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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

Global hand sanitizer market. A report published by Grand View Research in April 2020 provides the statistics on the global hand sanitizer market size in 2019. According to the findings, 77% of the
Study of why EMS workers leave the job. Refer to the Journal of Allied Health (Fall 2011) study of why emergency medical service (EMS) workers leave the profession, Exercise
(p. 158). Recall that in a sample of 244 former EMS workers, 127 were fully compensated while on the job, 45 were partially compensated, and 72 had noncompensated volunteer positions. Also, the
Content marketing and social media. Content marketing is a strategic marketing approach companies use to create online content that attracts and retains customers. The 9th annual (February 2019)
How do you prefer to get the news? Today, you have numerous options for getting the news: print (via a newspaper or magazine), television (through local, network, or cable channels), the Internet
Education subject preferences. An article published in the Chinese Journal of Sociology (Vol. 6, 2020) presents comparative evidence on the gender gap in educational achievement in Japan, China, and
Ambulance response time. Geographical Analysis (January 2010) presented a study of emergency medical service (EMS) ability to meet the demand for an ambulance. In one example, the researchers
Online Study for the Autumn 2020 Semester. In April 2020, the American Association of Collegiate Registrars and Admissions Officers published a report on students’ decision to attend in-person
Firefighters’ use of gas detection devices. Two deadly gases that can be present in fire smoke are hydrogen cyanide and carbon monoxide. Fire Engineering (March 2013) reported the results of a
Websites for small businesses. Visual Objects, a portfolio website, surveyed 529 small businesses about whether they have a website, why they have a website, and how they maintain their website. The
Random shuffling of songs on Spotify. Spotify is a musicstreaming service that offers both free and subscription options. Users can create playlists and choose to use Spotify’s random shuffling
Forensic evidence in a criminal court case. In our legal system, the use of DNA as forensic evidence is often regarded as the most reliable type of evidence. However, most of the DNA code is the
Risk of a natural gas pipeline accident. Process Safety Progress (December 2004) published a risk analysis for a natural gas pipeline between Bolivia and Brazil. The most likely scenario for an
Most likely coin-tossing sequence. In Parade Magazine’s (November 26, 2000) column “Ask Marilyn,” the following question was posed: “I have just tossed a [balanced] coin 10 times, and I ask
Encryption systems with erroneous ciphertexts. In cryptography, ciphertext is encrypted or encoded text that is unreadable by a human or computer without the proper algorithm to decrypt it into
Suppose the events B1 and B2 are mutually exclusive and complementary events, such that P1B12 = .75 and P1B22 = .25. Consider another event A such that P1A B12 = .3 and P1A B22 = .5.a. Find P1B1
Suppose the events B1, B2, and B3 are mutually exclusive and complementary events, such that P1B12 = .2, P1B22 = .4, and P1B32 = .5. Consider another event A such that P1A B12 = P1A B22 = .1, and
Suppose the events B1, B2, and B3 are mutually exclusive and complementary events, such that P1B12 = .2, P1B22 = .15, and P1B32 = .65. Consider another event A such that P1A2 = .4. If A is
Confidence of feedback information for improving quality. In the semiconductor manufacturing industry, a key to improved quality is having confidence in the feedback generated by production
Fingerprint expertise. A study published in Psychological Science (August 2011) tested the accuracy of experts and novices in identifying fingerprints. Participants were presented pairs of
Tests for Down syndrome. Currently, there are three diagnostic tests available for chromosome abnormalities in a developing fetus. The safest (to both the mother and fetus) and least expensive of
Fish contaminated by a plant’s toxic discharge. Refer to the US Army Corps of Engineers’ study on the DDT contamination of fish in the Tennessee River (Alabama), Example 1.5 (p. 33). Part of the
Company credit card records. A bank officer is analyzing the transactions of a company credit card, controlled by three directors, director 1, 2 and 3. Of the transactions, 25% were made by director
Effectiveness of new screening tests for a disease. Scientists have created a screening test for a newly emerged disease. The test needs to be checked to ensure that its results are accurate. It was
Nondestructive evaluation. Nondestructive evaluation (NDE) describes methods that quantitatively characterize materials, tissues, and structures by noninvasive means, such as X-ray computed
Spam Emails. Businesses often use spam email for advertisements because the cost per email is incredibly low and many emails can be sent out at the same time. However, some spam emails, known as
Intrusion detection systems. The Journal of Research of the National Institute of Standards and Technology (November–December 2003) published a study of a double intrusion detection system with
Forensic analysis of JFK assassination bullets. Following the assassination of President John F. Kennedy (JFK) in 1963, the House Select Committee on Assassinations (HSCA) conducted an official
Which of the following pairs of events are mutually exclusive? Justify your response.a. {The next customer entering a retail store is older than 30 years.}, {The next customer entering the same
A sample space consists of three sample points, S1, S2, and S3, with P1S12 = .1, and P1S22 = .2.a. Assign a probability to S3 to show that the sample points obey the two probability rules for a
For two events A and B, suppose P1A2 = .7, P1B2 = .5, and P1A ¨ B2 = .4. Find P1A ∪ B2.
Consider two events A and B, with P1A2 = .1, P1B2 = .2, and P1A ¨ B2 = 0.a. Are A and B mutually exclusive?b. Are A and B independent?
Two events, A and B, are independent, with P1A2 = .3 and P1B2 = .1.a. Are A and B mutually exclusive? Why?b. Find P1A B2 and P1B A2.c. Find P1A ∪ B2.
Given that P1A ¨ B2 = .4 and P1A B2 = .8, find P1B2. 3.100 From a production batch with 16 items, 8 items are randomly selected for quality assurance. In how many different ways can the sample
(p. 46). Recall that 12 auditors and 22 specialists were interviewed and asked to give their views on the use of specialists during an audit. Assume that of the 34 respondents, five auditors and 10
Types of random variables. Which of the following describe continuous random variables? Which describe discrete random variables?a. The number of cups of coffee sold in a cafeteria during lunchb.
Types of random variables at a health center. A health center is offering discounts to new customers. At the end of one month, the manager of the health center analyzes the data collected during the
NHTSA crash tests. Refer to the National Highway Traffic Safety Administration (NHTSA) crash tests of new car models, Exercise
(p. 136). Recall that the NHTSA developed a driver-side “star” scoring system, with results ranging from one star (*) to five stars (*****). The more stars in the rating, the better the level of
Water in a bottle. A bottle contains 16 ounces of water. The variable x represents the volume, in ounces, of water remaining in the bottle after the first drink is taken. What are the natural bounds
Executive pay. Refer to Glassdoor Economic Research’s list of the top-paid CEOs (Table 2.1). One variable saved CRASH CEO50 NW in the file is the CEO’s age in 2015. Is the age a discrete or
Banking. Give an example of a discrete random variable that would be of interest to a banker.
Economics. Give an example of a continuous random variable that would be of interest to an economist.
Retailing. Give two examples of discrete random variables that would be of interest to the manager of a clothing store.
Stock market. Give an example of a continuous random variable that would be of interest to a stockbroker.
A 95% confidence interval for a population mean was reported to be 152 to 160.If σ 15, what sample size was used in this study?Applications
A simple random sample with n 54 provided a sample mean of 22.5 and a sample standard deviation of 4.4.a. Develop a 90% confidence interval for the population mean.b. Develop a 95% confidence
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10.Suppose a simple random sample
Is your favorite TV program often interrupted by advertising? CNBC presented statistics on the average number of programming minutes in a half-hour sitcom (CNBC, February 23, 2006). The following
Consumption of alcoholic beverages by young women of drinking age has been increasing in the United Kingdom, the United States, and Europe (The Wall Street Journal, February 15, 2006). Data (annual
Disney’s Hannah Montana: The Movie opened on Easter weekend in April 2009. Over the three-day weekend, the movie became the number-one box office attraction (The Wall Street Journal, April 13,
The range for a set of data is estimated to be 36.a. What is the planning value for the population standard deviation?b. At 95% confidence, how large a sample would provide a margin of error of 3?c.
At 95% confidence, how large a sample should be taken to obtain a margin of error of .03 for the estimation of a population proportion? Assume that past data are not available for developing a
Many stock market observers say that when the P/E ratio for stocks gets over 20 the market is overvalued. The P/E ratio is the stock price divided by the most recent 12 months of earnings.Suppose you
Annual salary plus bonus data for chief executive officers are presented in the BusinessWeek Annual Pay Survey. A preliminary sample showed that the standard deviation is $675 with data provided in
Refer to the NCP data in Table 13.4. Set up the ANOVA table and test for any significant difference in the mean examination score for the three plants. Use α .05.
The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains (Consumer Reports website). One of the variables in the study is meal
The following data are from a completely randomized design. In the following calculations, use α .05.a. Use analysis of variance to test for a significant difference among the means of the three
Refer to exercise 15.Use Fisher’s LSD procedure to develop a 95% confidence interval estimate of the difference between the means for manufacturer 1 and manufacturer 2.
The following data are from an experiment designed to investigate the perception of corporate ethical values among individuals specializing in marketing (higher scores indicate higher ethical
To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained.Machine 1 Machine 2 Machine 3 Machine 4 6.4 8.7 11.1 9.9 7.8 7.4
Refer to exercise 18.Use the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experimentwise error rate of.05 is desired.
Consider the experimental results for the following randomized block design. Make the SELF test calculations necessary to set up the analysis of variance table.Use α .05 to test for any significant
An experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table Use α .05 to test for any significant differences.Applications
The calculations for a factorial experiment involving four levels of factor A, three levels of factor B, and three replications resulted in the following data: SST 280, SSA 26, SSB 23, SSAB
Set up the ANOVA table and test for any significant main effects and any interaction effect. Use α .05.Applications
Consider the following time series data.Week 123456 Value 18 13 16 11 17 14 Using the naive method (most recent value) as the forecast for the next week, compute the following measures of forecast
Exercises 1 and 2 used different forecasting methods. Which method appears to provide the more accurate forecasts for the historical data? Explain.
Consider the following time series data.Month 1234567 Value 24 13 20 12 19 23 15a. Compute MSE using the most recent value as the forecast for the next period. What is the forecast for month 8?b.
Consider the following time series data.Week 123456 Value 18 13 16 11 17 14a. Construct a time series plot. What type of pattern exists in the data?b. Develop the three-week moving average forecasts
Consider the following time series data.Month 12 34567 Value 24 13 20 12 19 23 15 Construct a time series plot. What type of pattern exists in the data?a. Develop the three-week moving average
Refer again to the gasoline sales time series data in Table 18.1.a. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent observation, and 1/6 for third most recent
Could you always find a set of weights that would make the MSE at least as small for a weighted moving average than for an unweighted moving average? Why or why not?
With the gasoline time series data from Table 18.1, show the exponential smoothing forecasts using α .1.a. Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of α
With a smoothing constant of α .2, equation (18.2) shows that the forecast for week 13 of the gasoline sales data from Table 18.1 is given by F13 .2Y12 + .8F12. However, the forecast for week 12 is
For the Hawkins Company, the monthly percentages of all shipments received on time over the past 12 months are 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84, and 83.a. Construct a time series plot. What
Corporate triple-A bond interest rates for 12 consecutive months follow.9.5 9.3 9.4 9.6 9.8 9.7 9.8 10.5 9.9 9.7 9.6 9.6a. Construct a time series plot. What type of pattern exists in the data?b.
The values of Alabama building contracts (in $ millions) for a 12-month period follow.240 350 230 260 280 320 220 310 240 310 240 230a. Construct a time series plot. What type of pattern exists in
The following time series shows the sales of a particular product over the past 12 months.a. Construct a time series plot. What type of pattern exists in the data?b. Use α .3 to compute the
Ten weeks of data on the Commodity Futures Index are 7.35, 7.40, 7.55, 7.56, 7.60, 7.52, 7.52, 7.70, 7.62, and 7.55.a. Construct a time series plot. What type of pattern exists in the data?b. Compute
The Nielsen ratings (percentage of U.S. households that tuned in) for the Masters Golf Tournament from 1997 through 2008 follow (Golf Magazine, January 2009).The rating of 11.2 in 1997 indicates that
Consider the following time series data.t 1 23 45 Yt 6 11 9 14 15a. Construct a time series plot. What type of pattern exists in the data?b. Develop the linear trend equation for this time series.c.
Refer to the time series in exercise 17.Use Holt’s linear exponential smoothing method with α .3 and .5 to develop a forecast for t 6.
Consider the following time series.t 1 2 34567 Yt 120 110 100 96 94 92 88a. Construct a time series plot. What type of pattern exists in the data?b. Develop the linear trend equation for this time
Consider the following time series.t 1234567 Yt 82 60 44 35 30 29 35a. Construct a time series plot. What type of pattern exists in the data?b. Using Minitab or Excel, develop the quadratic trend
Because of high tuition costs at state and private universities, enrollments at community colleges have increased dramatically in recent years. The following data show the enrollment (in thousands)
The Seneca Children’s Fund (SCF) is a local charity that runs a summer camp for disadvantaged children. The fund’s board of directors has been working very hard in recent years to decrease the
The president of a small manufacturing firm is concerned about the continual increase in manufacturing costs over the past several years. The following figures provide a time series of the cost per
FRED® (Federal Reserve Economic Data), a database of more than 3000 U.S. economic time series, contains historical data on foreign exchange rates. The following data show the foreign exchange rate
Automobile unit sales at B. J. Scott Motors, Inc., provided the following 10-year time series.a. Construct a time series plot. Comment on the appropriateness of a linear trend.b. Using Minitab or
Giovanni Food Products produces and sells frozen pizzas to public schools throughout the eastern United States. Using a very aggressive marketing strategy they have been able to increase their annual
Forbes magazine ranks NFL teams by value each year. The following data are the value of the Indianapolis Colts from 1998 to 2008 (Forbes website).a. Construct a time series plot. What type of pattern
Consider the following time series data.a. Construct a time series plot. What type of pattern exists in the data?b. Use the following dummy variables to develop an estimated regression equation to
The quarterly sales data (number of copies sold) for a college textbook over the past three years followa. Construct a time series plot. What type of pattern exists in the data?b. Use the following
Air pollution control specialists in southern California monitor the amount of ozone, carbon dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data exhibit
South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from
Three years of monthly lawn-maintenance expenses ($) for a six-unit apartment house in southern Florida follow.a. Construct a time series plot. What type of pattern exists in the data?b. Develop an
The quarterly sales data follow.a. Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend effects in the data: Qtr1 1 if Quarter 1,
Refer to the Costello Music Company time series in exercise 49.a. Deseasonalize the data and use the deseasonalized time series to identify the trend.b. Use the results of part (a) to develop a
Hudson Marine has been an authorized dealer for C&D marine radios for the past seven years. The following table reports the number of radios sold each year.Year 1234 5 6 7 Number Sold 35 50 75 90 105

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