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statistical techniques in business
Questions and Answers of
Statistical Techniques in Business
A school district wants to estimate the mean number of snow days that they can expect each year. A sample of the number of snow days taken over the last 10 years is given in Table 4.11.a. Find and
Acidity and alkalinity of soil are typically measured on the \(\mathrm{pH}\) scale, which has a range from \(0-14\). A pH of 7 is considered neutral, a \(\mathrm{pH}\) of \(0-7\) is acidic, and a
A machine pours soda into 12-ounce bottles. If the standard deviation of the amount of soda poured exceeds 0.23 ounces, then this is an indication that the machine is not working correctly. To see if
An organizational psychologist developed a 2-week training program in order to improve team behavior in an organization. The program consisted of working with teams to promote a more inclusive and
You may have heard that texting while driving can increase the time taken for you to react to avoid an accident. In order to test this, a university set up a driving simulator where 13 participants
Tire manufacturers are often interested in comparing the wear patterns of their tires with that of the other competitors. One way of comparing the wear patterns is to look at both the mean tread life
Which candidate will win the upcoming presidential election? A survey of 1,300 likely voters found that 652 planned to vote for Candidate A, 600 planned to vote for Candidate \(\mathrm{B}\), and the
A new program was created to help people smoke less. Table 5.13 gives the average number of cigarettes smoked (per day) before participating in the program and the average number of cigarettes (per
Table 5.14 gives the yearly starting salaries for male and female bachelor's degree graduates who majored in the social sciences.a. Find and interpret a \(99 \%\) confidence interval for the
Can deep-breathing techniques help reduce mathematics anxiety? A researcher was interested in knowing if students who practice deep-breathing techniques tend to have less anxiety toward mathematics.
A random sample of 2,750 students who majored in the social sciences found that 908 defaulted on their student loans, and a random sample of 3,560 students who majored in the physical sciences found
Two different presses are used to press shirts for a laundry service. A random sample of the number of shirts that can be pressed in 5 minutes for each type of press is given in Table 5.16.a. Find
A new small engine claims that it can get more miles per gallon (MPG) than the competitor's model. To verify this claim, a random sample of seven engines of each type are put through a series of
A heating and air-conditioning company wants to estimate the number of emergency service calls they receive during the week and on weekends so as to decide how many technicians to have on call. A
A survey was given to a random sample of \(1,650 \mathrm{dog}\) owners and a random sample of 1,300 cat owners. The survey asked if they used flea and tick prevention on their pets. Of the 1,650 dog
A new computer operating system was designed so that it does not need as many updates as the current operating system. A random sample of the number of updates for each operating system over the
A landscaper wants to compare the variability in germination rates between two different brands of grass seed. In order to do this, a random sample of 15 plots of land was planted with each type of
We can also test whether two populations' means differ by some constant, \(C\). The procedure is similar to testing whether two population means are different from each other; however, the possible
A survey asked 50 consumers to rate their level of satisfaction with a certain brand of laundry detergent. The responses to the survey were either very satisfied with the detergent, satisfied with
Describe each of the following variables as quantitative or qualitative, discrete or continuous, and classify the scale as nominal, ordinal, interval, or ratio:a. Social security numbersb. IQ scorec.
The partial data set given in Table 1.4 consists of a selection of variables for a ferry company that describe the revenue, time of day the ferry left the dock, number of passengers on the ferry,
Can your diet make you happier? A researcher wants to know if the food you eat has an effect on your happiness. A random sample of 41 adult participants completed a survey on happiness and a
Explain why a random sample is one of the best ways to obtain a sample that is representative of the population.
A stratified random sample can be obtained by first partitioning a population into disjoint groups (or strata) and then taking random samples from each of the strata. For instance, a stratified
In a binomial distribution, n = 8 and π = .30. Find the probabilities of the following events.a. x = 2.b. x ≤ 2 (the probability that x is equal to or less than 2).c. x ≥ 3 (the probability that
Topten is a leading source on energy-efficient products. Their list of the top seven vehicles in terms of fuel efficiency for 2022 includes three Hondas.a. Determine the probability distribution for
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?
SpaceX is a private company that builds and launches rockets into space. Some are manned, some are not. NASA engineers estimate (through computer simulations and modeling) a probability of 1 in 276
For Exercises 27 through 32, use the following information on food items for the years 2012 and 2022.Compute a simple price index for each of the four items. Use 2012 as the base period.
The 2009 RBC Canadian Open golf tournament was played at the Glen Abbey Golf Club in Oakville, Ontario. During the second round, Leif Olson, Arjun Atwal, Casey Wittenberg, and Briny Baird all aced
For Exercises 27 through 32, use the following information on food items for the years 2012 and 2022.Compute a simple aggregate price index. Use 2012 as the base period. Item Margarine
For Exercises 27 through 32, use the following information on food items for the years 2012 and 2022.Compute the Laspeyres price index for 2022 using 2012 as the base period. Item Margarine
In 2022, 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
For Exercises 27 through 32, use the following information on food items for the years 2012 and 2022.Compute the Paasche index for 2022 using 2012 as the base period. Item Margarine
For Exercises 27 through 32, use the following information on food items for the years 2012 and 2022.Determine Fisher’s ideal index using the values for the Laspeyres and Paasche indexes computed
For Exercises 33 through 38, use the following information. Betts Electronics purchases three replacement parts for robotic machines used in its manufacturing process. Information on the price of the
For Exercises 39 through 44, use the following price information for selected foods for 2015 and 2022 given in the table.Compute a simple aggregate price index. Use 2015 as the base period.
The following data report total, monthly U.S. gasoline sales in millions of dollars from January 2020 to December 2021. (To find the data, go to the site
Using the following time series data of U.S. new car sales ($ millions), respond to the following items. (The data are sourced from https://www.census.gov/retail/index.html#mrts. Find “Monthly
Consider the variable average ticket sale in the Home Depot data presented here. This variable indicates, for example, that customers spent an average of $39.13 on goods during a store visit in 1993.
Use the variables average ticket sale and number of associates to forecast net sales. Are these two independent variables reasonable predictors of net sales?You will need the help of a software
Liam Chu runs a car wash chain with outlets scattered throughout Chicago. He is concerned that some local managers are giving away free washes to their friends. He decides to collect data on the
Ezra McMahan is the owner of Sharkey Chevy, Buick, GMC. At the start of the year, Ezra instituted a customer opinion program to find ways to improve service. The day after the service is performed,
Refer to the Baseball 2021 data, which includes information on the 2021 Major League Baseball season. The data include the mean player salary since 2010. Plot the information and develop a linear
In a residential section of Southern California, a realtor believes that 80% of one-bedroom apartments rent between $1,950 and $2,450. What is the probability of selecting a random sample of 50
According to an IRS study, 30% of taxpayers can prepare, copy, and electronically file a 1040 tax form between 1.5 and 2.0 hours. A consumer watchdog agency selects a random sample of 25 taxpayers.
Refer to the Baseball 2021 data, which report information on the 30 Major League Baseball teams for the 2021 season.a. At the .10 significance level, is there a difference in the variation in team
Mr. Keagan Profit is studying companies going public for the first time. He is particularly interested in the relationship between the size of the offering and the price per share. a. Determine
Jody’s Florist has 15 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 15 trucks, six have brake problems. Five trucks are
In a Poisson distribution μ = 0.4.a. What is the probability that x = 0?b. What is the probability that x > 0?
General Electric Company (GE) is a high-tech industrial company that operates worldwide through its four industrial segments, Power, Renewable Energy, Aviation, and Healthcare, and its financial
General Electric Company (GE) is a high-tech industrial company that operates worldwide through its four industrial segments, Power, Renewable Energy, Aviation, and Healthcare, and its financial
Johnson & Johnson is the world’s largest and most broadly based healthcare company, with corporate offices in New Brunswick, New Jersey. Its common stock is listed on the New York Stock
Johnson & Johnson is the world’s largest and most broadly based healthcare company, with corporate offices in New Brunswick, New Jersey. Its common stock is listed on the New York Stock
Johnson & Johnson is the world’s largest and most broadly based healthcare company, with corporate offices in New Brunswick, New Jersey. Its common stock is listed on the New York Stock
Johnson & Johnson is the world’s largest and most broadly based healthcare company, with corporate offices in New Brunswick, New Jersey. Its common stock is listed on the New York Stock
Aliyah Edwards is employed by the state bureau of economic development. There is a demand for a leading economic index to review past economic activity and to forecast future economic trends in the
Refer to the Baseball 2021 data. Compute the mean number of home runs per game. To do this, first find the mean number of home runs per team for 2021. Next, divide this value by 162 (a season
In parts a, b, and c, use the t-distribution in Appendix B.5 to determine the margin of error in estimating the population mean with a 95% confidence interval if:a. s = 10 and n = 10.b. s = 10 and n
Ms. Malika Wilson is considering running for mayor of Bear Gulch, Montana. Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch. A sample of 400 voters reveals
Use the t-distribution in Appendix B.5 to determine z-values, using three decimals, for a:a. 95% confidence interval.b. 90% confidence interval.c. 80% confidence interval.Appendix B.5
Dr. Hume is a professor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed the normal
Refer to the Baseball 2021 data, which report information on the 30 Major League Baseball teams for the 2021 season. Over the last decade, the mean attendance per team followed a normal distribution
A professor writes a statistics test and estimates that 90% of test takers will complete the test in 1 hour or less. She gives the test to a class of 100 students. What is the probability that 5 or
At the Heathrow Airport in London, England, an airport administrator believes that the proportion of delayed flights is .15 per day. What is the probability of selecting a sample of 50 flights on a
A population proportion is 0.90. From this population you select random samples of 60.a. Test the conditions necessary to apply the central limit theorem to the distribution of sample proportions.
In Phoenix, a Rideshare company believes that 50% of all rides originate at the Sky Harbor International Airport. The company decides to sample 30 rides during a particular day.a. Test the conditions
The population mean proportion is .30. We decide to sample the population by randomly selecting 25 items and computing sample proportions.a. Can we use the normal distribution to approximate the
The population mean proportion is .80. We decide to sample the population by randomly selecting 40 items and computing sample proportions.a. Can we use the normal distribution to approximate the
The following table shows a breakdown of the 117th U.S. Congress by party affiliation. (There are two independent senators included in the count of Democratic senators. There are two vacant House
A population proportion is 0.35. From this population you select random samples of 50.a. Test the conditions necessary to apply the central limit theorem. Are they satisfied? Why?b. What is the
A population proportion is 0.70. From this population you select random samples of 30.a. Test the conditions necessary to apply the central limit theorem. Are they satisfied? Why?b. What is the
Collect a random assortment of at least 30 coins (pennies, nickels, dimes, quarters, etc.). Make a frequency table beginning with the current year and counting backward to record the ages (in years)
Refer to the Baseball 2021 data, which report information on the 30 Major League Baseball teams for the 2021 season. Assume the 2021 data represents a sample.a. Develop a 95% confidence interval for
Dr. Kendi Sadek is an industrial psychologist. She is currently studying stress among executives of Internet companies. She has developed a questionnaire that she believes measures stress. A score
Police Chief Dannie Wilkin of River City reports 500 traffic citations were issued last month. A sample of 35 of these citations showed the mean amount of the fine was $54, with a standard deviation
In 2003, the Accreditation Council for Graduate Medical Education (ACGME) implemented new rules limiting work hours for all residents. A key component of these rules is that residents should work no
An important factor in selling a residential property is the number of times real estate agents show a home. A sample of 15 homes recently sold in the Buffalo, New York, area revealed the mean number
Past surveys reveal that 30% of tourists going to Las Vegas to gamble spend more than $1,000. The Visitor’s Bureau of Las Vegas wants to update this percentage.a. How many tourists should be
The estimate of the population proportion should be within plus or minus .05, with a 99% level of confidence. The best estimate of the population proportion is .15. How large a sample is required?
We want to estimate the population mean within 5, with a 95% level of confidence. The population standard deviation is estimated to be 15. How large a sample is required?
A population’s standard deviation is 10. We want to estimate the population mean with a margin of error of 2, with a 95% level of confidence. How large a sample is required?
Schadek Silkscreen Printing Inc. purchases plastic cups and imprints them with logos for sporting events, proms, birthdays, and other special occasions. Vardon Schadek, the owner, received a large
A health care agency is studying differences between three hospitals in Tulsa, Oklahoma: Saint Francis Hospital, Oklahoma Surgical Hospital, and Hillcrest Hospital South. The agency is interested in
Sydney Fitzpatrick is the vice president for Nursing Services at St. Luke’s Memorial Hospital. Recently Sydney noticed in the job postings for nurses that those who are unionized seem to offer
A 2022 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
Marlee Singh is the comptroller for Meek Industries. Marlee believes that the current cashflow problem at Meek is due to the slow collection of accounts and that more than 60% of the accounts are
Refer to the Baseball 2021 data, which report information on the 30 Major League Baseball teams for the 2021 season.a. At the .05 significance level, can we conclude that there is a difference in the
Refer to the Baseball 2021 data, which report information on the 30 Major League Baseball teams for the 2021 season.TeamLeagueYear OpenedTeam SalaryAttendanceWinsERABAHRNet worth
Did you ever purchase a bag of M&??s candies and wonder about the distribution of colors? Did you know in the beginning they were all brown? Now, peanut M&M’s are 12% brown, 15% yellow, 12%
Using the following data, apply a two-tailed Wilcoxon rank-sum test to determine if the two populations are different. Use the .05 significance level. Population A Population B 38, 45, 56, 57, 61,
At the Warren County Fair, one of the animal events was evaluating hogs on several criteria. Based on the criteria the hogs were rank ordered. Wally Sedwick, director of the Warren County Fair, and
Refer to the Baseball 2021 data, which report information on the 30 Major League Baseball teams for the 2021 season. Set up a variable that divides the teams into two groups, those that had a winning
Using the following data, apply a two-tailed Wilcoxon rank-sum test to determine if the two populations are different. Use the .05 significance level. Population A Population B 12, 14, 15, 19, 23,
A recent national survey of patient visits found that 53% of patient visits were to primary care physicians, 19% to medical specialists, 17% to surgical specialists, and 11% to
A lottery that picks 5 balls from 10 balls numbered 0 through 9 is played once weekly. Over many weeks, the following table shows the frequency of each digit selected in the lottery is fair, each
Jaime Mendoza decides to buy a fuel-efficient used car. Here are several vehicles Jaime is considering, with the estimated cost to purchase and the age of the vehicle.a. Create a scatter plot of the
The owner of the Liberty Movie Theater Group wishes to investigate the relationship between The owner of the Liberty Movie Theater Group wishes to investigate the relationship between purchasing a
A marketing executive is studying online services, and is researching the effect of web page hits, advertising budget, and price on a service’s number of subscriptions. A sample of 25 online
Refer to the Baseball 2021 data, which report information on the 30 Major League Baseball teams for the 2021 season. Let the number of games won be the dependent variable and the following variables
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