Questions and Answers of Statistical Techniques in Business and Economics 1

A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. Assume the population standard deviation for
Fry Brothers Heating and Air Conditioning Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air-conditioning units in homes. Tom Fry, the owner, would like to
Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift than on the day shift. The mean number of units produced
A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population
The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida,
The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected
The null and alternate hypotheses are:H0: μd = 0H1: μd ≠ 0The following paired observations show the number of traffic citations given for speeding by Officer Dhondt and Officer Meredith of the
The null and alternate hypotheses are:H0: μd ≤ 0H1: μd > 0The following sample information shows the number of defective units produced on the day shift and the afternoon shift for a sample of
Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. The
Assume the sample populations do not have equal standard deviations and use the .05 significance level:(a) Determine the number of degrees of freedom and round down to the nearest integer value(b)
Assume the sample populations do not have equal standard deviations and use the .05 significance level:(a) Determine the number of degrees of freedom and round down to the nearest integer value(b)
Assume the sample populations do not have equal standard deviations and use the .05 significance level:(a) Determine the number of degrees of freedom and round down to the nearest integer value(b)
Following are the 36 players on the opening-day roster of the 2018 Boston Red Sox Major League Baseball team, their salaries, and fielding positions.Sort the players into two groups, all pitchers
The null and alternate hypotheses are:H0: μ1 = μ2H1: μ1 ≠ μ2A random sample of 10 observations from one population revealed a sample mean of 23 and a sample standard deviation of 4. A random
Do married and unmarried women spend the same amount of time per week using Facebook? A random sample of 45 married women who use Facebook spent an average of 4.0 hours per week on this social media
Refer to the Baseball 2018 data, which report information on the 30 Major League Baseball teams for the 2018 season.a. Conduct a test of hypothesis to determine whether the mean salary of the teams
Listed is the annual rate of return (reported in percent) for a sample of 12 taxable mutual funds.Using the .05 significance level, is it reasonable to conclude that the mean rate of return is more
An Etsy store receives an average of 6.5 returns per day from online shoppers. For a sample of 12 days, it received the following numbers of returns.At the .01 significance level, can we conclude the
According to ValuePenguin.com, the current 30-year mortgage rate is now less than 5%. A sample of eight small banks in the Midwest revealed the following rates (in percent):At the .01 significance
A 2019 survey of American households with two or more children indicated the mean annual interest paid on household debt was $8,000. A sample of 12 households reported the following annual paid
Refer to Table 10–3 and the example just completed. With n = 100, σ = 400, X̅ c = 10,078, and μ1 = 10,100, verify that the probability of a Type II error is .2912.Data From Table 10-3: Selected
Refer to Table 10–3 and the example just completed. With n = 100, σ = 400, X̅ c = 9,922, and μ1 = 9,880, verify that the probability of a Type II error is .1469.Data From Table 10-3: Selected
Given the following hypotheses:H0: μ = 100H1: μ ≠ 100A random sample of six resulted in the following values: 118, 105, 112, 119, 105, and 111. Assume a normal population. Using the .05
Given the following hypotheses:H0: μ ≥ 20H1: μ > 20A random sample of five resulted in the following values: 18, 15, 12, 19, and 21. Assume a normal population. Using the .01 significance
The mean income per person in the United States is $60,000, and the distribution of incomes follows a normal distribution. A random sample of 10 residents of Wilmington, Delaware, had a mean of
The management of GoGo Carts is considering a new method of assembling its golf cart. The present method requires a mean time of 42.3 minutes to assemble a cart. The mean assembly time for a random
Given the following hypotheses:H0: μ = 400H1: μ ≠ 400A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using
Given the following hypotheses:H0: μ ≤ 10H1: μ > 10A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 3. Using
Refer to the Lincolnville School District bus data.a. Develop a 95% confidence interval for the mean bus maintenance cost.b. Develop a 95% confidence interval for the mean bus odometer miles.Data
Refer to the Baseball 2018 data, which report information on the 30 Major League Baseball teams for the 2018 season. Assume the 2018 data represents a sample.a. Develop a 95% confidence interval for
A survey of 36 randomly selected iPhone owners showed that the purchase price has a mean of $650 with a sample standard deviation of $24.a. What is the point estimate of the population mean?b. What
Based on a sample of 50 U.S. citizens, the American Film Institute found that a typical American spent 78 hours watching movies last year. The standard deviation of this sample was 9 hours.a. Develop
A survey of 25 randomly sampled judges employed by the state of Florida found that they earned an average wage (including benefits) of $65.00 per hour. The sample standard deviation was $6.25 per
As part of their business promotional package, the Milwaukee Chamber of Commerce would like an estimate of the mean cost per month to lease a one-bedroom apartment. The mean cost per month for a
A state meat inspector in Iowa has would like to estimate the mean net weight of packages of ground chuck labeled “3 pounds.” Of course, he realizes that the weights cannot always be precisely 3
Thirty-six items are randomly selected from a population of 300 items. The sample mean is 35 and the sample standard deviation 5. Develop a 95% confidence interval for the population mean.
Suppose the U.S. president wants to estimate the proportion of the population that supports his current policy toward revisions in the health care system. The president wants the margin of error to
Schadek Silkscreen Printing Inc. purchases plastic cups and imprints them with logos for sporting events, proms, birthdays, and other special occasions. Zack Schadek, the owner, received a large
Netflix is considering a new romcom (romantic comedy) series. Before making a final decision, the producers design an experiment to estimate the proportion of viewers who would watch the series. A
Historically, Widgets Manufacturing Inc. produces 250 widgets per day. Recently the new owner bought a new machine to produce more widgets per day. A sample of 16 days’ production revealed a mean
A research firm surveyed 49 randomly selected Americans to determine the mean amount spent on coffee during 1 week. The sample mean was $20 per week. The population distribution is normal with a
A recent federal report indicated that 27% of children ages 2 to 5 ate a vegetable at least five times a week. How large a sample is needed to estimate the true population proportion within 2% with a
Refer to the Baseball 2018 data, which report information on the 30 Major League Baseball teams for the 2018 season. Over the last decade, the mean attendance per team followed a normal distribution
A recent study by the Greater Los Angeles Taxi Drivers Association showed that the mean fare charged for service from Hermosa Beach to Los Angeles International Airport is $25 and the standard
Majesty Video Production Inc. wants the mean length of its advertisements to be 30 seconds. Assume the distribution of ad length follows the normal distribution with a population standard deviation
eComputers Inc. recently completed the design for a new laptop model. Top management would like some assistance in pricing the new laptop. Two market research firms were contacted and asked to
The 24 retail stores located in the Mall of America numbered 00 through 24 are:a. If the following random numbers are selected, which retail stores should be contacted for a survey? 11, 65, 86, 62,
A normal population has a mean of $60 and standard deviation of $12. You select random samples of nine.a. Apply the central limit theorem to describe the sampling distribution of the sample mean with
Using a random number generator from statistical software, create five sets (columns) of 50 random numbers between 0 and 9.a. Create a frequency distribution and a histogram summarizing all 250
A normal population has a mean of $75 and standard deviation of $5. You select random samples of 40.a. Apply the central limit theorem to describe the sampling distribution of the sample mean with n
Consider all of the coins (pennies, nickels, quarters, etc.) in your pocket or purse as a population. Make a frequency table beginning with the current year and counting backward to record the ages
Suppose P(A) = .40 and P(B | A) = .30. What is the joint probability of A and B?
The following is a list of 24 Marco’s Pizza stores in Lucas County. The stores are identified by numbering them 00 through 23. Also noted is whether the store is corporate owned (C) or manager
Refer to the data set that reports information on the 30 Major League Baseball teams for the 2018 season.a. For the variable salary, compute the mean, median, range, standard deviation, and
A recent graduate from a business college is hired by a marketing firm in sales. Her first year’s estimated income is $35,000. She did research on starting salaries for similar positions and found
Best Electronics Inc. offers a “no hassle” returns policy. The daily number of customers returning items follows the normal distribution. The mean number of customers returning items is 10.3 per
A recent study reported that Americans spend an average of 270 minutes per day watching TV. Assume the distribution of minutes per day watching TV follows a normal distribution with a standard
In 2018, the U.S. Department of Agriculture issued a report (http://www.cnpp.usda.gov/ sites/default/files/CostofFoodNov2018.pdf) indicating a family of four spent an average of $1,054.50 per month
You visit a friend who lives in the suburbs of Chicago. You decide to take a commuter train into the city. Your friend says that a train stops at the station every 30 minutes. Without any more
If a continuous random variable, x, is normally distributed with a mean of 100 and a standard deviation of 15:a. What is the probability that x = 100? Why?b. What is the probability that x = 113.56?
If a continuous random variable, x, is uniformly distributed with a minimum value of 5 and a maximum value of 25:a. What is the probability that x = 10? Why?b. What is the probability that x = 13.4?
The lifetime of LCD TV sets follows an exponential distribution with a mean of 100,000 hours. Compute the probability a television set:a. Fails in less than 10,000 hours.b. Lasts more than 120,000
For the most recent year available, the mean annual cost to attend a private university in the United States was $50,900. Assume the distribution of annual costs follows the normal probability
Among the 30 largest U.S. cities, the mean one-way commute time to work is 25.8 minutes. The longest one-way travel time is in New York City, where the mean time is 39.7 minutes. Assume the
In New York State, the mean salary for high school teachers in 2017 was $81,410 with a standard deviation of $9,500. Only Alaska’s mean salary was higher! Assume New York’s state salaries follow
The Internal Revenue Service reported the average refund in 2017 was $2,878 with a standard deviation of $520. Assume the amount refunded is normally distributed.a. What percent of the refunds are
The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of $29.81 per hour and a standard deviation of $9.31 per hour. What is the probability that the hourly
A normal population has a mean of 12.2 and a standard deviation of 2.5.a. Compute the z value associated with 14.3.b. What proportion of the population is between 12.2 and 14.3?c. What proportion of
A normal population has a mean of 20.0 and a standard deviation of 4.0.a. Compute the z value associated with 25.0.b. What proportion of the population is between 20.0 and 25.0?c. What proportion of
The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college 2 years ago, and each is now earning $70,000 per year. Rachel works in the retail industry, where the mean salary
For the year 2018, Fred Friendly completed a total of 80 returns. He developed the following table summarizing the relationship between number of dependents and whether or not the client received a
The following table shows a breakdown of the 116th U.S. Congress by party affiliation. (There are two independent senators included in the count of Democratic senators. There are two vacant House
In a 2018 report, the Internal Revenue Service indicated the mean refund was $2,750 with a standard deviation of $850. Assume the distribution of the refunds follows the normal distribution.a. What
Fred decided to study the number of exemptions claimed on personal tax returns he prepared for 2018. The data are summarized in the following table.Exemptions Percent1 . .
Geoff Brown is the manager for a small telemarketing firm and is evaluating the sales rate of experienced workers in order to set minimum standards for new hires. During the past few weeks, he has
A uniform distribution is defined over the interval from 2 to 5.a. What are the values for a and b?b. What is the mean of this uniform distribution?c. What is the standard deviation?d. Show that the
A uniform distribution is defined over the interval from 6 to 10.a. What are the values for a and b?b. What is the mean of this uniform distribution?c. What is the standard deviation?d. Show that the
Refer to the Baseball 2018 data. Compute the mean number of home runs per game. To do this, first find the mean number of home runs per team for 2018. Next, divide this value by 162 (a season
In 2019, sales information shows that 30% of new cars and light trucks in the United States were leased. Zook Motors in Kane, Pennsylvania, sold 40 cars and light trucks last month, 10 of them were
According to the “January theory,” if the stock market is up at the end of January, it will be “up” for the year. If it is “down” at the end of January, it will be “down” for the
According to the U.S. government, it costs more to make a penny, $0.0241, than a penny’s value, $0.01. The U.S. government has considered eliminating pennies from its currency. Canada and Australia
The 1989 U.S. Open golf tournament was played on the East Course of the Oak Hills Country Club in Rochester, New York. During the second round, four golfers scored a hole in one on the par 3 sixth
Listed below are the 15 states with the largest populations. In addition, each state is classified with the variable, coastline, based on whether a state borders the Gulf of Mexico, the Atlantic
The PEW Research Institute recently conducted a survey of adult Americans regarding Internet shopping. The survey found that 15% of the respondents made a retail purchase on the Internet last week. A
An investment will be worth $1,000, $2,000, or $5,000 at the end of the year. The probabilities of these values are .25, .60, and .15, respectively. Determine the mean and variance of the
In a Poisson distribution μ = 4.a. What is the probability that x = 2?b. What is the probability that x ≤ 2?c. What is the probability that x > 2?
Refer to the Baseball 2018 data, which reports information on the 30 Major League Baseball (MLB) teams for the 2018 season.a. In the Major Baseball League, each team plays 162 games in a season.
In a Poisson distribution μ = 0.4.a. What is the probability that x = 0?b. What is the probability that x > 0?
A youth basketball team has 12 players on the roster. Seven of the team members are boys and five are girls. The coach writes each player’s name on a sheet of paper and places the names in a hat.
Statistics from the Port Authority of New York and New Jersey show that 85% of the vehicles using the Lincoln Tunnel use E-Z Pass to pay the toll rather than stopping at a toll booth. Twelve cars are
American households increasingly rely on cell phones as their exclusive telephone service. It is reported that 49.2% of American households still have landline phone service. We decide to randomly
A recent survey by the American Accounting Association revealed 52% of accountants have the Certified Public Accounting (CPA) certificate. Suppose we select a sample of 15 accountants.a. What is the
The U.S. Postal Service reports 95% of first-class mail within the same city is delivered within 2 days of the time of mailing. Six letters are randomly sent to different locations.a. What is the
In a binomial situation, n = 5 and π = .40. Find the probabilities for all possible values of the random variable, x.
In a binomial situation, n = 4 and π = .20. Find the probabilities for all possible values of the random variable, x.
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 250 customers on the number of hours cars are parked.Number of Hours
Refer to the North Valley Real Estate data, which report information on homes sold during the last year.a. Sort the data into a table that shows the number of homes that have a pool versus the number
A company uses three backup servers to secure its data. The probability that a server fails is 0.05. Assuming that the failure of a server is independent of the other servers, what is the probability
Mookie Betts of the Boston Red Sox had the highest batting average for the 2018 Major League Baseball season. His average was .346. So, the likelihood of his getting a hit is .346 for each time he
Refer to the following picture.a. What is the picture called?b. What rule of probability is illustrated?c. B represents the event of choosing a family that receives welfare payments. What does P(B) +

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