both occur? 0 0.50 1.00 Cannot be determined from the information given

Cannot be determined from the information given

If an experiment consists of five outcomes with P(O1) = 0.10, P(O2) = 0.20, P(O3) = 0.30, P(O4) = 0.15, then P(O5) is 0.75 0.25 0.50 Cannot be determined from the information given.

Cannot be determined from the information given.

If P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.25, then P(A|B) is: 1.4 1.8 0.714 0.556

0.556

If cov(x, y) = 20, S2,x = 15 s2,y = 49 then the sample coefficient of correlation r is:

0.714

If P(A) = 0.65, P(B) = 0.58, and P(A and B) = 0.26, then P(A or B) is: 1.23 0.97 0.18 0.11

0.97

Suppose P(A) = 0.50, P(B) = 0.75, and A and B are independent. The probability of the complement of the event (A and B) is: .5 × .25 = .125 0.50 + .25 = .75 1 − (.50 + .25) = .25 1 − (.5 × .75) = .625

1 − (.5 × .75) = .625

If the two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs? 0.00 0.50 1.00 Cannot be determined from the information given.

1.00

If two events are collectively exhaustive, what is the probability that one or the other occurs? 0.00 0.50 1.00 Cannot be determined from the information given.

1.00

The probability of the union of two mutually exclusive events A and B is 0.

False - not necessarily exhaustive.

P(A) + P(B) = 1 for any events A and B that are mutually exclusive.

False - they might not be exhaustive

Which of the following statements about the mean is not always correct? The sum of the deviations from the mean is zero. Half of the observations are on either side of the mean. The mean is a measure of the central location. The value of the mean times the number of observations equals the sum of all observations.

Half of the observations are on either side of the mean.

A sample of 20 observations has a standard deviation of 3. The sum of the squared deviations from the sample mean is: 20. 23. 29. 171.

171.

The interquartile range is the difference between the: largest and smallest numbers in the data set. 25th percentile and the 75th percentile. median and the mean. None of these choices.

25th percentile and the 75th percentile.

The average score for a class of 30 students was 75. The 20 male students in the class averaged 70. The 10 female students in the class averaged: 75. 85. 65. 70.

85.

The Empirical Rule states that the approximate percentage of measurements in a data set (providing that the data set has a bell shaped distribution) that fall within two standard deviations of their mean is approximately: 68%. 75%. 95%. 99%.

95%.

Which measures of central location and variability are considered to be resistant to extreme values? The mean and standard deviation. The mode and variance. The median and interquartile range. None of these choices.

The median and interquartile range.

If the observations are in the millions, a standard deviation of 10 would be considered small. If the observations are all less than 50, a standard deviation of 10 would be considered large.

True

In a bell shaped distribution, there is no difference in the values of the mean, median, and mode.

True

Quartiles divide the observations in a data set into four parts with the same amount of data in each part.

True

Suppose the probability that a person owns both a cat and a dog is 0.10. Also suppose the probability that a person owns a cat but not a dog is 0.20. The marginal probability that someone owns a cat is 0.30.

True

The standard deviation is expressed in terms of the original units of measurement but the variance is not.

True

You think you have a 90% chance of passing your next advanced financial accounting exam. This is an example of subjective approach to probability.

True

μ is a population parameter and is a sample statistic.

True

The collection of all possible outcomes of an experiment is called: a simple event a sample space a sample a population

a sample space

If the correlation coefficient r = 1.00, then all the observations must fall exactly on: a straight line with a slope that equals 1.00. a straight line with a negative slope. a straight line with a positive slope. a horizontal straight line with a zero slope.

a straight line with a positive slope.

The length of the box in the box plot portrays the: A.median B.interquartile range C.range D.standard deviation

interquartile range

The length of the box in the box plot portrays the: median. interquartile range. range. third quartile.

interquartile range.

The probability of the intersection of two events A and B is denoted by P(A and B) and is called the: marginal probability joint probability conditional probability of A given B conditional probability of B given A

joint probability

Which of the following is a property of r, the coefficient of correlation? r always lies between 0 and 1. r has no units. If you switch the values of X and Y, the sign of r changes. All of these choices are true.

r has no units.

The distance between the 25th percentile and the median is always the same as the distance between the median and the 75th percentile.

False

The value of the standard deviation may be either positive or negative, while the value of the variance will always be positive.

False

When the standard deviation is expressed as a percentage of the mean, the result is the coefficient of correlation.

False

A and B are disjoint events, with P(A) = 0.20 and P(B) = 0.30. Then P(A and B) is: 0.50 0.10 0.00 0.06

0.00

If two events are mutually exclusive, what is the probability that both occur at the same time? 0.00 0.50 1.00 Cannot be determined from the information given.

0.00

In a perfectly symmetric bell shaped "normal" distribution: the mean equals the median. the median equals the mode. the mean equals the mode. All of these choices are true.

All of these choices are true.

Which of the following is a measure of variability? The interquartile range The variance The coefficient of variation All of these choices are true.

All of these choices are true.

Which of the following statements is true regarding the data set 8, 8, 8, 8, and 8? The range equals 0. The standard deviation equals 0. The coefficient of variation equals 0. All of these choices are true.

All of these choices are true.

Assume that A and B are independent events with P(A) = 0.30 and P(B) = 0.50. The probability that both events will occur simultaneously is 0.80.

False

If two variables do not demonstrate any positively or negatively linear association, then these two variables must be independent.

False

Which of the following best describes the concept of marginal probability? It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs. It is a measure of the likelihood that a particular event will occur, if another event has already occurred. It is a measure of the likelihood of the simultaneous occurrence of two or more events. None of these choices.

It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs.

If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then P(A or B) is: 0.10 0.12 0.70 None of these choices

None of these choices

In a negatively skewed distribution, which of the following is the correct statement? The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3 The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation The distance from the smallest observation to Q2 is smaller than the distance from Q2 to the largest observation The distance from Q1 to Q3 is twice the distance from the Q1 to Q2

The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation

Which of the following statements is true for the following observations: 7, 5, 6, 4, 7, 8, and 12? The mean, median and mode are all equal. Only the mean and median are equal. Only the mean and mode are equal Only the median and mode are equal.

The mean, median and mode are all equal.

Which of these measures of central location is not sensitive to extreme values? The mean The median The mode All of these choices are true.

The median

Bayes' Law is a formula for revising an initial subjective (prior) probability value on the basis of new results, thus obtaining a new (posterior) probability value.

True

If A and B are independent events with P(A) = .40 and P(B) = .50, then P(A and B) = .20.

True

If the coefficient of correlation r = −.81, the standard deviations of x and y are 20 and 25, respectively, then cov(x, y) must be −405.0.

True

If the distribution of a data set were perfectly symmetric, the distance from Q1 to the median would always equal the distance from Q3 to the median in a box plot.

True

If A and B are mutually exclusive events with P(A) = 0.70, then P(B): can be any value between 0 and 1. can be any value between 0 and 0.70. cannot be larger than 0.30. equals 0.30.

cannot be larger than 0.30.

The strength of the linear relationship between two interval variables can be measured by the: coefficient of variation. coefficient of correlation. slope of the regression line. Y-intercept.

coefficient of correlation.

In a histogram, the proportion of the total area which must be to the left of the median is: exactly 0.50. less than 0.50 if the distribution is negatively skewed. more than 0.50 if the distribution is positively skewed. unknown.

exactly 0.50.

If two data sets have the same range: the distances from the smallest to largest observations in both sets will be the same. the smallest and largest observations are the same in both sets. both sets will have the same standard deviation. both sets will have the same interquartile range.

the distances from the smallest to largest observations in both sets will be the same.