Your marketing research team has identified four distinct groups of people (Type A, B, C, and D, where D represents “all others”) according to personality traits. You figure that market penetration for a new product will be highest among Type A personalities, with 38% purchasing the product within two years. Similarly, for Types B, C, and D, the market penetration will be 23%, 8%, and 3%, respectively. Assume that the personality types represent 18%, 46%, 25%, and 11%, respectively, of your target population. What overall market penetration should you expect among your target population?
> You are a contestant on a TV game show with five doors. There is just one prize behind one door, randomly selected. After you choose, the hosts deliberately open three doors (other than your choice) that do not have the prize. You have the opportunity to
> The probability of getting a patent is 0.6. If you get the patent, the conditional probability of being profitable is 0.9. However, given that you do not get the patent, the conditional probability of being profitable is only 0.3. Find the probability of
> Of the 925 tires your factory just produced, 17 are defective. a. Find the probability that a randomly selected tire is defective. b. Find the probability that a randomly selected tire is not defective. c. What kind of probability numbers are these?
> You feel that the schedule is reasonable provided the new manager can be hired in time, but the situation is risky regardless. You figure there is a 70% chance of hiring the new manager in time. If the new manager is hired in time, the chances for succes
> You have determined that 2.1% of the CDs that your factory manufactures are effective due to a problem with materials and that 1.3% are defective due to human error. Assuming that these are independent events, find the probability that a CD will have at
> Your production line has an automatic scanner to detect defects. In recent production, 2% of items have been defective. Given that an item is defective, the scanner has a 90% chance of identifying it as defective. Of the non defective items, the scanner
> Of your customers, 24% have high income, 17% are well educated. Furthermore, 12% both have high income and are well educated. What percentage of the well-educated customers has high income? What does this tell you about a marketing effort that is current
> You have followed up on people who received your catalog mailing. You found that 4% ordered the hat and 6% ordered the mittens. Given that they ordered the hat, 55% also ordered the mittens. a. What percentage ordered both items? b. What percentage order
> The probability that the project succeeds in New York is 0.6, the probability that it succeeds in Chicago is0.7,and the probability that it succeeds in both markets is 0.55. Find the conditional probability that it succeeds in Chicago given that it succe
> For the salary numbers: a. Construct a histogram. b. Describe the shape of the distribution. c. Summarize the distribution in general terms by giving the smallest salary and the largest salary.
> Suppose 35.0% of employees are staff scientists, 26.0% are senior employees, and 9.1% are both. Are “staff scientist” and “senior employee” independent events?
> You just learned good news: A prototype of the new product was completed ahead of schedule and it works better than expected. Would you expect “the conditional probability that this product will be successful given the good news” to be larger than, small
> Your group has been analyzing quality control problems. Suppose that the probability of a defective shape is 0.03, the probability of a defective paint job is 0.06, and that these events are independent. a. Find the probability of defective shape and def
> All 18 people in a department have just received across the- board pay raises of 3%. What has happened to a. The average salary for the department? b. The standard deviation of salaries? c. The range in salaries? d. The coefficient of variation of salari
> Compute the standard deviation of the data from Table 4.3.1 of Chapter 4 to find the variability in spending levels from one regular customer to another for last month. Write a paragraph summarizing these differences. Table 4.3.1: TABLE 4.3.1 Last
> Summarize the variability in the cost of a traditional funeral service using the standard deviation, based on the data in Table 3.8.10 of Chapter 3. Table 3.8.10: TABLE 3.8.10 Cost of Traditional Funeral Service Funeral Home Cost ($) Bleitz $2,180
> Using the data from Table 3.8.2 in Chapter 3, find the standard deviation and range to summarize the typical variability (or uncertainty) of the market response to stock buyback announcements. Table3.8.2: TABLE 3.8.2 Market Response to Stock Buybac
> Consider the running time of movies from Table 4.3.10 in Chapter 4. a. Find the standard deviation. What does this tell you about these movie times? b. Find the range. What does this tell you about these movie times? c. How many standard deviations from
> Find the standard deviation of the VAT taxes from Table 4.3.2 in Chapter 4. What does this tell you about international taxation practices from one country to another? Table 4.3.2: TABLE 4.3.2 Value-Added Tax Rates by Country Country Standard VAT R
> For the preceding problem, compare the coefficient of variation before and after the sales goal adjustment. Why does it change (or not change) in this way?
> For the salary numbers, separated according to gender: a. Construct a histogram for just the males. b. Construct a histogram for just the females using the same scale as in part a to facilitate comparison of male and female salaries. c. Compare these two
> You are sales manager for a regional division of a beverage company. The sales goals for your representatives have an average of $768,000 with a standard deviation of $240,000. You have been instructed to raise the sales goalofeachrepresentativeby$85,000
> For the previous problem, compare the coefficient of variation before and after the price increase. Why does it change (or not change) in this way? Data from Problem 28: Your costs had been forecast as having an average of $138,000 with a standard devi
> Your costs had been forecast as having an average of $138,000 with a standard deviation of $35,000. You have just learned that your suppliers are raising prices by 4% across the board. Now what are the average and standard deviation of your costs?
> Airline ticket prices are generally optimized for the airline’s benefit, not for the consumer’s benefit. On July 8, 2010, at the online travel agency website http:// www.expedia.com, the following airfares were proposed for round trip travel from Seattle
> Consider the dollar value (in thousands) of gifts returned to each of your department stores after the holiday season (Table 5.5.9). a. Compute the sample standard deviation. b. Interpret the standard deviation in a paragraph discussing the variation fro
> Consider the average price of a hotel room in 21 U.S. cities (Table 5.5.8) for the first half of 2015. a. Find the average price of a major-city hotel room in the United States, based on this data set. b. Find the sample standard deviation of these price
> Here are weights of recently produced sinks: 20.8, 20.9, 19.5, 20.8, 20.0, 19.8, 20.1, 20.5, 19.8, 20.3, 20.0, 19.7, 20.3, 19.5, 20.2, 20.2, 19.5, 20.5 Find the usual summary measure that tells approximately how far from average these weights are.
> Consider the percentage change in the value of the dollar with respect to Asia-Pacific currencies, year-to-date as of mid-October 2015 (Table 5.5.7). a. Find the standard deviation of these percentages. b. Interpret this standard deviation. In particular
> Consider interest rates on accounts at a sample of local banks: 3.00%, 4.50%, 4.90%, 3.50%, 4.75%, 3.50%, 3.50%, 4.25%, 3.75%, 4.00% a. Find the standard deviation of these interest rates. b. What does this standard deviation tell you about banks in this
> Using the data from Table 2.6.8 of Chapter 2 for daily values for the Dow Jones Industrial Average: a. Find the standard deviation of the net change. b. Find the range of net change. c. Find the standard deviation of the percent change. d. Find the range
> For the experience numbers: a. Construct a histogram. b. Describe the shape of the distribution. c. Summarize the distribution in general terms.
> Summarize the variability in admission prices for the theme parks shown in Table 5.5.6 by reporting the standard deviation, the range, and the coefficient of variation. Table 5.5.6: TABLE 5.5.6 Theme Park Admission Prices Theme Park Admission Price
> Using the data set from the previous problem concerning the ages and maintenance costs of five similar printing presses: a. Calculate the average maintenance cost of the presses. b. Calculate the standard deviation of the maintenance costs of the presses
> Consider the ages (in years) and maintenance costs (in thousands of dollars per year) for five similar printing presses (Table 5.5.12). a. Calculate the average age of the presses. b. Calculate the standard deviation of the ages of the presses. c. Calcul
> The performance claimed by mutual funds is often considerably better than what you would experience if you actually put your money on the line. Table 5.5.11 shows the annual return for internationally diversified bond funds both before adjustment and aft
> Your firm’s total advertising budget has been set for the year. You (as marketing manager) expect to spend about $1,500,000 on TV commercials, with an uncertainty of $200,000 as the standard deviation. Your advertising agency collects a fee of 15% of thi
> Find the amount of variability in the 5-year percent change in housing prices for U.S. regions using the data from Table 4.3.5 of Chapter 4. Table 4.3.5: TABLE 4.3.5 Percent Change in Housing Values over Five Years for U.S. Regions Percent Percent
> Active consumers make up 13.6% of the market and spend an average of $16.23 per month on your product. Passive consumers make up 23.8% of the market and spend $9.85. The remaining consumers have average spending of $14.77. Find the average spending for a
> Your firm has the following securities outstanding: common stock (market value $4,500,000; investors demand 17% annual rate of return), preferred stock (market value $1,700,000; current annual yield is 13%), and 20-year bonds (market value $2,200,000; cu
> Some people who work at your company would like to visually compare the income distributions of people who buy various products in order to better understand customer selections. For each of 16 products, a list of incomes of representative customers (who
> Summarize prices of funeral services using the average and median, based on the data in Table 3.8.10 of Chapter 3. Table 3.8.10: TABLE 3.8.10 Cost of Traditional Funeral Service Funeral Home Cost ($) Bleitz $2,180 Bonney-Watson 2,250 Butterworth's
> For the age numbers: a. Construct a histogram. b. Describe the shape of the distribution. c. Summarize the distribution in general terms.
> Your factory’s inventory level was measured 12 times last year, with the results shown below. Find the average inventory level during the year. 313, 891, 153, 387, 584, 162, 742, 684, 277, 271, 285, 845
> A mail-order sales company sent its new catalog initially to a representative sample of 10,000 people from its mailing list and received orders totaling $36,851. a. Find the average dollar amount ordered per person in this initial mailing. b. What total
> Find the upper quartile for the following box plot. 20 40 60 80 100 Quality
> Given the state taxes and populations for the East North Central States, as shown in Table4.3.4, compute the percapita state tax burden for this entire region.17 Table4.3.4: TABLE 4.3.4 State Population and State Population (Thousands) State Taxes
> A social group shows only movies of 100 min or less at its meetings. Consider the running times of selected films from a video library as shown in Table 4.3.10. a. What percentage of these movies can the group show? b. What is the name of the longest of
> A large outdoor recreational facility has three entrances. According to automatic vehicle counters, last year 11,976 vehicles entered at the first entrance, 24,205 at the second, and 7,474 at the third. A survey done at each entrance showed that the aver
> Using the data from Table 3.8.2 in Chapter 3, find the average and median to summarize the typical size of the market response to stock buyback announcements. Table3.8.2: TABLE 3.8.2 Market Response to Stock Buyback Announcements Three- Three- Mont
> A survey of 613 representative people within your current area indicates that they plan to spend a total of $2,135 on your products next year. You are considering expansion to a new city with 2.1 million people. a. Find the average expenditure per person
> If you had a list of the miles per gallon for various cars, which of the following is the only possibility for the 65th percentile: 65 cars, 65%, $13,860, or 27 miles per gallon?
> Describe and classify this database and its parts: a.* Is this a univariate, bivariate, ormulti variate data set? b. What are the elementary units? c. Which variables are qualitative and which are quantitative? d.* Is “training level” ordinal or nominal?
> Let us continue to look at the DJIA discussed in problem 26. Table2.6.8 shows 22 daily observations of the value of the DJIA, with 21 observations of the net change from one observation to the next, and the percent change in the DJIA from one observation
> The Dow Jones company calculates a number of stock market index numbers that are used as indicators of the performance of the New York Stock Exchange. The best known of these is the DJIA, which is calculated based on the performance of 30 stocks from com
> Consider the information recorded in Table 2.6.6 for a selection of household upright vacuum cleaners. a. What is an elementary unit for this data set? b. What kind of a data set is this: univariate, bivariate, or multivariate? c. Which of these variable
> Suppose a data set includes the variable “business organization” recorded as 1 = sole proprietor, 2 = partnership, 3 = S corporation, 4 = C corporation. Is this a quantitative or qualitative variable?
> The ease of assembling products is recorded using the scale 1 = very easy, 2 = easy, 3 = moderate, 4 = difficult, 5 = very difficult. Is this a quantitative, ordinal, or nominal variable?
> Suppose a database includes the variable “security type” for which 1 = common stock, 2 = preferred stock, 3 = bond, 4 = futures contract, and 5 = option. Is this a quantitative or qualitative variable?
> Consider the information about selected cell phones shown in Table 2.6.5. a. What is an elementary unit for this data set? b. Is this a univariate, bivariate, or multivariate data set? c. Is this a cross-sectional or time-series data set? d. Is â&#
> One column of a large inventory spreadsheet shows the name of the company that sold you each part. a. Is this variable quantitative or qualitative? b. Is this variable ordinal, nominal, or neither?
> A quality control inspector has rated each batch produced today on a scale from A through E, where A represents the best quality and E is the worst. a. Is this variable quantitative or qualitative? b. Is this variable ordinal, nominal, or neither?
> You are looking at the sales figures for 35 companies. a. Is this data set univariate, bivariate, or multivariate? b. Is this variable qualitative or quantitative? c. Is this variable ordinal, nominal, or neither?
> a. What fraction of the variation in experience can be explained by the fact that some employees are older than others? b. How much experience would you expect for a 42year-old individual? c. Find the 95% confidence interval for the experience of a new i
> Consider a listing of the bid price and the ask price for 18 different U.S. Treasury bonds at the close of trading on a particular day. a. Is this univariate, bivariate, or multivariate data? b. Is this cross-sectional or time-series data?
> a. What salary would you expect for a 50-year-old individual? b. Find the 95% confidence interval for a new individual (from the same population from which the data were drawn) who is 50 years old. c. Find the 95% confidence interval for the mean salary
> Viewing the database in Appendix A as a random sample from a much larger population, consider the annual salary values. a. Find the 95% confidence interval. b. Find the 99% confidence interval.
> Consider the following random sample of 15 employee numbers from this database: 66, 37, 56, 11, 32, 23, 53, 43, 55, 25, 7, 26, 36, 22, and 20. a. Find the percentage of women for this sample. b. Find the standard error for the percentage of women and int
> For each variable in this database, tell which of the following operations would be appropriate: a. Arithmetic (adding, subtracting, etc.). b. Counting the number of employees in each category. c. Rank ordering. d. Finding the percentage of employees in
> Show that this database is arranged in the form of a frame. In particular, how would you use it to gain access to population information for a particular employee?
> Viewing the database in Appendix A as a random sample from a much larger population, consider the percentage who are advanced (at training level B or C).Find the 99% confidence interval.
> Viewing the database in Appendix A as a random sample from a much larger population, consider the percentage of women. Find the 95% confidence interval.
> Viewing the database in Appendix A as a random sample from a much larger population, consider the experience values. a. Find the 95% confidence interval. b. Find the 99.9% confidence interval.
> You have a position open and are trying to hire a new person. Assume that the new person’s experience will follow a normal distribution with the mean and (sample) standard deviation of your current employees. a. Find the probability that the new person w
> Consider experience as the Y variable and age as the X variable. a. Draw a scatterplot and describe the relationship. b. Find the correlation coefficient. What does it tell you? Is it appropriate, compared to the scatterplot? c. Find the least-squares re
> Could it reasonably be that no ads are worthwhile, in a study for which 2 of 22 are significant?
> Is it better, as suggested, to multiply the endpoints of the confidence interval by the target mailing size?
> How risky is this proposition?
> Find the average future net payoff, less the cost of the lease. How much, on average, would you gain (or lose) by leasing this oil field?
> Continue the scenario analysis by computing the future net payoff implied by each of the future prices of oil. To do this, multiply the price of oil by the number of barrels, then subtract the cost of extraction. If this is negative, you simply won’t dev
> Would you indeed lose money if you leased and extracted immediately? How much money?
> Are Kellerman’s calculations correct?
> Do the sample sizes have to be equal in the one-way analysis of variance?
> Repeat exercise 1, parts b and c, using a 99% confidence interval. Is the population mean annual salary in the interval? Data from exercise 1: View this database as a population. Consider the following sample of five employee numbers from this database
> Name six properties of a data set that are displayed by a histogram.
> a. What fraction of the variation in salaries can be explained by the fact that some employees are older than others? b. What salary would you expect for a 42-year-old individual? c. Find the 95% confidence interval for the salary of a new individual (fr
> Take a close look at the data using summaries and graphs. What do you find?
> a. What is a random experiment? b. Why does defining a random experiment help to focus your thoughts about an uncertain situation?
> When may you use the least-significant-difference test to compare individual pairs of samples? When is this not permitted?
> Describe and give a formula for each of the following quantities, which are used in performing a one-way analysis of variance: a. Total sample size, n. b. Grand average,
> a. State the hypotheses for the one-way analysis of variance. b. Is the research hypothesis very specific about the nature of any differences?
> a. What kind of data set should be analyzed using the one-way analysis of variance? b. Why should not you use the unpaired t test instead of the one-way analysis of variance?
> Explain in what sense the analysis of variance involves actually analyzing variance—in particular, what variances are analyzed and why?
> a. Define a first-order autoregressive process in terms of the relationship between successive observations. b. What are the X and Y variables in the regression model to predict the next observation in a first-order autoregressive process? c. Describe th
> a. Define the random noise process in terms of the relationship between successive observations. b. Comment on the following: If it is a random noise process, then special time-series methods are not needed to analyze it. c. What are the forecast and for
> a. How is the flexibility of the Box-Jenkins ARIMA process approach helpful in time-series analysis? b. What is parsimony? c. How does the forecast relate to the actual future behavior of the estimated process? d. How do the forecast limits relate to the
> a. How is a linear trend estimated in trend-seasonal analysis? b. What kind of forecast does the linear trend represent? c. What do you do to produce a forecast from the linear trend? d. Which components are represented in this forecast? Which are missin
> Consider annual salary as the Y variable and age as the X variable. a. Draw a scatterplot and describe the relationship. b. Find the correlation coefficient. What does it tell you? Is it appropriate, compared to the scatterplot? c. Find the least-squares
> a. How do you compute the ratio-to-moving-average? Which components does it represent? b. What do you do to the ratio-to-moving-average to produce a seasonal index? Why does this work? c. What does a seasonal index represent? d. How do you seasonally adj
> a. How is the moving average different from the original series? b. For trend-seasonal analysis, why do we use exactly 1 year of data at a time in the moving average? c. Which components remain in the moving average? Which are reduced or eliminated?
