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mathematics
business statistics

Questions and Answers of Business Statistics

Match the item from the first column to the best item from the second.Identifies independent events(a) P(A and B) = P(A) × P(B|A)(b) P(A|B) = P(B|A) × P(A) >P(B)(c) P(A) = P(A|B)(d) 1 -
Match the item from the first column to the best item from the second.Identifies dependent events(a) P(A and B) = P(A) × P(B|A)(b) P(A|B) = P(B|A) × P(A) >P(B)(c) P(A) = P(A|B)(d) 1 - P(B|A)(e)
Match the item from the first column to the best item from the second.Bayes’ Rule(a) P(A and B) = P(A) × P(B|A)(b) P(A|B) = P(B|A) × P(A) >P(B)(c) P(A) = P(A|B)(d) 1 - P(B|A)(e) P(A) ≠
Match the item from the first column to the best item from the second.Multiplication Rule(a) P(A and B) = P(A) × P(B|A)(b) P(A|B) = P(B|A) × P(A) >P(B)(c) P(A) = P(A|B)(d) 1 - P(B|A)(e) P(A) ≠
Describe the outcomes of these random processes as either independent or dependent. Briefly explain your choice.Recording whether the manufacturer is located in Europe, Asia, or North America for a
Describe the outcomes of these random processes as either independent or dependent. Briefly explain your choice.Recording the type of accident reported to an auto insurance firm in the weeks
Describe the outcomes of these random processes as either independent or dependent. Briefly explain your choice.Tracking the number of visits to a major Web site day by day
Describe the outcomes of these random processes as either independent or dependent. Briefly explain your choice.Tracking the daily price of a share of stock in Microsoft
Describe the outcomes of these random processes as either independent or dependent. Briefly explain your choice.Recording the amount purchased by individual customers entering a large retail store
Describe the outcomes of these random processes as either independent or dependent. Briefly explain your choice.Counting the number of gallons of gasoline put into cars arriving at a service station
In the following Venn diagrams, we have drawn the sample space S as a square, and you may assume that the area of the regions is proportional to the probability. Describe the events A and B as either
In the following Venn diagrams, we have drawn the sample space S as a square, and you may assume that the area of the regions is proportional to the probability. Describe the events A and B as either
A pharmaceutical company has developed a diagnostic test for a rare disease. The test has sensitivity 0.99 (the probability of testing positive among people with the disease) and specificity 0.995
Seventy percent of customers at the snack counter of a movie theater buy drinks. Among those who buy drinks, 30% also purchase popcorn. What’s the probability that a customer at the counter buys a
Match the descriptive phrases to the symbols on the right. In these exercises, X denotes a random variable.Expected value of X.(a) E(X – µ)(b) 10X(c) (X – 0.04)/σ(d) X + 10(e) E(X – µ)2(f)
Match the descriptive phrases to the symbols on the right. In these exercises, X denotes a random variable.Variance of X(a) E(X – µ)(b) 10X(c) (X – 0.04)/σ(d) X + 10(e) E(X – µ)2(f)
Match the descriptive phrases to the symbols on the right. In these exercises, X denotes a random variable.Standard deviation of X(a) E(X – µ)(b) 10X(c) (X – 0.04)/σ(d) X + 10(e) E(X –
Match the descriptive phrases to the symbols on the right. In these exercises, X denotes a random variable.Shorthand notation for P(X = x)(a) E(X – µ)(b) 10X(c) (X – 0.04)/σ(d) X + 10(e) E(X
Match the descriptive phrases to the symbols on the right. In these exercises, X denotes a random variable.Has 10 times the standard deviation of X(a) E(X – µ)(b) 10X(c) (X – 0.04)/σ(d) X +
Match the descriptive phrases to the symbols on the right. In these exercises, X denotes a random variable.Is always equal to zero(a) E(X – µ)(b) 10X(c) (X – 0.04)/σ(d) X + 10(e) E(X –
Match the descriptive phrases to the symbols on the right. In these exercises, X denotes a random variable.Increases the mean of X by 10(a) E(X – µ)(b) 10X(c) (X – 0.04)/σ(d) X + 10(e) E(X –
Match the descriptive phrases to the symbols on the right. In these exercises, X denotes a random variable.Has standard deviation 1(a) E(X – µ)(b) 10X(c) (X – 0.04)/σ(d) X + 10(e) E(X –
If investors want portfolios with small risk (variance), should they look for investments that have positive covariance, have negative covariance, or are uncorrelated?
Does a portfolio formed from the mix of three investments have more risk (variance) than a portfolio formed from two?
If the covariance between the prices of two investments is 100,000, must the correlation between the two be close to 1?
If the correlation between the price of Microsoft stock and the price of an Xbox is 1, could you predict the price of an Xbox from knowing the price of Microsoft stock? How well?
Would it be reasonable to model the sequence of daily sales of a downtown restaurant as a sequence of iid random variables?
If percentage changes in the value of a stock are iid with mean 0, then how should we predict the change tomorrow if the change today was a 3% increase? How would the prediction change if the value
An insurance agent sells two types of policies to clients, both life insurance and auto insurance. The following joint distribution summarizes the number of life insurance policies sold to an
The relevance of variance and covariance developed for random variables in this chapter carries over to the analysis of returns on real stocks. The file €œdaily_stocks€ includes
One hundred customers visit a Web site during a 15-minute period. The number of these customers who make a purchase is modeled as a binomial random variable with n = 100 and p = 0.05. What model
A car dealer makes $1,000 on each vehicle sold. Assume 30% of customers entering the dealership make a purchase. If 50 customers enter the dealership in a day, can the binomial model be used to
If the office visits of a detail rep are Bernoulli trials, then which of these two sequences of six office visits is more likely (S stands for success and the rep sees the doctor, and F for failure):
Four customers in a taste test sample two types of beverage (called A and B here) and are asked which is preferred. If customers cannot tell the two beverages apart, are we more likely to see the
A software project requires 10 components to be completed within the next three months. Each component is produced by a programming team that operates independently of the other teams. Each team has
A venture capitalist invests in startup technology companies. She expects about 10% of these companies to be successful.(a) What is the probability that she will have to invest in more than four
Match each statement on the left to the notation on the right. X denotes a normally distributed random variable: X ~ N(µ, σ2). A googol, the namesake of Google, is 10100. The random variable Z
1. If you repeat the dice game several times, or perhaps in a class, you might find that Red occasionally comes out the winner. Seeing that all of the others lose with Red, how might it be that some
Match each statement on the left to the notation on the right. X denotes a normally distributed random variable: X ~ N(µ, σ2). A googol, the namesake of Google, is 10100. The random variable Z
1. M&M’s weigh 0.86 grams on average with SD = 0.04 grams, so the coefficient of variation is 0.04>0.86 < 0.047. Suppose that we decide to label packages by count rather than weight. The
Match each statement on the left to the notation on the right. X denotes a normally distributed random variable: X ~ N(µ, σ2). A googol, the namesake of Google, is 10100. The random variable Z
How large can a single observation from a normal distribution be?
If used to model data that have limits (such as the age of a customer using a credit card or amount spent by a customer), what problem does a normal model have?
Mosquitos carry numerous tropical diseases. A public health agency wants to identify the extent of mosquito breeding areas (e.g., standing water) within its community. Comment on the following
Would the skewness K3and kurtosis K4of the 100 observations shown in the following histogram both be close to zero, or can you see that one or the other would differ from zero? You don€™t
Would the skewness K3and kurtosis K4of the 100 observations shown in the following histogram both be close to zero, or can you see that one or the other would differ from zero? You don€™t
Robots gather the items for orders shipped by Amazon from bins located in vast warehouses. Computers know what should be in every bin, but sometimes items are missing from a bin. Evaluate the
An employer replaced its paycheck system with a paperless system that directly deposits payments into employee checking or savings accounts. To verify that proper deductions have been made, employees
Mark each statement True or False. If you believe that a statement is false, briefly explain why you think it is false.Larger surveys convey a more accurate impression of the population than smaller
Mark each statement True or False. If you believe that a statement is false, briefly explain why you think it is false.The wording of questions has been shown to have no influence on the responses in
Mark each statement True or False. If you believe that a statement is false, briefly explain why you think it is false.Sampling variation occurs when respondents change their answers to questions
1. If someone tells you the mean and SD of a variable, what had you better find out before trying to use the Empirical Rule?2. Another approach to working with skewed data is to remove the extreme
If the correlation between number of customers and sales in dollars in retail stores is r = 0.6, then what would be the correlation if the sales were measured in thousands of dollars? In euros? (1
A fitness center weighed 53 male athletes and then measured the weight that they were able to lift. The correlation was found to be r = 0.75. Can you interpret this correlation without knowing
To inflate the correlation, a conniving manager added $200,000 to the actual sales amount for each store in Exercise 25. Would this trickery make the correlation larger?Data from exercises 25If the
1. The timeplot in Figure 9 shows the price at the end of the month of one share of stock in Pfizer.What seems to be happening? How could you verify your answer?2. Figure 10 tracks the value of an
These data compare the on-time arrival performance of American and US Airways shortly before their merger in 2015. The table shows the status of 9,350 arrivals during January 2015.(a) On the basis of
Bold names shown with a question identify the data table for the problem.Trust Gallup reported the following results from a survey in 2015. The survey asked 1,527 adults to state how much they trust
Suppose you were looking at the histogram of the incomes of all of the households in the United States. Do you think that the histogram would be bell shaped? Skewed to the left or right?
Match the brief description to the item or value.The square root of the variance(a) Median(b) Mean(c) Standard deviation(d) Variance(e) Z-score(f) Two-thirds(g) Mode(h) Interquartile range(i)
Match the brief description to the item or value.The average of the values of a numerical variable(a) Median(b) Mean(c) Standard deviation(d) Variance(e) Z-score(f) Two-thirds(g) Mode(h)
Match the brief description to the item or value.Length of the box in the boxplot(a) Median(b) Mean(c) Standard deviation(d) Variance(e) Z-score(f) Two-thirds(g) Mode(h) Interquartile range(i)
Match the brief description to the item or value.Position of a peak in the histogram(a) Median(b) Mean(c) Standard deviation(d) Variance(e Z-score(f) Two-thirds(g) Mode(h) Interquartile range(i)
Bold names shown with a question identify the data table for the problem.EmploymentThis table shows percentages of men and women employed in four industries.(a) Is there association between the
A study of purchases at a 24-hour supermarket recorded two categorical variables: the time of the purchase (8 a.m to 8 p.m vs. late night) and whether the purchase was made by someone with children
A survey found that the favorite color of everyone who bought a vehicle overall is silver. In this case, should a new car dealer order most pick-up trucks to stock on its lot in silver?
Executives at a retailer are comparing items chosen by shoppers who either saw or did not see its most recent television advertising. Do the managers in charge of advertising hope to find association
The title of each of the following exercises identifies the data table to be used for the problem.Tech Stocks These data give the monthly returns on stocks in three technology companies: HP, IBM, and
The title of each of the following exercises identifies the data table to be used for the problem.Another column in this data file gives the rated combined fuel economy (in miles per gallon) for 413
The title of each of the following exercises identifies the data table to be used for the problem.A column in this data file gives the engine displacement in liters of 413 vehicles sold in the United
The data in this chapter concern the amount of space needed to hold various songs. What about the length, in minutes? Suppose you get 60 seconds of music from every megabyte of recorded songs.
This histogram shows the price in dollars of 218 used cars.(a) Suppose we converted the prices of these cars from dollars to euros, with an exchange rate of 1.1 dollars per euro. Describe the
The September 2014 issue of the Federal Reserve Bulletin results from the Survey of Consumer Finances, a national economic survey conducted by the Federal Reserve every three years. The survey found
The Census Bureau reported that the median household net worth in the United States was $68,800 in 2011. In contrast, the mean household net worth was $339,000. How is it possible for the mean to be
The Energy Policy Act of 2005 mandates that gasoline sold in the United States must average at least 2.78% ethanol in 2006. Does this mean that every gallon of gas sold has to include ethanol?
Suppose sales representatives average 45 hours per week on the road with standard deviation 5. Would it be surprising to meet a representative who spent 51 hours on the road last week? Do you need to
The range measures the spread of a distribution. It is the distance from the smallest value to the largest value. Is the range sensitive to the presence of outliers?
Many athletes use interval training to improve their strength and conditioning. Interval training requires working hard for short periods, say a minute, followed by longer intervals, say five
For the incomes of all of the households in the United States, which do you expect to be larger, the mean or the median?
Compare the bar chart of the variable described in the previous question with the pie chart of the same data. Which makes it easier to see that each category has the same number of cases?
This pie chart shows the type of college attended by the CEOs of America€™s 50 largest companies.8 Which category is the mode? Which category is the median? Other Ivy League 4 Public 26
A categorical variable has two values, male and female. Would you prefer to see a bar chart, a pie chart, or a frequency table? Why?
A data table with 100 rows includes a categorical variable that has five levels. Each level has 20 rows. Describe the bar chart.
Sketch by hand the pie chart of the data in the previous question.Data from previous questionDescribe the bar chart of a categorical variable for which 900 of the 1,000 rows of data are in one
Describe the bar chart of a categorical variable for which 900 of the 1,000 rows of data are in one category and the remaining 100 are distributed evenly among five categories.
What would happen if we were to generate a bar chart for a column that measures the amount spent by the last 200 customers at a convenience store?
This table summarizes shares of the U.S. wireless telephone market in 2011. To summarize these percentages together in a pie chart, what needs to be added? Company
These percentages summarize the responses of 530 senior executives when asked the question, €œWhich strategies have proved successful in promoting a data-driven culture in your
The Wall Street Journal on January 19, 2016, used a chart resembling the following one to illustrate the rising amounts that Netflix spends to provide streaming content online. Is this the bar chart
Share of bank loans that are in good standing, 30 days past due, and in defaultMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and
Number of cellular telephone customers rating their service as Poor, OK, Good, and GreatMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are
Customer choices of compact, zoom, and high-end digital camerasMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are shares.
Share of software purchases devoted to games, office work, and designMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are
Brand of computer chosen by new students of a large universityMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are shares.
Excuses given for not finishing homework assignmentsMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are shares. If not
Reason for customers hanging up when calling a computer help deskMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are
Destinations for travelers leaving the United States and heading abroadMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are
Counts of the type of automobile involved in police traffic stopsMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are
Number of cash-back coupons returned by purchasers of cameras, computers, and stereo equipmentMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are
Number of different types of defects found in computer equipmentMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are shares.

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