Questions and Answers of Practical Business Statistics

Do initial public offerings (IPOs) of stock significantly increase in value, on average, in the short term? Test using the data from Table 4.3.7 that show the performance of initial offerings as
The p-value is 0.0371. What conclusions can you reach and what error might have been made?
At a recent meeting, it was decided to go ahead with the introduction of a new product if “interested consumers would be willing, on average, to pay $20.00 for the product.” A study was
Your bakery produces loaves of bread with “1 pound” written on the label. Here are weights of randomly sampled loaves from today’s production: 1.02, 0.97, 0.98, 1.10, 1.00, 1.02, 0.98, 1.03,
Your factory’s inventory level was determined at 12 randomly selected times last year, with the following results: 313, 891, 153, 387, 584, 162, 742, 684, 277, 271, 285, 845 a. Find the
Some of your advertisements seem to get no reaction, as though they are being ignored by the public. You have arranged for a study to measure the public’s awareness of your brand before and after
Part of the assembly line will need adjusting if the consistency of the injected plastic becomes either too viscous or not viscous enough as compared with a value (56.00) your engineers consider
What standard error would you use to test whether a new observation came from the same population as a sample?
Suppose you have an estimator and would like to test whether or not the population mean value equals 0. What do you need in addition to the estimated value?
Suppose you learn that the p-value for a hypothesis test is equal to 0.0217. What can you say about the result of this test?
From a list of the 729 people who went on a cruise, 130 were randomly selected for interview. Of these, 112 said that they were very happy with the accommodations. Find the 95% confidence interval
Find the one-sided 95% confidence interval for the weight of candy bars after intervention, based on the data in Table 5.5.4, indicating that the population mean weight is no more than some
Find the 99.9% confidence interval for the weight of candy bars before intervention, based on the data in Table 5.5.4 of Chapter 5. TABLE 5.5.4 Weight (in Ounces) for Two Samples of Candy Bars
Find the 95% confidence interval for the amounts that your regular customers spent on your products last month, viewing the data from Table 4.3.1 of Chapter 4 as a random sample of customer
A market survey has shown that people will spend an average of $2.34 each for your product next year, based on a sample survey of 400 people. The standard deviation of the sample was $0.72. Find the
Table 9.6.2 shows the 2015 performance of stocks recommended by Gene Marcial, whose list was published in Forbes in December 2014. a. Compute the average and briefly describe its
Based on the following daily percent changes of the S&P 500 stock market index for June 2010 (accessed at http:// finance.Yahoo.com on July 13, 2010), find the 95% confidence interval for the
Comparison shopping is available on the Internet, and this is useful because exactly the same item is available at a variety of prices. Table 9.6.1 shows results from MySimon for prices of the Eureka
Your firm is in the market to hire an experienced vice president of information technology or information systems. If one is chosen at random from the population represented in the preceding problem,
A nationwide poll claims that the margin of error is no more than 4.3 percentage points for questions asked of half the sample (at the 95% confidence level). a. Verify this claim in a particular case
In a sample of 258 individuals selected randomly from a city of 750,339 people, 165 were found to be supportive of a new public works project. Find the 99.9% confidence interval for the support level
A recent survey of 252 customers, selected at random from a database with 12,861 customers, found that 208 are satisfied with the service they are receiving. Find the 99% confidence interval for the
A market survey has shown that people will spend an average of $15.48 each for your product next year, based on a sample survey of 483 people. The standard deviation of the sample was $2.52. Find the
Click-through rates were measured for each of 83 mobile advertising campaigns, and showed an average rate of 2.38%, with a standard error of 0.134%. Please note that this is not a binomial situation
Cost observations provided for 21 production situations have an average of $149.67 and a standard deviation of $38.85. a. Find and interpret the two-sided 95% confidence interval. b. Find
Main-course taste scores have been recorded for 48 restaurant diners on a scale from 1 to 5. The average score was 4.125, the standard error was 0.1099, and the 95% confidence interval extended from
Consumer preferences have been observed in a situation for which the standard error is known. Find the critical t value to use for each of the following confidence interval calculations: a.
Vaccine responses have been observed for 1,859 people. Find the critical t value to use for each of the following confidence interval calculations: a. Two-sided 95% confidence. b. Two-sided
Intensities have been measured for eight flashlights. Find the critical t value to use for each of the following confidence interval calculations: a. Two-sided 95% confidence. b. Two-sided
Your quality control department has just analyzed the contents of 20 randomly selected barrels of materials to be used in manufacturing plastic garden equipment. The results found an average of 41.93
Your hospital is negotiating with medical insurance providers, who would like to reduce the amount they pay as reimbursement for hospital stays. For a particular procedure, they would like to reduce
Your company prepares and distributes frozen foods. The package claims a net weight of 24.5 oz. A random sample of today’s production was weighed, and the results were summarized as follows:
Your agricultural firm is considering the purchase of some farmland, and an indication of the quality of the land will be helpful. A random sample of 62 selected locations planted with corn indicates
Why are critical t values generally larger than 1.960 for a two-sided 95% confidence interval?
Which fact about a normal distribution leads to the factor 2 (or 1.960) in the approximate confidence interval statement?
What does a confidence interval tell you about the population that an estimated value alone does not?
In what important way does statistical inference go beyond summarizing the data?
A survey of 823 randomly selected adults in the United States finds that 63% support current government policies. Find the usual measure that indicates approximately how far this sample percentage is
Find the average and the standard error for the weight of candy bars before intervention, based on the data in Table 5.4 of Chapter 5.
Find the average and the standard error for the strength of cotton yarn used in a weaving factory, based on the data in problem 23 of Chapter 4.
Find the average and the standard error for the amounts that your regular customers spent on your products last month, viewing the data from problem 2 of Chapter 4 as a sample of customer orders.
Find the standard error of the average for the following data set representing quality of agricultural produce: 16:7,17:9,23:5,13:8,15:9,15:2,12:9,15:7
Economists often make forecasts of future conditions. Consider the US unemployment rate for June 2015 as predicted in October 2014 as part of a survey of economists, as shown in Table 8.6.4. a.
You have analyzed a project using four scenarios, with the results shown in Table 8.6.1. Suppose you actually have 40 projects just like this one and they pay off independently of one another. Find
The population mean is $65 and the population standard deviation is $30. Find the probability that the average of 35 randomly selected transactions is between $55 and $60. You may assume that the
A farmer has five identical cornfields, each of which independently produces a normally distributed harvest with a mean of 80,000 bushels and a standard deviation of 15,000 bushels. Find the
You have interviewed 369 people out of a population of 30,916 and found that 51.8% expect to vote for the challenger in the upcoming election. Find the standard error of this estimate.
Deposits have a mean of $125 and a standard deviation of $36. Find the standard deviation of the average amount of 12 randomly selected deposits.
You have estimated the inventory value of your competition as $384,000 but later learn that the true inventory value was $416,000. Find the estimation error.
You have eight machines operating independently. The mean production rate for each machine is 20.3 tons/day, and the standard deviation is 1.4 tons/day. Approximately how much uncertainty is there in
The population mean productivity is 35, the population standard deviation is 10, and the sample size is 15. Find the standard deviation of the total amount represented by a random sample.
The mean account balance is $500 and the standard deviation is $120 for a large population of bank accounts. Find the standard deviation of the average balance of groups of eight accounts (chosen
Draw a random sample of eight invoices from a population of 500 overdue billings, starting with row 17, column 5 of the table of random digits.
Draw a random sample of five contracts from a population of 362 recent contracts with cost overruns, starting with row 13, column 5 of the table of random digits.
Draw a random sample of four firms from a population of 86 suppliers, starting with row 30, column 4 of the table of random digits.
Draw a random sample of three account numbers from a population of 681 accounts receivable documents, starting with row 6, column 2 of the table of random digits.
Select a random sample of four without replacement from the following metal products corporations: Gillette, Crown Cork & Seal, MASCO, Tyco Laboratories, Illinois Tool Works, McDermott, Ball,
Select a random sample of three without replacement from the following (very small) population of firms: IBM, GM, Ford, Shell, HP, Boeing, and ITT. Use the following sequence of random digits:
Which of the following samples is likely to be the most representative of the population of all employees at IBM? a. The 10 oldest and most experienced researchers at the Thomas J. Watson
Which of the following samples is likely to be the most representative of the population of all registered voters in the United States? a. A sample of 200 people at a Denver shopping
What do the standard errors Sx and Sp indicate for a binomial situation?
a. What is a statistic? b. What is the parameter?
Customers arrive at random times, with an exponential distribution for the time between arrivals. Currently, the mean time between customers is 6.34 minutes. a. Since the last customer arrived,
Suppose 17% of the items in a large warehouse are defective. You have chosen a random sample of 350 items to examine in detail. Find the probability that more than 20% of the sample is defective.
Although you do not know the exact total amount of payments you will receive next month, based on past experience you believe it will be approximately $2,500 more or less than $13,000, and will
Assume that electronic microchip operating speeds are normally distributed with a mean of 2.5 GHz and a standard deviation of 0.4 GHz. What percentage of your production would you expect to be
You are a farmer about to harvest your crop. To describe the uncertainty in the size of the harvest, you feel that it may be described as a normal distribution with a mean value of 80,000 bushels and
The amount of ore (in tons) in a segment of a mine is assumed to follow a normal distribution with mean 185 and standard deviation 40. Find the probability that the amount of ore is less than 175
Based on recent experience, you expect this Saturday’s total receipts to have a mean of $2,353.25 and a standard deviation of $291.63 and to be normally distributed. a. Find the probability of
The quality control section of a purchasing contract for valves specifies that the diameter must be between 2.53 and 2.57 cm. Assume that the production equipment is set so that the mean diameter is
Find the probability that you will see moderate improvement in productivity, meaning an increase in productivity between 6 and 13. You may assume that the productivity increase follows a normal
You are planning to make sales calls at eight firms today. As a rough approximation, you figure that each call has a 20% chance of resulting in a sale and that firms make their buying decisions
You have just performed a survey interviewing 358 randomly selected people. You found that 94 of them are interested in possibly purchasing a new cable TV service. How much uncertainty is there in
An election coming up next week promises to be very close. In fact, assume that 50% are in favor and 50% are against. Suppose you conduct a poll of 791 randomly selected likely voters. Approximately
know that one of your customers has been having trouble with the recession and may not be able to make the loan payment that is due next week. You believe there is a 60% chance that the payment of
A new project has an uncertain cash flow. A group meeting has resulted in a consensus that a reasonable way to view the possible risks and rewards is to say that the project will pay $50,000 with
On a given day, assume that there is a 30% chance you will receive no orders, a 50% chance you will receive one order, a 15% chance of two orders, and a 5% chance of three orders. Find the expected
An investment will pay $105 with probability 0.7, and $125 with probability 0.3. Find the risk (as measured by standard deviation) for this investment.
a. How do you tell if a random variable has a binomial distribution? b. What is a binomial proportion? c. What are n, π, X, and p?
You are in the process of assessing your firm’s online marketing strategy, and would like to know whether visitors to your Website who arrive from a search engine ad (after searching for your
As part of an assessment of the role of organized activities for your user base, you have compiled the following facts regarding attendance at the most recent User Conference and subsequent software
Do studies have an impact on future activities in society? A study of New Jersey adults found that those who studied civics in school were more likely to vote in a recent election.17 Specifically,
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)
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
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
You have determined that 2.1% of the CDs that your factory manufactures are defective due to a problem with materials and that 1.3% are defective due to human error. Assuming that these are
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
The probability that the project succeeds in New York is 0.6, the probability that it succeeds in Chicago is 0.7, and the probability that it succeeds in both markets is 0.55. Find the conditional
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
Your firm is interested in learning more about customers’ purchasing patterns on its Web site and how they relate to the frequency of online site visits. The probability that a customer’s visit
The probability of getting a big order currently under negotiation is 0.32. The probability of losing money this quarter is 0.54. a. Assume that these are mutually exclusive events. Find the
You are responsible for a staff of 32 out of the 118 workers in a rug-weaving factory. Next Monday a representative will be chosen from these 118 workers. Assume that the representative is chosen at
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
What is a joint probability table?
What are mutually exclusive events?
1. Are Kellerman’s calculations correct? These are the first items to verify. 2. Take a close look at the data using appropriate statistical methods. 3. Are Kellerman’s conclusions
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
Using the data from Table 2.6.7 of Chapter 2 for the 30 Dow Jones Industrial companies percent changes since January 2015: a. Find the standard deviation of the percent change. b. Find the
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 Percent Change in Housing Values over

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