Applied Economic Statistics

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T/F The sum of all the probabilities of simple events in a sample space equals one.
True
T/F Grandma's predicting rain based on how much her arthritis is acting up is an example of the classical view of probability.
False
T/F Independent events are mutually exclusive.
False
T/F If events A and B are dependent, it can be concluded that one event causes the other.
False
T/F The probability of A and its complement (A´) will always sum to one.
True
T/F The general law of addition for probabilities says P(A or B) = P(A) P(B).
False
T/F When two events A and B are independent, the probability of their intersection can be found by multiplying their probabilities.
True
T/F Two events are mutually exclusive when they contain no outcomes in common.
True
T/F The union of two events is all outcomes in either or both, while the intersection is only those events in both.
True
T/F Baye's Theorem shows how to revise a prior probability to obtain a conditional or posterior probability when another event's occurrence is known.
True
T/F A contingency table is a cross-tabulation of frequencies for two categorical variables.
True
T/F A random variable is a function or rule that assigns a numerical value to each outcome in the sample space of a stochastic (chance) experiment.
True
T/F A discrete random variable has a countable number of distinct values.
True
T/F The expected value of a discrete random variable E(X) is the sum of all X values weighted by their respective probabilities.
True
T/F The Poisson distribution describes the number of occurrences within a randomly chosen unit of time or space.
True
T/F Although the shape of the Poisson distribution is positively skewed, it becomes more nearly symmetric as its mean becomes larger.
True
T/F The hypergeometric distribution is not applicable if sampling is done with replacement.
True
T/F The gender of a randomly chosen unborn child is a Bernoulli event.
True
T/F The expected value of a random variable is its mean.
True
T/F The Poisson distribution has only one parameter.
True
Events A and B are mutually exclusive when:
A) their joint probability is zero
B) they are independent events
C) P(A)P(B) = 0
D) P(A)P(B) = P(A | B)
A) their joint probability is zero
Regarding the rules of probability, which of the following statements is correct?

A) If A and B are independent events, then P(B) = P(A)P(B).
B) The sum of two mutually exclusive events is one.
C) The probability of A and its complement will sum to one.
D) If event A occurs, then its complement will also occur.
C) The probability of A and its complement will sum to one.
Information was collected on those who attended the opening of a new movie. The analysis found that 56 percent of the moviegoers were female, 26 percent were under age 25, and 17 percent were females under the age of 25. Find the probability that a moviegoer is either female or under age 25.

A) .79
B) .82
C) .62
D) .89
B) .82
A company is producing two types of ski goggles. Thirty percent of the production is of type A, and the rest is of type B. Five percent of all type A goggles are returned within 10 days after the sale, whereas only two percent of type B are returned. If a pair of goggles is returned within the first 10 days after the sale, the probability that the goggles returned are of type B is:

A) .014
B) .140
C) .070
D) .483
D) .483
The manager of Ardmore Pharmacy knows that 25 percent of the customers entering the store buy prescription drugs, 65 percent buy over-the-counter drugs, and 18 percent buy both types of drugs. What is the probability that a randomly selected customer will buy at least one of these two types of drugs?

A) .90
B) .85
C) .72
D) .65
C) .72
If four items are chosen at random without replacement from seven items, in how many ways can the four items be arranged, treating each arrangement as a different event (i.e., if order is important)?

A) 35
B) 840
C) 5040
D) 24
B) 840
A discrete probability distribution:

A) is a listing of all possible values of the random variable
B) assigns a probability to each possible value of the random variable.
C) can assume values between -1 and +1.
D) none of the above
B) assigns a probability to each possible value of the random variable.
Which distribution is most nearly appropriate to describe the number of fatalities in Texas in a given year due to poisonous snakebites?

A) Binomial
B) Poisson
C) Hypergeometric
D) Geometric
B) Poisson
A die is rolled. If it rolls to a 1, 2, or 3 you win $2. If it rolls to a 4, 5, or 6 you lose $1. Find the expected winnings.

A) $0.50
B) $3.00
C) $1.50
D) $1.00
A) $0.50
A carnival has a game of chance: a fair coin is tossed. If it lands heads you win $1.00 and if it lands tails you lose $0.50. How much should a ticket to play this game cost if the carnival wants to break even?

A) $0.25
B) $.50
C) $.75
D) $1.00
A) $0.25
On average, a major earthquake (Richter scale 6.0 or above) occurs three times a decade in a certain California county. Find the probability that at least one major earthquake will occur within the next decade.

A) .7402
B) .1992
C) .1494
D) .9502
C) .1494
Jankord Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks. Typically, 10 percent are returned. If eight rings are sold today, what is the probability that fewer than three will be returned?

A) .9950
B) .9619
C) .0331
D) .6780
B) .9619
The probability that a visitor to an animal shelter will adopt a dog is .20. Out of nine visits, what is the probability that at least one dog will be adopted?

A) .8658
B) .3020
C) .5639
D) .1342
A) .8658
A random variable is binomially distributed with n = 16 and π = .40. The expected value and standard deviation of the variables are:

A) 2.00 and 1.24
B) 4.80 and 4.00
C) 6.40 and 1.96
D) 2.00 and 1.
C) 6.40 and 1.96
All of the following are characteristics of the normal distribution, except:

A) it is symmetric
B) it is bell shaped
C) area under the curve is a
D) it is a discrete distribution
D) it is a discrete distribution
Light bulbs are normally distributed with an average lifetime of 1000 hours and a standard deviation of 250 hours. The probability that a light bulb picked at random will last less than 1500 hours is about:

A) 97.72 percent.
B) 95.44 percent
C) 75.00 percent.
D) 68.00 percent.
A 97.72 percent.
A random variable X is best described by a continuous uniform distribution from 20 to 45 inclusive. The mean of this distribution is:

A) 30.5
B) 31.5
C) 32.5
D) 33.5
C) 32.5
If arrivals occur at a mean rate of 3.6 events per hour, the exponential probability of waiting less than 0.5 hour for the next arrival is:

A) .7122
B) .8105
C) .8347
D) .7807
C) .8347
The price-earnings ratio for firms in a given industry follows the normal distribution. In this industry, a firm whose price-earnings ratio has a standardized value of z = 1.00 is approximately in the highest ______ percent of firms in the industry.

A) 16 percent
B) 34 percnt
C) 68 percent
D) 75 percent
A) 16 percent
T/F A continuous uniform distribution is always symmetric
True
T/F The mean, median, and mode of a normal distribution will always be the same.
True
T/F Any normal distribution has a mean of 0 and a standard deviation of 1.
False
T/F Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data.
True
T/F Inferential statistics refers to generalizing from a sample to a population, estimating unknown parameters, drawing conclusions, and making decisions.
True
T/F Descriptive statistics refers to summarizing data rather than generalizing about the population
True
T/F A strong correlation between A and B would imply that B is caused by A
False
T/F In last year's annual report, Thompson Distributors indicated that it had 12 regional warehouses. This is an example of ordinal level data.
False
T/F Judgment sampling and convenience sampling are non-random sampling techniques
True
T/F Ratio data are distinguished from interval data by the presence of a zero reference point.
True
T/F The number of checks processed at a bank in a day is an example of categorical data.
False
T/F Your weight recorded at your annual physical would not be ratio data because you cannot have zero weight.
False
T/F Internet surveys posted on popular websites have no bias since anyone can reply
False
T/F Log scales are common because most people are familiar with them
False
T/F A pie chart can generally be used instead of a bar chart.
False
T/F Sturges' Rule is merely a suggestion, not an ironclad requirement
True
T/F The second quartile is the same as the median.
True
T/F Given the data set 10, 5, 2, 6, 3, 4, 20, the median value is 5.
True
T/F When data are right-skewed, we expect the median to be greater than the mean.
False
T/F The sum of the deviations around the mean is always zero
True
T/F The Empirical Rule can be applied to any distribution, unlike Chebyshev's theorem.
False
T/F A data set with two values that are tied for the highest number of occurrences is called bimodal
True
T/F The Empirical Rule assumes that the distribution of data follows a normal curve.
True
The NASA experiences with the Challenger and Columbia disasters suggest that:

A) statistics is not applicable to space endeavors
B) limited data may still contain important clues.
C) good engineers can eliminate risks in space flight
D) space flight is only slightly more risky than commercial air travel
B) limited data may still contain important clues.
"Bob didn't wear his lucky T-shirt to class, so he failed his chemistry exam." This best illustrates which fallacy?

A) Small sample generalization
B) Poor survey methods
C) Post hoc reasoning
D) More than one of the above
C) Post hoc reasoning
An investment firm rates bonds for AardCo Inc. as "B+" while bonds of Deva Corp. are rated "AA." Which level of measurement would be appropriate for such data?

A) Nominao
B) Ordinal
C) Interval
D) Ratio
B) Ordinal
An advantage of convenience samples is that:

A) the required sample size is easier to calculate
B) sampling error can be reduced
C) computation of statistics is easier
D) they are often quicker and cheaper.
D) they are often quicker and cheaper.
Thirty work orders are selected from a filing cabinet containing 500 work order folders by choosing every 15th folder. Which sampling method is this?

A) Simple random sample
B) Systematic sample
C) Stratified sample
D) Cluster sample
B) Systematic sample
A random sample is one in which the:

A) probability that an item is selected for the sample is the same for all population items.
B) population items are selected haphazardly by experienced workers
C) items to be selected from the population are specified based on expert judgment.
D) probability of selecting a population item depends on the item's data value.
A) probability that an item is selected for the sample is the same for all population items.
When we are choosing a random sample and we do not place chosen units back into the population, we are:

A) sampling with replacement
B) sampling without replacement
C) using a systematic sample.
D) using a voluntary sample.
B) sampling without replacement
The width of a class in a frequency distribution is known as the:

A) midpoint.
B) class limit
C) bin frequency
D) class interval
D) class interval
A histogram can be defined as:

A) a chart whose bar widths show the cumulative frequencies of data values.
B) a chart whose bar widths indicate class intervals and whose areas indicate frequencies
C) a chart whose bar widths show class intervals and whose heights indicate frequencies.
D) a chart whose bar heights represent the value of each data point.
C) a chart whose bar widths show class intervals and whose heights indicate frequencies.
Consider the following data: 6, 7, 17, 51, 3, 17, 23, and 69. The range and the median are:

A) 69 and 17.5
B) 66 and 17.5.
C) 66 and 17.
D) 69 and 17.
C) 66 and 17.
In the following data set {7, 5, 0, 2, 7, 15, 5, 2, 7, 18, 7, 3, 0}, the value 7 is:

A) the mean
B) the mode
C) both the mean and mode
D) both the median and mode
B) the mode
Three randomly chosen Colorado students were asked how many times they went rock climbing last month. Their replies were 5, 6, 7. The coefficient of variation is:

A) 16.7 percent
B) 13.6 percent
C) 20.0 percent
D) 35.7 percent
A) 16.7 percent
Three randomly chosen Colorado students were asked how many times they went rock climbing last month. Their replies were 5, 6, 7. The standard deviation is:

A) 1.212
B) 0.816
C) 1.000
D) 1.056
C) 1.000
Five homes were recently sold in Oxnard Acres. Four of the homes sold for $400,000 while the fifth home sold for $2.5 million. Which measure of central tendency best represents a typical home price in Oxnard Acres?

A) The mean or median
B) The median or mode
C) The mean or mode.
D) The midrange or mean
B) The median or mode
Which is a characteristic of the mean as a measure of center?

A) Deviations do not sum to zero when there are extreme values
B) It is less reliable than the mode when the data are continuous
C) It utilizes all the information in a sample
D) It is usually equal to the median in business data.
C) It utilizes all the information in a sample