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business statistics communicating
Business Statistics 10th Global Edition David Groebner, Patrick Shannon, Phillip Fry - Solutions
TOMRA Systems ASA is a Norwegian company that manufactures reverse vending machines (RVMs). In most cases, RVMs are used in markets that have deposits on beverage containers, offering an efficient and convenient method of identifying the deposit amount of each container returned and providing a
At the annual meeting of the Golf Equipment Manufacturer’s Association, a speaker made the claim that at least 30% of all golf clubs being used are knockoff clubs that look very much like the more expensive originals. This claim prompted the association to conduct a study to see if the problem
The Inland Empire Food Store Company has stated in its advertising that the average shopper will save more than$5.00 per week by shopping at Inland stores. A consumer group has decided to test this assertion by sampling 50 shoppers who currently shop at other stores. Suppose the company selects the
The Haines Lumber Company makes plywood for the furniture industry. One of its products is 3/4-inch oak veneer panels. It is very important that the panels conform to specifications. One specification calls for the panels to be made to an average thickness of 0.75 inch. Suppose each hour, 5 panels
To determine whether the Wilson Company is complying with federal requirements for cleaning its wastewater, sample measurements are taken every so often. One requirement is that the average pH level not exceed 7.4. Suppose a sample of 95 pH measurements has been taken. The data for these
The Air Frame Company sells cellular phones and airtime in several northwestern states. The marketing manager stated that the average age of its customers is under 40. This came up in conjunction with a proposed advertising plan that is to be directed toward a young audience. Before actually
A university is measuring the proportion of successful applicants from the pool of total applicants for their business faculty. From one report of an entire open day, a representative sample of size 335 is taken from the population of applicants to a university’s MBA program.It shows 190
The senior vice president for human resources at a hightech company often initiates surveys concerning the company’s personnel. A typical survey asked, “Do you feel it’s OK for your company to monitor your Internet use?” Of the 405 respondents, 223 chose “Only after informing me.” The
The personnel manager for a large airline has claimed that, on average, workers are asked to work no more than 3 hours overtime per week. Assume that the standard deviation in overtime hours per worker is 1.2 hours.Suppose the union negotiators wish to test this claim by sampling payroll records
The Sledge Tire and Rubber Company plans to warranty its new mountain bike tire for 12 months. However, before it does this, the company wants to be sure that the mean lifetime of the tires is at least 18 months under normal operations. The company plans to test this statistically using a random
Due to an unhealthy lifestyle, an unbalanced diet, or a family history of high cholesterol, children may also have high cholesterol. The National Health and Nutrition Examination Survey (NHANES) claimed that the prevalence of high total cholesterol among U.S. children and adolescents was 7.4%. To
The makers of Free Run Dog Food have an automated filling machine that can be set at any targeted fill level between 10 and 40 pounds. At the end of every shift(eight hours), 16 bags are selected at random and the mean and standard deviation of the sample are computed. Based on these sample
Technological changes in golf clubs have affected the way golfers of all abilities are able to play the game. The impact seems to be especially great for professionals.Suppose there is a controversy over whether professional and amateur players should have different rules for what constitutes legal
In a population of coffee drinkers, the average daily consumption is three cups of coffee per day. A manager wants to know if his colleagues tend to drink more than the national average of cups of coffee per day. He asked 50 colleagues to state how many cups of coffee they consumed each day and
Sanchez Electronics sells electronic components for car stereos. It claims that the average life of a component exceeds 4,000 hours. To test this claim, it has selected a random sample of n = 12 of the components and traced the life between installation and failure. The following data were
The Mortimor Chemical Company develops and manufactures pharmaceutical drugs for distribution and sale in the United States. The pharmaceutical business can be very lucrative when useful and safe drugs are introduced into the market. Whenever the Mortimor research lab considers putting a drug into
Recall that the power of the test is the probability the null hypothesis is rejected when H0 is false. Explain whether power is definable if the given parameter is the value specified in the null hypothesis.
An industry expert claimed that sporting goods stores average sales of $260 a square foot. A hypothesis test was requested to determine if the data supported the statement made by the expert using an a = 0.05 and a sample size of 41. Calculate the probability that the data will indicate that
Suppose, consultants for a national hotel chain conducted a review of hotel bills and found that on average, errors in hotel bills resulted in overpayment of$11.35 per night. To determine if such mistakes are being made at a major hotel chain, the CEO requested a survey yielding the following
The union negotiations between labor and management at the Stone Container paper mill in Minnesota hit a snag when management asked labor to take a cut in health insurance coverage. As part of its justification, management claimed that the average insurance claims filed by union employees did not
A telemarketing supervisor is inspecting the duration of outgoing calls made by his telemarketer. Base on past results, the average length of an outgoing telephone call from a telemarketer has been 168 seconds.The supervisor wishes to check whether that average has decreased after the introduction
The amount a person should eat depends on their age and the amount of physical activity undertaken by them. The recommended average daily calories intake for a woman aged over 50 and with low physical activity is 1,600 calories. A nutritionist believes the average daily calorie intake of women aged
A real estate conglomerate is analyzing the household size in a region for the purpose of developing a piece of land. Based on a land management’s report, several years ago the region had an average household size of 3.14 persons with the population standard deviation of 0.82 people. The
At an automobile service center, the labor charges for repairs are based on a standard time specified for each type of repair. The average time specified for a common replacement is one hour with a standard deviation of 0.72 hour. The center’s manager is trying to maintain the quality of service,
A bank is trying out a new system through which it hopes to reduce its customers’ waiting time and keep them satisfied. The bank manager hopes that the new system will reduce the customers’ waiting time—from beginning till checking out—to not more than 5 minutes. The new system will reduce
A cosmetics factory owns a machine that automatically fills its best-selling facial cream jars—4 ounces per jar.The machine is set to have a mean of 4.1 ounces per jar. Given all other factors, the process shifted the mean away from 4.1 by an under fill. The machine has to stop its production.
The following hypotheses are to be tested:H0: p Ú 0.35 HA: p 6 0.35 A random sample of 400 is taken. Using each set of information following, compute the power of the test.a. a = 0.01, true p = 0.32b. a = 0.025, true p = 0.33c. a = 0.05, true p = 0.34
The following hypotheses are to be tested:H0: p … 0.65 HA: p 7 0.65 A random sample of 500 is taken. Using each set of information following, compute the power of the test.a. a = 0.01, true p = 0.68b. a = 0.025, true p = 0.67c. a = 0.05, true p = 0.66
Consider the following hypotheses:H0: m = 30 HA: m 30 A sample of size 50 is to be taken from a population with a standard deviation of 13. The hypothesis test is to be conducted using a significance level of 0.05. Determine the probability of committing a Type II error whena. m = 22b. m = 25c. m
Solve for beta when the “true” population mean is 103 and the following information is given:H0: m … 100 HA: m 7 100 a = 0.05 s = 10 n = 49
You are given the following null and alternative hypotheses:H0: m … 500 HA: m 7 500 a = 0.01 Calculate the probability of committing a Type II error when the population mean is 505, the sample size is 64, and the population standard deviation is known to be 36.
You are given the following null and alternative hypotheses:H0: m Ú 4,350 HA: m 6 4,350 a = 0.05a. If the true population mean is 4,345, determine the value of beta. Assume the population standard deviation is known to be 200 and the sample size is 100.b. Referring to parta, calculate the power of
You are given the following null and alternative hypotheses:H0: m = 1.20 HA: m 1.20 a = 0.10a. If the true population mean is 1.25, determine the value of beta. Assume the population standard deviation is known to be 0.50 and the sample size is 60.b. Referring to parta, calculate the power of the
You are given the following null and alternative hypotheses:H0: m = 200 HA: m 200 a = 0.10 Calculate the probability of committing a Type II error when the population mean is 197, the sample size is 36, and the population standard deviation is known to be 24.
Suppose that the Seadoo of Canada company standard for customer satisfaction is 95% “highly satisfied.”Company managers recently completed a customer survey of 700 customers from around the world. The responses to the question “What is your overall level of satisfaction with Seadoo?” are
A study of cell phone users found cell phones give people personal power, allow unprecedented mobility, and give people the ability to conduct their business on the go. Interesting enough, gender differences can be found in phone use. Women see their cell phone as a means of expression and social
Suppose 40% of investors have funded a Roth IRA rollover from an employer-sponsored retirement account.The HR manager for a Florida company selected a random sample of 90 households in the greater Miami area, and respondents were asked whether they had ever funded a Roth IRA account with a rollover
Suppose a national survey indicated that 56% of women have had experience with a global positioning system (GPS) device. The survey indicated that 66% of the men surveyed have used a GPS device.a. If the survey was based on a sample size of 200 men, do these data indicate that the proportion of men
In a toy production line, a quality control inspector plays an important role with regard to safety. The inspector will inspect the product color, style, labels, and markings. An ideal toy production line reported that more than 70% of the toys in the entire population meet required specifications.
Hyperoptic is one of the new broadband providers, offering ultrafast Internet speeds of up to 1 Gbps. Fiberoptic cables had been installed in buildings and then connected to individual apartments, which is used in most office and home networks today. A report stated that only 20% of all the
In a fruit canning process, the canned fruits are processed to inactivate molds, yeasts, and possible acid-tolerant bacteria. A technician is running tests on a new kind of fruit canning process. By using the old process, 10% of the fruit cans showed visible discoloration after 6 months. The
Many banks and other financial institutions have raised the minimum payment customers must pay on their outstanding credit card balances. Suppose a claim is made that more than 40% of all credit card holders pay the minimum payment. To test this claim, a random sample of payments made by credit
In May 2015, the Ministry of Health Malaysia reported that there are 5 million smokers in the country, aged 18 years and above, which is about 17% of the total population. As a result of tobacco-related complications, every year this group contributed to about 20,000 premature deaths. The ministry
As the principal at Lake Elementary Kindergarten, you want to build on the reading habit of the children attending the play school. However, based on the experiences of teachers at the play school, more than half of the children were reported to have preferred outdoor activities to reading. To
An academic report shows that students scored better in the marketing module offered by the academy in comparison to other modules offered. Based on this information, you suspect there are more students who are in favor of the marketing module. You conduct an online survey for a group of 385
An issue that faces individuals investing for retirement is allocating assets among different investment choices.Suppose a study conducted 10 years ago showed that 65% of investors preferred stocks to real estate as an investment. In a recent random sample of 900 investors, 360 preferred real
A test has the following hypotheses:H0: p … 0.45 HA: p 7 0.45 The sample size is 30, and the sample proportion is 0.55.a. For an a = 0.025, determine the critical value.b. Calculate the numerical value of the test statistic.c. State the test’s conclusion.d. Determine the p-value.
For the following hypothesis test:H0: p Ú 0.75 HA: p 6 0.75 a = 0.025 with n = 100 and p = 0.66, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
For the following hypothesis test:H0: p = 0.40 HA: p 0.40 a = 0.01 with n = 64 and p = 0.42, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
Given the following null and alternative hypotheses H0: p Ú 0.60 HA: p 6 0.60 test the hypothesis using a = 0.01 assuming that a sample of n = 200 yielded x = 105 items with the desired attribute.
Determine the appropriate critical value(s) for each of the following tests concerning the population proportion:a. upper-tailed test: a = 0.025, n = 48b. lower-tailed test: a = 0.05, n = 30c. two-tailed test: a = 0.02, n = 129d. two-tailed test: a = 0.10, n = 36
A key factor in the world’s economic condition is the population growth of countries. The file called Country Growth contains data for 232 countries.Consider these countries to be all the countries in the world. (Source: The World Factbook, 2015 population estimates, www.cia.gov.)a. From this
The Consumer Expenditures report released by the U.S. Bureau of Labor Statistics found the average annual household spending on food at home in 2014 was $3,971. Suppose a random sample of 137 households in Detroit was taken to determine whether the average annual expenditure on food at home was
The owner of an Axion health club franchise believes that the average age of her members is under 55 years. To test this, a random sample of 30 was selected; the following sample data are the ages of the sampled individuals:40 55 78 27 55 33 51 76 54 67 40 31 60 61 50 42 78 80 25 38 74 46 48 57 30
The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces. At the end of every shift (eight hours), 16 boxes are selected at random.Based on these sample results, the production control manager determines whether the
An internal report issued by the marketing manager for a national oil-change franchise indicated that the mean number of miles between oil changes for franchise customers is at least 3,600. One Texas franchise owner conducted a study to determine whether the marketing manager’s statement was
A mail-order business prides itself in its ability to fill customers’ orders in six days or less on average.Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. Based on this sample information, he decides
A doctor is experimenting with a new medicine, which will reduce the average time of recovery for her patients. In her previous records, one patient took an average time of four hours to recover from his illness.Ten patients had been selected for her experiment and their body temperatures had been
A sample taken from a population yields a sample mean of 58.4. Calculate the p-value for each of the following circumstances:a. HA: m 7 58, n = 16, s = 0.8b. HA: m 45, n = 41, s = 35.407c. HA: m 45, n = 41, s = 35.407d. HA: m 6 69; data: 60.1, 54.3, 57.1, 53.1, 67.4
For the following hypothesis test:H0: m … 70 HA: m 7 70 with n = 20, x = 71.2, s = 6.9, and a = 0.1, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
For the following hypothesis test:H0: m = 60.5 HA: m 60.5 a = 0.05 with n = 15, s = 7.5, and x = 62.2, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
For the following hypothesis test:H0: m Ú 23 HA: m 6 23 a = 0.025 with n = 25, s = 8, and x = 20, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
For the following hypothesis test:H0: m … 45 HA: m 7 45 a = 0.02 with n = 80, s = 9, and x = 47.1, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the appropriate p-valued. the conclusion
For the following hypothesis test:H0: m = 200 HA: m 200 a = 0.01 with n = 64, s = 9, and x = 196.5, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
Provide the relevant critical value(s) for each of the following circumstances:a. HA: m 7 13, n = 15, s = 10.3, a = 0.05b. HA: m 21, n = 23, s = 35.40, a = 0.02c. HA: m 35, n = 41, s = 35.407, a = 0.01d. HA: m 6 49; data: 12.5, 15.8, 44.3, 22.6, 18.4; a = 0.10e. HA: x 7 15, n = 27, s = 12.4
Determine whether each of the following pairs of hypotheses is valid for a hypothesis test. Explain reasons for any pair that is indicated to be invalid.a. H0: m = 15, HA: m 7 15b. H0: m = 20, HA: m 20c. H0: m 6 30, HA: m 7 30d. H0: m … 40, HA: m Ú 40e. H0: x … 45, HA: x 7 45f. H0: m … 50,
National Products is a distributor of printer and copier paper for commercial use. The data file called Sales contains the annual, year-to-date sales values for each of the company’s customers. Suppose the internal audit department has decided to audit a sample of these accounts. Specifically,
The Jordeen Bottling Company did an extensive sampling of its soft-drink inventory in which 5,000 cans were sampled. Employees weighed each can and used these weights to determine the fluid ounces in the cans.The data are in a file called Jordeen. Based on this sample data, should the company
In 2015, Mortal Kombat X was one of the most popular video games (source: Chris Morris, “‘Mortal Kombat’secrets discovered after 24 years,” http://fortune.com, Feb. 26, 2016). The file titled KOMBATX contains a sample of the retail prices paid for Mortal Kombat X in 2015.a. Calculate a 95%
In an article titled “Airport screeners’ strains, sprains highest among workers,” Thomas Frank reported that the injury rate for airport screeners was 29%, far exceeding the 4.5% injury rate for the rest of the federal workforce. The 48,000 full- and part-time screeners were reported to have
A random sample of 25 4-wheel-drive pickups of the same year and model revealed the following miles per gallon (mpg) values:12.4 13.0 12.6 12.1 13.1 13.0 12.0 13.1 11.4 12.6 9.5 13.25 12.4 10.7 11.7 10.0 14.0 10.9 9.9 10.2 11.0 11.9 9.9 12.0 11.3 Assume that the population for mpg for this model
Arco Manufacturing makes electronic video recorders.As part of its quality efforts, the company wishes to estimate the mean number of days a video recorder is used before it needs repair. A pilot sample of 40 video recorders indicates a sample standard deviation of 200 days. The company wishes its
The Yap family has a total of three members. They spend 30 hours every day on the Internet.a. Calculate the average time spent on the Internet in a day by each member of the Yap family.b. If the amount of time spent on the Internet daily is normally distributed, determine the standard deviation of
As a financial consultant with AIA, Sebastian is assisting his client to determine the average annual return on mutual funds. He selected a random sample of 60 returns, which shows a mean of 12% and assumed the population standard deviation to be 4%.a. Estimate the 95% confidence interval for the
Examine the equation for the margin of error when estimating a population mean e = z s2n Indicate the effect on the margin of error resulting from an increase in each of the following items:a. confidence levelb. z-valuec. standard deviationd. sample sizee. standard error Business Applications
David was measuring the amount of time he spends watching TV every day. To analyze his habits, for 14 days David recorded the amount of time he spent watching TV. He determines an average of 30 minutes with a standard deviation of 3 minutes was spent.He used the same data set to construct a
When we need to estimate the population mean, and the population standard deviation is unknown, we are hit with a “double whammy” when it comes to the margin of error. Explain what the “double whammy” is and why it occurs. (Hint: Consider the sources of variation in the margin of error.)
The Emerging Workforce Study conducted by Harris Interactive on behalf of Spherion, a leader in providing value-added staffing, recruiting, and workforce solutions, utilized a random sample of 225 senior human resources executives (source: www.spherion.com). The survey asked which methods the
According to the Retirement Confidence Survey, in 2015, 36% of individuals expected to begin retirement after the age of 65 (source: 2015 RCS Fact Sheet # 2, Expectations about retirement, www.ebri.org/).Suppose a recent random sample of 90 households in the greater Miami area was taken and
Suppose that 34% of workers between the ages of 35 and 44 own a 401(k)-type retirement plan. Suppose the Atlanta Chamber of Commerce conducted a survey to determine the participation rate of 35- to 44-year-old working adults in the Atlanta metropolitan area who have 401(k)-type retirement plans.
An automobile’s color is one of the factors that influences a consumer’s demand for it. Suppose a car manufacturer in your country is planning to launch a new model and is deciding on the colors that can be offered. The manufacturer is wondering whether silver, at 28.3%, is still leading choice
Suppose a survey of individuals between the ages of 26 and 82 indicated that 66% of seniors, 61% of Baby Boomers, and 58% of Generation X expect IRAs to be their primary source of income in retirement. The margin of error was given as {5 percentage points.a. Calculate a 95% confidence interval for
According to studies by the Pew Research Center and the United Nations (UN), immigrants have a proven economic benefit. Based on reports, between 2005 and 2015, countries in the Middle East have seen the greatest proportion of immigrants in the world compared to its population size. The UN study
A courier company is trying to improve the quality of the services provided to its customers. For local deliveries, the company guarantees that all orders will be delivered within 24 hours. To justify the accuracy of their services, a preliminary study was conducted with a sample size of 200
Many companies have started to feature female models who are not the traditional thin women who have graced magazine covers for the last 20 to 25 years.Suppose Calvin Klein conducted a survey of 1,000 women in which 91% of the respondents said they were satisfied with what they see in the mirror.
A sport teacher is selecting students who will be attending the school’s Annual Sports Day. He needs to identify students who will qualify for the high jump competition. Based on his past experience, he identifies that the physical constitution, along with light weight, is one of the important
Most major airlines allow passengers to carry one luggage item (of a certain maximum size) and one personal item onto the plane. However, suppose the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to
The television landscape has changed as networks compete with streaming services such as Netflix and Hulu. Suppose that CBS plans to conduct interviews with television viewers in an attempt to estimate the proportion of viewers in the 18–49 age group who watch “most” of their television on
A survey of 499 women revealed that 38% wear flats to work.a. Use this sample information to develop a 99%confidence interval for the population proportion of women who wear flats to work.b. Suppose we also wish to estimate the proportion of women who wear athletic shoes to work with a margin of
According to a study, over the three years almost twothirds of newspapers in a country published less foreign news compared to local news. Only 10% of the editors said they considered foreign news “very essential” to their papers. To justify this issue, a major metropolitan newspaper selected a
A random sample of 40 television viewers was asked if they had watched the current week’s The Voice. The following data represent their responses:no no no yes no no no yes no yes no no no yes no no no no yes no yes no no no no yes no no no no no no no no no no no no no noa. Calculate the
Premium Information Solutions, Inc., specializes in providing call center services for companies that wish to outsource their call center activities. Premium Information Solutions is currently negotiating with a new client who wants to be billed for the number of minutes that Premium Information
According to the Office of Personnel Management(www.OPM.gov), in 2015 the average hourly wage rate for federal employees was slightly higher than $43.The file titled Paychecks contains a random sample of the hourly amounts paid to state and local government workers.a. Generate the margin of error
Bruce Leichtman is president of Leichtman Research Group, Inc. (LRG), which specializes in research and consulting on broadband, media, and entertainment industries. In a survey, the company determined the cost of HDMI Digital Antenna systems ranged from about $25 to $200 (source: “Everything you
More than ever before, film production companies are gravitating toward Eastern Europe. Studios there have a reputation of skilled technical work at a relatively low cost. Bulgaria is one country with costs below those of Hollywood. As an example, weekly soundstage rental prices are quoted as $3.77
The average monthly cable television bill is estimated to be $99.10 (source: Yoni Heisler, “The average cable bill has increased by nearly 40% in 5 years,” http://bgr.com, Sep. 9, 2015). Suppose the study used to arrive at this estimate had a margin of error of $1.25 and a confidence level of
The Longmont Computer Leasing Company wishes to estimate the mean number of pages that will be printed in a month on its leased printers. The plan is to select a random sample of printers and record the number on each printer’s counter at the beginning of May. Then, at the end of May, the number
Apart from being fun, toys are an important part of the physical and mental development of children. Parents play a role in assisting their children in picking the right toys. An industrial designer wants to determine the average amount of time that parents take in selecting the right toys for
The Northwest Pacific Phone Company wishes to estimate the average number of minutes its customers spend on long-distance calls per month. The company wants the estimate made with 99% confidence and a margin of error of no more than 5 minutes.a. Assume that the standard deviation for longdistance
With the high cost of fuel and intense competition, the major airline companies have had a very difficult time financially in recent years. Many carriers are now charging for checked bags. One carrier is considering charging a two-tiered rate based on the weight of checked bags. Before deciding at
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