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statistics for business and economics

Questions and Answers of Statistics For Business And Economics

A Senate committee consists of six Democrats and five Republicans. In how many ways can a subcommittee consisting of four Democrats and four Republicans be formed?
You believe you have come up with a fool-proof way to win at roulette.Because the odds are nearly 50–50 that red will come up and nearly 50–50 that black will come up in roulette, you believe
At the beginning of each week, a company decides how much to spend on newspaper ads for that week. It spends either $250 or $500 each week on newspaper ads. Assuming there is an equal probability of
A car salesman meets 12 customers each week. His probability of making a sale in the first meeting with a customer is .3. When he gets the second meeting with the same customer, the probability of
A life insurance company knows with certainty that all people will die someday.Does it make sense for the insurance company to use probability theory to set its life insurance rates?
Consider the sample space S = {A, B, C, D, E, F, G} and the following events:Are the following sets of events mutually exclusive, collectively exhaustive, both, or neither? I = {A, C, E, G} II = {B,
State the complement of each of the following events:(a) Drawing a spade from a full deck of cards(b) Inflation of less than 5 % per year(c) GNP growth of more than 4 % per year
The figure below is a plot of salary and experience of employees of the Endicott Company. Answer the following questions by using a Venn diagram.(a) The probability of experience between 3 and 5
All the students of a university are assigned ID numbers. The ID number consists of the first three letters of a student’s last name, followed by four numbers. How many possible different ID
Suppose there are four events A, B, C, and D. The following information is given: P(A) = .5 P(B) = .15 P(C) = .20 P(AUD) = .72 P(A | B) = .25 P(AC) = .04 P(AD) = .03
Assume you have applied to two different universities A and B. In the past, 30 % of students who applied to University A were accepted, while University B accepted 45 % of the applicants. Assume
Suppose 20 % of the employees of company ABC have only a high school diploma, 60 % have bachelor degrees, and 20 % have graduate degrees Of those with only a high school diploma, 15 % hold management
A sports magazine wants to learn something about its subscribers. The subscribers are classified as teenagers or older people and as being in school or holding a job. The magazine sends out a
The following picture helps you obtain the probability that events A, B, and C, happen jointly. Write down the formula for obtaining P(ANBNC).
A hospital found that the probability of a power failure in a certain time period is .00001. To guarantee the functioning of the hospital, the hospital installed a backup system that has a
Predict the monthly sales for next month if $400 is spent on advertising. Use a 95% prediction interval.
Refer to the sales-appraisal simple linear regression in previous examples. Find a 95% confidence interval for the mean monthly sales when the appliance store spends $400 on advertising.Previous
Calculate the coefficient of determination for the advertising-sales example.Obtaining the Value of The data are repeated in Table 11.4 for convenience. Interpret the result. Table 11.4
Legalized gambling is available on several riverboat casinos operated by a city in Mississippi. The mayor of the city wants to know the correlation between the number of casino employees and the
Refer to the simple linear regression analysis of the advertising-sales data, Examples 11.2 and 11.3. Conduct a test (at α = .05) to determine if sales revenue (y) is linearly related to advertising
Refer to the advertising–monthly sales data presented in Table 11.1. Consider the straight-line model, E(y) = β0 + β1x, where y = sales revenue (thousands of dollars) and x = advertising
Consider a study designed to estimate the linear relationship between the percentage of jobs outsourced to another country by a U.S. company and the size (number of employees) of the company. In
A large firm has established what it hopes is an objective system of deciding on annual pay increases for its employees. The system is based on a series of evaluation scores determined by the
Refer to Example 9.10. Suppose the same factorial experiment is performed on four other brands (E, F, G, and H), and the results are as shown in Table 9.16. Repeat the factorial analysis and
The USGA is interested in knowing whether the difference in distance traveled by any two golf ball brands depends on the club used. Consequently, the USGA tests four different brands (A, B, C, D) of
Apply Bonferroni’s procedure to the data in Example 9.8. Use an experimentwise error rate (EER) of .05 to rank the mean distances of the four golf ball brands. Interpret the results.Example
Refer to Example 9.7. Suppose the randomized block design of part b is employed, employing a random sample of 10 golfers, with each golfer using a driver to hit four balls, one of each brand, in a
Refer to Examples 9.4–9.6. Suppose the USGA wants to compare the mean distances associated with the four brands of golf balls when struck by a driver but wishes to employ human golfers rather than
Refer to the completely randomized design of Example 9.4, in which we concluded that at least two of the four brands of golf balls are associated with different mean distances traveled when struck
Refer to the completely randomized design ANOVA conducted in Example 9.4.Are the assumptions required for the test approximately satisfied?Example 9.4Suppose the USGA wants to compare the mean
Suppose we want to compare the taste preferences of consumers for three different brands of bottled water (say, Brands A, B, and C) using a random sample of 15 bottled water consumers. Set up a
Use Appendix tables V, VI, VII, and VII to estimate the p-values for the following cases:a. F = 6.29; ν1 = 5, ν2 = 10b. F = 2.84; ν1 = 3, ν2 = 5c. F = 7.21; ν1 = 7, ν2 = 6d. F = 2.98; ν1 =
Use Tables V, VI, VII, and VIII in Appendix D to find each of the following F-values:a. F.05, ν1 = 4, ν2 = 4b. F.01, ν1 = 4, ν2 = 4c. F.10, ν1 = 30, ν2 = 40d. F.025, ν1 = 15, ν2 = 12
Identify whether the following levels of factors are qualitative or quantitative.a. Method of payment (cash, check, and credit card)b. Hotel service rating (1 for Fair, 2 for Average, 3 for Good,
1. Explain why both of the situations in Activity 8.1 and Activity 8.2 are observational experiments. What key elements of a designed experiment are missing in each situation?2. A movie company
In this activity, you will compare the mean amounts transferred for two different Bank of America customers as well as design some studies that might help the marketing department determine where to
Identify the rejection region for each of the following cases. Assume ν1 = 7 and ν2 = 9.a. Ha: σ21 < σ22, α = .05b. Ha: σ21 > σ22, α = .01c. Ha: σ21 ≠ σ22, α = .1 with s21 >
Given ν1 and ν2, find the following probabilities:a. ν1 = 2, ν2 = 30, P(F ≤ 5.39)b. ν1 = 24, ν2 = 10, P(F < 2.74)c. ν1 = 7, ν2 = 1, P(F ≥ 236.8)d. ν1 = 40, ν2 = 40, P(F > 2.11)
A paired difference experiment yielded the following results:a. Determine whether these data are sufficient to infer whether the two population means differ at the 10% significance
In this activity, we continue our study of the Bank of America Keep the Change savings program by looking at the measures of central tendency and variability for the three data sets collected.1.
Refer to Example 11.2 and the simple linear regression of the advertising-sales data in Table 11.1.a. Compute an estimate of σ.b. Give a practical interpretation of the estimate.Example 11.2Refer
A large brokerage firm wants to determine whether the service it provides to affluent clients differs from the service it provides to lower-income clients. A sample of 500 clients is selected, and
In this Activity, For convenience, the table shown in that activity is repeated here.1. Determine whether the table above and the similar tables that you found for Activity 3.1 are contingency
Consider the problem of determining the highest level of education attained by each of n = 100 salespersons at a large company. Suppose we categorize level of education into one of five
In this activity, you will study the difference between binomial and multinomial experiments.1. A television station has hired an independent research group to determine whether television viewers in
Suppose the USGA wants to compare the mean distances associated with four different brands of golf balls when struck with a driver. A completely randomized design is employed, with Iron Byron, the
Suppose the USGA is interested in comparing the mean distances the four brands of golf balls travel when struck by a five-iron and by a driver. Ten balls of each brand are randomly selected, five to
The USGA (United States Golf Association) regularly tests golf equipment to ensure that it conforms to USGA standards. Suppose it wishes to compare the mean distance traveled by four different brands
A retailer sells both the Apple iPhone and Google Android cell phones online.Assume that 80% of the phones the retailer sells online are iPhones and 20% are Androids.a. Use the steps given in Chapter
A company sent its employees to attend two different English courses. The company is interested in knowing if there is any difference between the two courses attended by its employees. When the
Use the Internet to find the daily box office receipts for two different hit movies during the first 8 weeks after their releases. In this activity, you will compare the mean daily box office
Use a statistical software package to conduct the test in Example 8.6. Find and interpret the p-value of the test.Example 8.6A consumer advocacy group wants to determine whether there is a difference
New fertilizer compounds are often advertised with the promise of increased crop yields. Suppose we want to compare the mean yield μ1 of wheat when a new fertilizer is used with the mean yield μ2
Consider the experiment of tossing fair coins. Define the following event:A: {Observing at least one head}.a. Find P(A) if 2 coins are tossed.b. Find P(A) if 10 coins are tossed.
Consider the experiment of tossing two balanced coins. Find the probability of observing at least one head.
Find the probability that the standard normal random variable z falls between -1.33 and 1.33
Assume that μ = 2.62 is the population mean and σ = 4.1 is the population standard deviation.a. Using n = 70 and the normal distribution with the mean and standard deviation above, run the applet
Choose a population parameter pertinent to your major area of interest—a population that has an unknown mean, or if the population is binomial, an unknown probability of success. For example, a
Find zα/2 for each of the following:a. α = .10 b. α = .01c. α = .05 d. α = .20
Refer to Example 6.1 and the problem of estimating μ, the average amount of money owed by a bank’s delinquent debtors. The overdue amounts for the n = 100 delinquent accounts are shown in Table
Consider the large bank that wants to estimate the average amount of money owed by its delinquent debtors, μ. The bank randomly samples n = 100 of its delinquent accounts and finds that the sample
Use the applet Confidence Intervals for a Mean (the impact of confidence level) to investigate the effect of the sample size on the proportion of confidence intervals that contain the mean when the
Use the applet Confidence Intervals for a Mean (the impact of not knowing the standard deviation) to compare proportions of z-intervals and t-intervals that contain the mean for a population that is
Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the
A random sample of n measurements was selected from a population with unknown mean μ and known standard deviation σ. Calculate a 95% confidence interval for μ for each of the following
Consider the pharmaceutical company that desires an estimate of the mean increase in blood pressure of patients who take a new drug. The blood pressure increases (points) for the n = 6 patients in
Use the applet Confidence Intervals for a Mean (the impact of not knowing the standard deviation) to compare proportions of z-intervals and t-intervals that contain the mean for a population with a
Some quality-control experiments require destructive sampling (i.e., the test to determine whether the item is defective destroys the item) in order to measure some particular characteristic of the
Use the applet Confidence Intervals for a Proportion to investigate the effect of the value of p on the number of confidence intervals that contain the population proportion p for a fixed sample
Use the applet Confidence Intervals for a Proportion to investigate the effect of the sample size on the number of confidence intervals that contain the population proportion p for a value of p close
A food-products company conducted a market study by randomly sampling and interviewing 1,000 consumers to determine which brand of breakfast cereal they prefer. Suppose 313 consumers were found to
Many public polling agencies conduct surveys to determine the current consumer sentiment concerning the state of the economy. For example, the Bureau of Economic and Business Research (BEBR) at the
According to the Bureau of Labor Statistics, the probability of injury while working at a jewelry store is less than .01. Suppose that in a random sample of 200 jewelry store workers, 3 were injured
The manufacturer of official NFL footballs uses a machine to inflate its new balls to a pressure of 13.5 pounds. When the machine is properly calibrated, the mean inflation pressure is 13.5 pounds,
Let t0 be a particular value of t. Use Table III in Appendix D to find t0 values such that the following statements are true.a. P(-t0 0) = .95 where df = 10b. P(t ≤ -t0 or t ≥ t0) where df = 10c.
A cellular telephone manufacturer that entered the postregulation market too quickly has an initial problem with excessive customer complaints and consequent returns of the cell phones for repair or
Let t0 be a specific value of t. Use Table III in Appendix D to find t0 values such that the following statements are true.a. P(t ≥ t0) = .025 where df = 11b. P(t ≥ t0) = .01 where df = 9c. P(t
A specialty manufacturer wants to purchase remnants of sheet aluminum foil.The foil, all of which is the same thickness, is stored on 1,462 rolls, each containing a varying amount of foil. To obtain
Refer to the U.S. Army Corps of Engineers study of contaminated fish in the Tennessee River. The Corps of Engineers has collected data for a random sample of 144 fish contaminated with DDT. (The
Refer to Example 6.12. Find a 95% confidence interval for σ, the true standard deviation of the contaminated fish weights.Example 6.12Refer to the U.S. Army Corps of Engineers study of contaminated
Use Table III, Appendix D to determine the t0 values for each of the following probability statements and their respective degrees of freedom (df).a. P(t ≤ t0) = .25 with df = 15b. P(t ≥ t0) =
In each of the following instances, determine whether you would use a z- or t-statistic (or neither) to form a 90% confidence interval and then state the appropriate z- or t-statistic value for the
Use the Internet or a newspaper or magazine to find an example of a claim made by a company about the reliability or efficiency of one of its products. In this activity, you represent a consumer
Use the applet Hypothesis Test for a Mean to investigate the frequency of Type I and Type II errors. For this exercise, use n = 100 and the normal distribution with mean 50 and standard deviation
A metal lathe is checked periodically by quality-control inspectors to determine whether it is producing machine bearings with a mean diameter of .5 inch. If the mean diameter of the bearings is
In this activity, we will test claims that the mean amount transferred for any single purchase is $0.50 and that the mean amount that Bank of America matches for a customer during the first 90 days
Cigarette advertisements are required by federal law to carry the following statement: “Warning: The surgeon general has determined that cigarette smoking is dangerous to your health.” However,
Refer to the quality-control test set up in Example 7.3. Recall that a machine is designed to discharge a mean of 12 ounces of cereal per box. A sample of 100 boxes yielded the fill amounts (in
A manufacturer of cereal wants to test the performance of one of its filling machines.The machine is designed to discharge a mean amount of 12 ounces per box, and the manufacturer wants to detect any
Consider the one-tailed test of hypothesis, H0: μ = 100 versus Ha: μ > 100.a. Suppose the test statistic is z = 1.44. Find the p-value of the test and the rejection region for the test when α =
Find the observed significance level (p-value) for the test of the mean filling weight in Examples 7.3 and 7.5. Interpret the result.Examples 7.5Refer to the quality-control test set up in Example
Knowledge of the amount of time a patient occupies a hospital bed—called length of stay (LOS)—is important for allocating resources. At one hospital, the mean LOS was determined to be 5 days. A
Use the applet Hypotheses Test for a Proportion to investigate the effect of the true population proportion p on the probability of a Type I error occurring. For this exercise, use n = 100, and
A major car manufacturer wants to test a new engine to determine whether it meets new air pollution standards. The mean emission m of all engines of this type must be less than 20 parts per million
Find the observed significance level for the test described in Example 7.8. Interpret the result.Example 7.8A major car manufacturer wants to test a new engine to determine whether it meets new air
Recall the quality-control study in Example 7.5, in which we tested to determine whether a cereal box filling machine was deviating from the specified mean fill of μ = 12 ounces. The test setup is
The reputations (and hence sales) of many businesses can be severely damaged by shipments of manufactured items that contain a large percentage of defectives.For example, a manufacturer of alkaline
Refer to the fill weights for the sample of ten 16-ounce cans in Table 7.6. Do the data provide sufficient evidence to indicate that the true standard deviation σ of the fill measurements of all
In Example 7.10 we found that we did not have sufficient evidence, at the α = .01 level of significance, to indicate that the fraction defective p of alkaline batteries was less than p = .05. How
If a hypothesis test were conducted using α = .05, for which of the following p-values would the null hypothesis be rejected?a. .06b. .10c. .01d. .001e. .251f. .042

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