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Business Statistics
The 311 cases that make up this data set are types of cars sold in the 2016 model year in the United States. The variables include the weights (in thousands of pounds) and urban driving mileage (in
R&D Expenses This table contains accounting and financial data that describe 409 companies operating in the semiconductor industry in 2014. One column gives the expenses on research and
In the examples of autocorrelation in regression in this chapter, the Durbin Watson statistic D was less than 2. What would it mean about the data if one found a significant value of D > 2? Does
Management of a retail chain has been tracking the growth of sales, regressing the company’s sales versus the number of outlets. Their data are weekly, spanning the last 65 weeks, since the
For each data table, before answering the questions, determine whether the simple regression model is a reasonable description of the association between the two indicated variables. In particular,
For each data table, before answering the questions, determine whether the simple regression model is a reasonable description of the association between the two indicated variables. In particular,
Referring to the previous scenario, suppose that during the first 12 weeks, this company was the only clothing retailer in a busy mall. During the second 12 weeks, a rival company opened. Then,
A company tracks the level of sales at retail outlets weekly for 36 weeks. During the first 12 weeks, a fixed level of advertising was used each week to draw in customers. During the second 12 weeks,
Suppose that large diamonds (more than 1.5 carats) sold at retail tend to be of very mixed quality, whereas small diamonds have consistent quality (more uniform color, clarity, and attractive cut).
You suspect that the pattern relating sales (Y) to levels of advertising (X) is not linear (perhaps a log transformation is needed to represent diminishing marginal returns). Explain how you can
The mileage data in Figure 20.2 excludes hybrid cars. If these were added to the data, would they produce positive or negative residuals in Figure 20.3?Figure 20.2Figure 20.3 35 30 25 15 10 3 4 5
If an equation uses the log of the explanatory variable, as in ŷ = b0 + b1 log x, then what does the intercept b0 tell you?
If an equation uses the reciprocal of the explanatory variable, as in ŷ = b0 + b11/x, then what does the intercept b0 tell you?
The section Behind the Math: Different Logs shows that, because logs to different bases are proportional, we can use either base-10 logs or natural logs in regression when estimating elasticity. The
The section Behind the Math: Different Logs shows that logs to different bases are proportional to one another. For example, loge x = (loge 10) log10 x < 2.303 log10 x. If Sales is the variable
If quantity sold increases with price, would the elasticity be positive, negative, or zero?
If the elasticity of quantity with respect to price is close to zero, how are the price and quantity related?
Can you think of any lurking factors behind the relationship between weight and fuel consumption among car models?
If diamonds have a linear relationship with essentially no fixed costs, which costs more: a single 1-carat diamond or two 1/2 -carat diamonds? Does that make sense to you?
If the correlation between X and Y is 0.8 and the slope in the regression of Y on X is 1.5, then which of X or Y has larger variation?
If the standard deviation of X matches the standard deviation of Y, then what is the relationship between the slope in a least squares regression of Y on X and the correlation between X and Y?
A customized milling operation uses the equation $200 plus $150 per hour to give price estimates to customers. If it pays a fixed fee to ship these orders, how should it change this equation if the
A package delivery service uses a regression equation to estimate the fuel costs of its trucks based on the number of miles driven. The equation is of the form Estimated Dollars = b0 + b1 Miles. If
This histogram summarizes residuals from a fit that regresses the number of items produced by 50 employees during a shift on the number of years with the company. Estimate se from this plot. 10 - 8-
From looking at this plot of the residuals from a linear equation, estimate the value of se. Micrasan Eicei $100.00 $75.00 4. $sa.00 $25.00 10 50.00 11 12 (525.00) 13 14 15 16 17 (550.00) (S75.00) 18
In general, is the linear least squares regression equation of Y on X the same as the equation for regressing X on Y?
On a sheet of paper, write the numerals 1, 2, 3, and 4 in large print. Ask several friends to pick a number “at random.” (Don’t let anyone see what others pick. We want independent choices.)(a)
Where should the control limits for an X-bar chart be placed if the design of the process sets a = 0.0027 with the following parameters (assume that the sample size condition for control charts has
Where should the control limits in an X-bar chart be placed if the design of the process sets a = 0.01 with the following parameters (assume that the sample size condition for control charts has been
An X-bar control chart monitors the mean of a process by checking that the average stays between µ - 3σ/√n and µ + 3σ/√n. When the process is under control,(a) What is the probability that
Match each item on the left with its correct description on the right.p̂ ± se(p̂)(a) Sampling distribution of X̅(b) Margin of error(c) 100% confidence interval for p(d) Estimated standard error
Match each item on the left with its correct description on the right.2se(X̅)(a) Sampling distribution of X̅(b) Margin of error(c) 100% confidence interval for p(d) Estimated standard error of
Match each item on the left with its correct description on the right.N(µ, σ2/n)(a) Sampling distribution of X̅(b) Margin of error(c) 100% confidence interval for p(d) Estimated standard error of
Match each item on the left with its correct description on the right.s/√n(a) Sampling distribution of X̅(b) Margin of error(c) 100% confidence interval for p(d) Estimated standard error of Y̅(e)
Match each item on the left with its correct description on the right.σ/√n(a) Sampling distribution of X̅(b) Margin of error(c) 100% confidence interval for p(d) Estimated standard error of
Match each item on the left with its correct description on the right.1/(0.05)2(a) Sampling distribution of X̅(b) Margin of error(c) 100% confidence interval for p(d) Estimated standard error of
Match each item on the left with its correct description on the right.[0, 1](a) Sampling distribution of X̅(b) Margin of error(c) 100% confidence interval for p(d) Estimated standard error of Y̅(e)
Match each item on the left with its correct description on the right.√p̂(1 – p̂)/n(a) Sampling distribution of X̅(b) Margin of error(c) 100% confidence interval for p(d) Estimated standard
Match each item on the left with its correct description on the right.t0.025,n-1(a) Sampling distribution of X̅(b) Margin of error(c) 100% confidence interval for p(d) Estimated standard error of
Mark each statement True or False. If you believe that a statement is false, briefly explain why you think it is false.To guarantee a margin of error of 0.05 for the population proportion p, a survey
Mark each statement True or False. If you believe that a statement is false, briefly explain why you think it is false.The 95% t-interval for m works best if the sample data are normally distributed.
What are the chances that X̅ > µ?
What is the coverage of the confidence interval [p̂ to 1]?
A summary of sales of a department store says that the average retail purchase was $125 with a margin of error equal to $15. What does the margin of error mean in this context?
A news report summarizes a poll of voters and then adds that the margin of error is plus or minus 4%. Explain what that means.
In a survey of employees, Watson-Wyatt reported that 51% had confidence in the actions of senior management. 17 To be 95% confident that at least half of all employees have confidence in senior
Match the description of each concept with the correct symbol or term.Identifies the alternative hypothesis(a) t-statistic(b) µ0(c) p-value(d) p-value < α(e) Type I error(f) z-statistic(g) Type
Match the description of each concept with the correct symbol or term.Largest α-level for which a test rejects the null hypothesis(a) t-statistic(b) µ0(c) p-value(d) p-value < α(e) Type I
Match the description of each concept with the correct symbol or term.Occurs if the p-value is larger than a when H0 is false(a) t-statistic(b) µ0(c) p-value(d) p-value < α(e) Type I error(f)
The biostatistician who designed a study for investigating the efficacy of a new medication was fired after the study. The tested null hypothesis states that the drug is no better than a placebo. The
Suppose that 2% of the modifications proposed to improve browsing on a Web site actually do improve customers’ experience. The other 98% have no effect. Now imagine testing 100 newly proposed
Match each definition on the left with a mathematical expression or term on the right.Difference between the averages in two samples(a) t = -4.6(b) t = 1.3(c) µ1
Match each definition on the left with a mathematical expression or term on the right.Estimate of the standard error of the difference between two sample means(a) t = -4.6(b) t = 1.3(c) µ1
Match each definition on the left with a mathematical expression or term on the right.Avoids confounding in a two-sample comparison(a) t = -4.6(b) t = 1.3(c) µ1
Match each definition on the left with a mathematical expression or term on the right.Test statistic indicating a statistically significant result if α = 0.05 and H0: µ1
Match each definition on the left with a mathematical expression or term on the right.Test statistic indicating that a mean difference is not statistically significant if α = 0.05(a) t
Match each definition on the left with a mathematical expression or term on the right.The number of degrees of freedom in a paired t-test(a) t = -4.6(b) t = 1.3(c) µ1
Match each definition on the left with a mathematical expression or term on the right.Multiple factors explain the difference between two samples(a) t = -4.6(b) t = 1.3(c) µ1
Mark each statement True or False. If you believe that a statement is false, briefly explain why you think it is false.If the standard two-sample t-test rejectsH0: µ1 – µ2 ≤ $100, then µ1 is
The value of r2 = 1 if data lie along a single line. Is it possible to fit a linear regression for which r2 is exactly equal to zero?
If the busy commuter in Exercise 21 decides to do more testing, how should she decide on the mode of transportation? Should she, for example, drive for a week and then take public transit for a week?
A business offers its employees free membership in a local fitness center. Rather than ask the employees if they like this benefit, the company developed a measure of productivity for each employee
Without doing all the calculations, which of these 2 × 2 tables has the largest value of chi-squared? The smallest? (Each table has n = 100.) (a) (c) (b) 25 50 25 30 20 20 25 25 30 50 2.
Without doing all the calculations, which of these 3 × 2 tables has the largest value of chi-squared? The smallest? (Each table has n = 150.) (b) (a) (c) 27 26 42 23 24 19 37 13 27 23 31 18 32 25
This is a bar chart of the number of defaults on mortgages in a collection of loans during the credit crisis that began in 20072008. The bar chart identifies the type of income
The following bar chart shows the number of major and minor league baseball players that were suspended for using steroids during the 2008 season. Can we use these counts to test whether the rate of
A stock market analyst recorded the number of stocks that went up or went down each day for 5 consecutive days, producing a contingency table with two rows (up or down) and five columns (Monday
A market research firm gathered a random sample of 150 customers. The firm randomly assigned 50 of these to rate the current product and assigned 50 each to rate new versions of the product. The firm
A bank makes loans to many types of customers. Some of these customers default on their loans. How could analysts at the bank use x2 to identify characteristics associated with customers who default
Inventory counts are seldom perfect because of misplaced items or misfiled sales reports. How could managers use x2 to decide whether expected inventory counts differ substantially from the actual
Managers in the human resources department suspect that sick-day absentee rates are higher on some weekdays than others. What test can they use to investigate this claim?
A manager in the previous question thinks that the absentee rate is the same on Monday and Friday, but different from the rate on Tuesday through Thursday. What method should she use to test her
Match each description on the left with its mathematical expression on the right.Symbol for the standard deviation of the residuals(a) r2(b) b0(c) y̅(d) b1(e) X(f) ŷ(g) b0 + b1(h) Y(i) y –
This data set tracks monthly performance of stock in Apple from January 1990 through December 2015, a total of 312 months. The data include returns on the entire stock market, Treasury Bills
After calculating the correlation, the analyst at the fitness center in Exercise 26 discovered that the scale used to weigh the athletes was off by 5 pounds; each athlete’s weight was measured as 5
Cramer’s V (Chapter 5) measures dependence and varies from 0 to 1. The correlation also measures dependence but varies from - 1 to + 1. Why doesn’t it make sense for V also to take on negative
The visual test for association can be used to help distinguish whether the pattern in a plot is real or imagined. The original ought to stand out clearly. If you look at four plots, one the original
The visual test for association requires you to compare several plots. One has the original data, and the others show the data with scrambled coordinates. Would it help in finding the original if
Bold names shown with a question identify the data table for the problem. The title of each of the following exercises identifies the data table to be used for the problem.Drive Preferences These
Cars These data report characteristics of 413 types of cars sold in the United States in 2016. One column gives the official mileage (combined MPG), and another gives the rated horsepower.(a) Make a
Find the matching item from the second column.Independent events(a) P(A and B) ≠ P(A) × P(B)(b) Ac(c) S(d) P(A or B) + P(A and B) = P(A) + P(B)(e) P(A or B) ≤ P(A) + P(B)(f) A and B(g) P(A and
Find the matching item from the second column.Disjoint events(a) P(A and B) ≠ P(A) × P(B)(b) Ac(c) S(d) P(A or B) + P(A and B) = P(A) + P(B)(e) P(A or B) ≤ P(A) + P(B)(f) A and B(g) P(A and B) =
Find the matching item from the second column.Union(a) P(A and B) ≠ P(A) × P(B)(b) Ac(c) S(d) P(A or B) + P(A and B) = P(A) + P(B)(e) P(A or B) ≤ P(A) + P(B)(f ) A and B(g) P(A and B) = 0(h) A
Find the matching item from the second column.Intersection(a) P(A and B) ≠ P(A) × P(B)(b) Ac(c) S(d) P(A or B) + P(A and B) = P(A) + P(B)(e) P(A or B) ≤ P(A) + P(B)(f) A and B(g) P(A and B) =
Find the matching item from the second column.Complement of A(a) P(A and B) ≠ P(A) × P(B)(b) Ac(c) S(d) P(A or B) + P(A and B) = P(A) + P(B)(e) P(A or B) ≤ P(A) + P(B)(f ) A and B(g) P(A and B)
Find the matching item from the second column.Sample space(a) P(A and B) ≠ P(A) × P(B)(b) Ac(c) S(d) P(A or B) + P(A and B) = P(A) + P(B)(e) P(A or B) ≤ P(A) + P(B)(f ) A and B(g) P(A and B) =
Find the matching item from the second column.Addition Rule(a) P(A and B) ≠ P(A) × P(B)(b) Ac(c) S(d) P(A or B) + P(A and B) = P(A) + P(B)(e) P(A or B) ≤ P(A) + P(B)(f ) A and B(g) P(A and B) =
Find the matching item from the second column.Complement Rule(a) P(A and B) ≠ P(A) × P(B)(b) Ac(c) S(d) P(A or B) + P(A and B) = P(A) + P(B)(e) P(A or B) ≤ P(A) + P(B)(f ) A and B(g) P(A and B)
Find the matching item from the second column.Boole’s inequality(a) P(A and B) ≠ P(A) × P(B)(b) Ac(c) S(d) P(A or B) + P(A and B) = P(A) + P(B)(e) P(A or B) ≤ P(A) + P(B)(f ) A and B(g) P(A
Find the matching item from the second column.Dependent events(a) P(A and B) ≠ P(A) × P(B)(b) Ac(c) S(d) P(A or B) + P(A and B) = P(A) + P(B)(e) P(A or B) ≤ P(A) + P(B)(f ) A and B(g) P(A and B)
A market research assistant watches five customers as they leave a store. He records whether the customer is carrying a store bag that indicates any customer made a purchase. He writes down a yes or
A company seeks to hire engineering graduates who also speak a foreign language. Should you describe the combination of talents as an intersection or a union?
Customers visit a store with several departments. A randomly chosen customer goes to the sporting goods department. After wandering for a bit, she buys a pair of running shoes. This event is most
The combination of which two of the following characteristics would produce the sort of data needed in order for the Law of Large Numbers to guarantee that a proportion converges to a probability?(a)
The manager of a beachside vacation resort tracks the local weather. Each day, she records a 1 if the day is cloudy. She records a 0 if the day is sunny. The following plot shows a sequence from her
A market analyst on TV makes predictions such as saying that there is a 25% chance that the market will move up the next week. What do you think is the meaning of such a phrase?
A basketball player who has missed his last seven consecutive shots then makes the game-winning shot. When speaking to reporters afterward, the player says he was very confident that last time
Intel and AMD compete to put their processing chips into personal computers. In 2014, Intel claimed 93% of the laptop market and 83% of the market for desktop computers. In 2010, Intel commanded 86%
Match the item from the first column to the best item from the second.Probability of B given A(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.Probability of Bc given A(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)
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