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business statistics communicating
Business Statistics 10th Global Edition David Groebner, Patrick Shannon, Phillip Fry - Solutions
Soft drink bottling companies such as Coca-Cola use quality-control techniques to assure that the average amount of cola in the cans is 12 ounces. Suppose that a small standard deviation of 0.05 ounce is acceptable. Any significant difference from this standard deviation would reflect badly on the
The Littleton Corporation manufactures high-speed electronic cables and focuses on products for the specialty electronics and data networking markets, including connectivity. One of its products is a fiberoptic cable. It is designed to have an overall diameter of 0.440 inch. A standard deviation
A medical research group is investigating what differences might exist between two pain-killing drugs, Azerlieve and Zynumbic. The researchers have already established there is no difference between the two drugs in terms of the average amount of time required before they take effect. However, they
Maher Saddles, Inc., produces bicycle seats. Maher’s operations manager has recently made a change in the production process for the company’s high-end seat.After waiting for the process to become stable, he took a random sample of 25 assembly times and found a standard deviation of 47 seconds.
In response to customer surveys, a candy company has recently increased the size of the chopped nuts used in its caramel nut bar. The marketing manager is concerned that this change will affect the variability in the cooking temperature and compromise the taste and consistency of the candy. The
Consider testing the hypothesis HA: s21 7 s22 using samples of respective sizes 6 and 11. Note that we could represent this hypothesis as HA: s21>s22 7 1. The samples yield s21= 42.2 and s22= 1.1. It hardly seems worth the time to conduct this test, since the test statistic will obviously be very
Much of the emphasis of modern quality-control efforts involves identifying sources of variation in the processes associated with service or manufacturing operations.Discuss why variation in a process may affect quality.
The First Night Stage Company operates a small, nonprofit theater group in Milwaukee. This company’s representatives proposed two different solicitation brochures. They are interested in determining whether there is a difference in the standard deviation of dollars returned between the two
The Celltone company is in the business of providing cellular phone coverage. Recently, it conducted a study of its customers who have purchased either the Basic Plan or the Business Plan service. At issue is the number of minutes of use by the customers during the midnight-to-7:00 a.m. time period
The human resources director of a Fortune 500 company recently asked her staff to conduct a study of the airline miles traveled by executives of the company during the most recent calendar year. The analyst assigned to the project randomly sampled 20 male executives and 20 female executives. Of
A national fitness chain is considering being a representative for a weight loss program. The company has narrowed the choice of programs down to two options. Before making the selection, the company has asked each weight loss program to submit a random sample of 40 individuals who were on the
Considering again the return of your clients’ retirement portfolio described in question 11-15. Recall you had 28 observations for the domestic return series with a standard deviation of 11.21%. Now you decided to investigate whether the return to your client’s retirement portfolio will be
As purchasing agent for the Horner-Williams Company, you have primary responsibility for securing highquality raw materials at the best possible price. One particular material that the Horner-Williams Company uses a great deal of is aluminum. After careful study, you have been able to reduce the
In an effort to better understand current donation patterns, the manager of a public broadcast radio station is studying past data. A staff member from a neighboring state has speculated that male viewers’donations have greater variability in amount than do those of females. To test this, the
You are given two random samples with the following information:Item Sample 1 Sample 2 1 19.6 21.3 2 22.1 17.4 3 19.5 19.0 4 20.0 21.2 5 21.5 20.1 6 20.2 23.5 7 17.9 18.9 8 23.0 22.4 9 12.5 14.3 10 19.0 17.8 Based on these samples, test at a = 0.10 whether the true difference in population
You are given the following null and alternative hypotheses H0: s21= s22 HA: s21 s22 and sample information Sample 1 Sample 2 n1 = 11 n2 = 21 s1 = 15 s2 = 33a. If a = 0.02, state the decision rule for the hypothesis.b. Test the hypothesis and indicate whether the null hypothesis should be rejected.
Find the appropriate critical F-value, from the F-distribution table, for each of the following:a. D1 = 16, D2 = 14, a = 0.01b. D1 = 5, D2 = 12, a = 0.05c. D1 = 16, D2 = 20, a = 0.01
You are given the following null and alternative hypotheses H0: s21… s22 HA: s21 7 s22 and sample information Sample 1 Sample 2 n1 = 21 n2 = 12 s21= 345.7 s22= 745.2a. If a = 0.01, state the decision rule for the hypothesis. (Be careful to pay attention to the alternative hypothesis to construct
You are given the following null and alternative hypotheses H0: s21… s22 HA: s21 7 s22 and sample information Sample 1 Sample 2 n1 = 13 n2 = 21 s21= 1,450 s22= 1,320a. If a = 0.05, state the decision rule for the hypothesis.b. Test the hypothesis and indicate whether the null hypothesis should be
The Pet Health and Food Corporation is a producer of pet food. One of its products is Wonderfood, which is a dry cat food that comes in various sizes. The company guarantees that 32% of this cat food is crude protein. In the 6.6-pound (3-kilogram) size, this would mean that 2.11 pounds are crude
Many homes are heated with oil furnaces. The file titled Homeheat contains a sample of heating costs for selected households. Assume that historical data indicate that household heating costs have a standard deviation of about $100.Conduct a test of hypothesis to see if the variability in heating
As an insurance agent, you are studying on the return of your clients’ retirement portfolio to enhance their profits. Accordingly, you want to investigate whether domestic equities appear to have an average of 17.67%at 5% significance level. Recall that Malaysian equities returned 12.94% with a
The consistency of the diameters of wheel bearings is vital to the operation of the wheel. The specifications require that the variance of these diameters be no more than 0.0015 centimeter squared. The diameter is continually monitored by the quality-control team.Twenty subsamples of size 10 are
A software design firm has developed a prototype educational computer game for children. One of the important factors in the success of a game like this is the time it takes the child to play the game. Two factors are important: the mean time it takes to play and the variability in time required
A key measure for airlines is the number of minutes a plane deviates from the scheduled arrival time.Experience indicates that even under the best of circumstances, there will be inherent variability.Suppose one major airline has set standards that require the planes to have a standard deviation
Athletes tend to have lower resting heart rates because training programs that build speed, fitness, muscle, and endurance also train their heart muscles to pump a higher volume of blood with each heartbeat. An athletic nutrition manufacturer is looking for the best supplements that take less
In 2005, a researcher found that Ethiopia had the highest GDP growth rate in their population that year.The researcher is interested to know whether the GDP rates grow as the country becomes richer based on the population’s individual annual income. She established that the average individual
Examine the sample obtained from a normally distributed population:5.2 10.4 5.1 2.1 4.8 15.5 10.2 8.7 2.8 4.9 4.7 13.4 15.6 14.5a. Calculate the variance.b. Calculate the probability that a randomly chosen sample would produce a sample variance at least as large as that produced in part a if the
You are given the following null and alternative hypotheses:H0: s2 = 50 HA: s2 50a. Test when n = 12, s = 9, and a = 0.10. Be certain to state the decision rule.b. Test when n = 19, s = 6, and a = 0.05. Be certain to state the decision rule.
The following sample data have been collected for testing whether a population standard deviation is equal to 40. Conduct the appropriate hypothesis test using a = 0.05.318 255 323 325 334 354 266 308 321 297 316 272 346 266 309
You are given the following null and alternative hypotheses:H0: s2 = 100 HA: s2 100a. Test when n = 27, s = 9, and a = 0.10. Be certain to state the decision rule.b. Test when n = 17, s = 6, and a = 0.05. Be certain to state the decision rule.
Vintner Mortgage Company’s board of directors asked the president whether the company had a difference in the proportions of loan defaults between residential and commercial customers. To prepare an answer to this question, company officials selected a random sample of 200 residential loans and
Suppose that as part of a study on student loan debt, a national agency that underwrites student loans is examining the differences in student loan debt for undergraduate students. One question the agency would like to address specifically is whether the mean undergraduate debt of nonminority
Reviewers from the Oregon Evidence-Based Practice Center at the Oregon Health and Science University investigated the effectiveness of prescription drugs in assisting people to fall asleep and stay asleep (source:S. Carson, M.S. McDonagh, et al., “Drug class review:Newer drugs for insomnia,”
A football academy recently hired a new instructor to coach the players. A survey was conducted to determine whether the new instructor is performing well in the academy. For this purpose, two groups of players coached by different instructors were selected. Team A was coached by an older
Suppose a random sample taken in 2016 of 900 adults between the ages of 25 and 34 years of age indicated that 396 owned a home. In 1984, a random sample of 900 adults in the same age group showed that 432 owned a home. At the 0.02 level of significance, is there a difference between the proportions
To provide “extra distance” to golf balls, a golf equipment manufacturer has developed a new batch of golf balls. When testing the driving distance using a mechanical driving device, the manufacturer sampled 100 new developed golf balls, which give an average distance of 285 yards and a
A research was conducted to evaluate the effectiveness of a client’s new advertising campaign. A pre-survey was conducted through telephonic interviews for 150 households regarding the awareness of the new product in a selected area. Around 60 households were labeled to be “aware.” The new
The Eaton Company sells breakable china through a mail-order system that has been very profitable. One of its major problems is freight damage. It insures the items at shipping, but the inconvenience to the customer when a piece gets broken can cause the customer not to place another order in the
Allstate Insurance is one of the major automobile insurance companies in the country. The western region claims manager instructed an intern in her department to develop a confidence interval estimate of the difference between the mean years that male customers have been insured by Allstate versus
Bach Photographs is a photography business with studios in two locations. The owner is interested in monitoring business activity closely at the two locations. Among the factors in which he is interested is whether the mean customer orders per day for the two locations are the same. A random sample
A trainer designed a new training program for building muscle strength and increase the underlying strength and power qualities in elite athletes in an attempt to improve athletic performance. Twenty athletes were randomly selected and they were divided into 10 pairs, each pair having equal
Assuming the distributions for females and males are normally distributed, examine the following information.Female Male nf = 20 nm = 15 xf = 9 xm = 12 sf = 7 sm = 8a. Construct a 95% confidence interval for mf - mm by assuming the population variances are not equal.b. If given sf = 4 and sm = 3,
Consider the following samples obtained from two normally distributed populations whose variances are equal:Sample 1: 11.2 11.2 7.4 8.7 8.5 13.5 4.5 11.9 Sample 2: 11.7 9.5 15.6 16.5 11.3 17.6 17.0 8.5a. Suppose that the samples were independent. Perform a test of hypothesis to determine if there
One of the questions on a survey of business managers in different parts of the world was whether executives ranked innovation as the top priority for the coming year. Suppose the responses from 400 executives in the United States and 300 in Asia are given in the file titled Priority.a. Determine
As part of a nationwide study on home Internet use, suppose that researchers randomly sampled 150 urban households and 150 rural households. Among the questions asked of the sampled households was whether they used the Internet to download and play computer games. The survey results for this
The Coca-Cola Company and PepsiCo have dominated the non alcoholic beverage industry for several years. The competition between these two companies, which is called the Cola Wars, is legendary. It has been finally declared that Coca-Cola is 8.1% more favorable in the American market compared to
One of the most popular economic issues being discussed recently is whether employers should be required to pay male and female employees the same salary for the same job. Data were collected via an Internet site where visitors were asked to submit their votes on the issue.a. Compare if there is
It has been noted that the average age of first-time mothers is increasing. This is because more women are receiving formal education and are entering the workforce. They marry and have children at a later stage in life. Though older mothers might have a healthy pregnancy and childbirth, they do
A company conducted a survey on the launch of two types of health drinks. The first type of healthy drink contains fruit vitamins, minerals, and antioxidants. The second contains vegetable nutrition, potassium, dietary fiber, folate (folic acid), vitamin A, and vitamin C. A random sample of 500
Independent random samples of size 50 and 75 are selected. The sampling results in 35 and 35 successes, respectively. Test the following hypotheses:a. H0: p1 - p2 = 0 vs. HA: p1 - p2 0.Use a = 0.05.b. H0: p1 - p2 Ú 0 vs. HA: p1 - p2 6 0.Use a = 0.05.c. H0: p1 - p2 … 0 vs. HA: p1 - p2 7 0.Use a
Given the following null and alternative hypotheses H0: p1 - p2 … 0.0 HA: p1 - p2 7 0.0 and the following sample information Sample 1 Sample 2 n1 = 60 n2 = 80 x1 = 30 x2 = 24a. Based on a = 0.02 and the sample information, what should be concluded with respect to the null and alternative
Given the following null and alternative hypotheses and level of significance H0: p1 = p2 HA: p1 p2 a = 0.10 together with the sample information Sample 1 Sample 2 n1 = 120 n2 = 150 x1 = 42 x2 = 57 conduct the appropriate hypothesis test using the p-value approach. What conclusion should be
Given the following sample information randomly selected from two populations Sample 1 Sample 2 n1 = 200 n2 = 150 x1 = 40 x2 = 27a. Determine if the sample sizes are large enough so that the sampling distribution for the difference between the sample proportions is approximately normally
A study addressed the per-person spending at selected airports for merchandise, excluding food, gifts, and news items. A file titled Revenues contains sample data selected from airport retailers in 2012 and again in 2015.a. Conduct a hypothesis test to determine if the average amount of retail
The file titled House contains data for a sample showing the average and median housing prices for selected areas in the United States in November 2015 and November 2016. Assume the data can be viewed as samples of the relevant populations.a. Discuss whether the two samples are independent or
An article in The American Statistician (M. L. R.Ernst, et al., “Scatterplots for unordered pairs,” 50(1996), pp. 260–265) reports on the difference in the measurements by two evaluators of the cardiac output of 23 patients using Doppler echocardiography. Both observers took measurements from
The United Way raises money for community charity activities. In one community, the fundraising committee was concerned about whether there is a difference in the proportion of employees who give to United Way depending on whether the employer is a private business or a government agency. A random
Production engineers at Sinotron believe that a modified layout on its assembly lines might increase average worker productivity (measured in the number of units produced per hour). However, before the engineers are ready to install the revised layout officially across the entire firm’s
One of the advances that helped to diminish carpal tunnel syndrome is ergonomic keyboards. The ergonomic keyboards may also increase typing speed.Ten administrative assistants were chosen to type on both standard and ergonomic keyboards. The resulting word-per-minute typing speeds follow:Ergonomic:
Consider the following samples obtained from two normally distributed populations whose variances are equal:Sample 1: 11.2 11.2 7.4 8.7 8.5 13.5 4.5 11.9 Sample 2: 11.7 9.5 15.6 16.5 11.3 17.6 17.0 8.5a. Suppose that the samples were independent.Perform a test of hypothesis to determine if there is
The following samples are observations taken from the same elements at two different times:Unit Sample 1 Sample 2 1 15.1 4.8 2 12.3 5.7 3 14.9 6.2 4 17.5 9.4 5 18.1 2.3 6 18.4 4.7a. Assume that the populations are normally distributed and construct a 90% confidence interval for the difference in
A paired sample study has been conducted to determine whether two populations have equal means.Twenty paired samples were obtained with the following sample results:d = 12.45 sd = 11.0 Based on these sample data and a significance level of 0.05, what conclusion should be made about the population
The following sample data have been collected from a paired sample from two populations. The claim is that the first population mean will be at least as large as the mean of the second population. This claim will be assumed to be true unless the data strongly suggest otherwise.Sample 1 Sample 2
You are given the following results of a paireddifference test:d = -4.6 sd = 0.25 n = 16a. Construct and interpret a 99% confidence interval estimate for the paired difference in mean values.b. Construct and interpret a 90% confidence interval estimate for the paired difference in mean values.
The following paired sample data have been obtained from normally distributed populations. Construct a 90% confidence interval estimate for the mean paired difference between the two population means.Sample # Population 1 Population 2 1 3,693 4,635 2 3,679 4,262 3 3,921 4,293 4 4,106 4,197 5 3,808
The following dependent samples were randomly selected. Use the sample data to construct a 95%confidence interval estimate for the population mean paired difference.Sample 1 Sample 2 Sample 1 Sample 2 22 31 23 31 25 24 25 27 27 25 28 31 26 32 27 31 22 25 23 26 21 27
Suppose that one national airline had an objective of getting an additional $5 to $10 per trip in revenue from its customers through the implementation of various fees. Surveys could be used to determine the success of the company’s actions. The file titled AirRevenue contains results of samples
The Fairfield Inn and the Residence Inn are two of the hotel brands owned by Marriott. At a recent meeting, a manager posed the question whether the average length of stay was different at these two properties in the United States. A summer intern was assigned the task of testing to see if there is
Suppose a job-placement firm would like to know if the 2015 average starting salary for chemical engineering majors is higher than the 2015 average starting salary for electrical engineering majors. To conduct its test, the job-placement firm has selected a random sample of 124 electrical
Suppose a study has been conducted to determine whether there is a difference between student debt at private, for-profit universities and public universities.It was found from random samples that the private, for-profit colleges’ average debt was $38,300 and the public colleges average was
Being “connected” is very important to people of all ages these days. One way people stay connected is by sending text messages. Suppose a study was conducted at a major state university to determine whether the mean number of texts sent per day differed between male and female undergraduate
Suppose a major retailer replaced some of the traditional checkout stands with automated self-checkout facilities.After making the change in some test stores, the company performed a study to determine whether the average purchase through a self-checkout facility was less than the average purchase
A major paint manufacturer came out with a new paint product designed to be used in areas that are particularly prone to periodic moisture and hot sun. The R&D department set up a test in which two random samples of paint were selected. The first sample consisted of 25 one-gallon containers of the
A grocery store manager believes that the mean amount spent by customers on dairy products per visit is higher in stores in which the dairy section is in the central part of the store compared with stores that have the dairy section at the rear of the store. To consider relocating the dairy
The management of the Seaside Golf Club regularly monitors the golfers on its course for speed of play.Suppose a random sample of golfers was taken in 2015 and another random sample of golfers was selected in 2016. The results of the two samples (in minutes) are as follows:2015 2016 x1 = 225 x2 =
High Mountain produces a variety of climbing and mountaineering equipment. One of its products is a traditional three-strand climbing rope. An important characteristic of any climbing rope is its tensile strength.High Mountain produces the three-strand rope on two separate production lines: one in
Consider the following two independently chosen samples whose population variances are not equal to each other:Sample 1 12.1 13.4 11.7 10.7 14.0 Sample 2 10.5 9.5 8.2 7.8 11.1a. Using a significance level of 0.025, test the null hypothesis that m1 - m2 … 0.b. Calculate the p-value.
You are given the following null and alternative hypotheses:H0: m1 - m2 = 0 HA: m1 - m2 0 and the following sample information:Sample 1 Sample 2 n1 = 125 n2 = 120 s1 = 31 s2 = 38 x1 = 130 x2 = 105a. Develop the appropriate decision rule, assuming a significance level of 0.05 is to be used.b. Test
The following statistics were obtained from independent samples from populations that have normal distributions:1 2 ni 41 51 xi 25.4 33.2 si 5.6 7.4a. Use these statistics to conduct a test of hypothesis if the alternative hypothesis is m1 - m2 6 -4. Use a significance level of 0.01.b. Determine
Given the following null and alternative hypotheses, conduct a hypothesis test using an alpha equal to 0.05.(Note: The population standard deviations are assumed to be known.)H0: m1 … m2 HA: m1 7 m2 The sample means for the two populations are as follows:x1 = 144 x2 = 129 s1 = 11 s2 = 16 n1 = 40
You are given the following null and alternative hypotheses:H0: m1 Ú m2 HA: m1 6 m2 together with the following sample information:Sample 1 Sample 2 n1 = 14 n2 = 18 x1 = 565 x2 = 578 s1 = 28.9 s2 = 26.3a. Assuming that the populations are normally distributed with equal variances, test at the 0.10
The following null and alternative hypotheses have been stated:H0: m1 - m2 = 0 HA: m1 - m2 0 To test the null hypothesis, random samples have been selected from the two normally distributed populations with equal variances. The following sample data were observed:Sample from Population 1 Sample
A decision maker wishes to test the following null and alternative hypotheses using an alpha level equal to 0.05:H0: m1 - m2 = 0 HA: m1 - m2 0 The population standard deviations are assumed to be known. After the sample data are collected, the test statistic is computed to be z = 1.78a. Using the
The Federal Reserve reported in its comprehensive Survey of Consumer Finances, released every three years, that the average income of families in the United States increased between in 2010 and 2013. A sample of incomes was taken in 2010 and again in 2013. After being adjusted for inflation, the
Berhhart Billiards, Inc., conducted an experiment to measure the speed a cue ball attains when struck by various weighted pool cues. The conjecture is that a light cue generates faster speeds while breaking the balls at the beginning of a game of pool. Anecdotal experience has indicated that a
Recently, Logston Enterprises was notified by a law firm representing several female employees that a lawsuit was going to be filed claiming that the company gave males preferential treatment when it came to pay raises. The Logston human resources manager has requested that an estimate be made of
Delfonte’s Restaurant is a popular Italian eatery in the Bay Area in northern California. Recently, there has been a dispute among the wait staff regarding the amount of tips waiters receive on the lunch shift and on the dinner shift. Before making any adjustments in schedules or other policies,
A research paper stated that graduates in Malaysia have the fourth lowest salary expectations in the Asia-Pacific(APAC) region. The survey also found that female graduates have lower salary expectations as compared to their male counterparts. While 50 female business graduates in Malaysia expected
One of the key factors in concrete work is the time it takes for the concrete to “set up.” Suppose a concrete supplier is considering a new additive that can be put in the concrete mix to help reduce the setup time. Before going ahead with the additive, the company plans to test it against the
Two companies that manufacture batteries for electronics products have submitted their products to an independent testing agency. The agency tested 200 of each company’s batteries and recorded the lengths of time the batteries lasted before failure. The following results were determined:Company A
A pet food producer manufactures and then fills 25-pound bags of dog food on two different production lines located in separate cities. In an effort to determine whether differences exist between the average fill rates for the two lines, a random sample of 19 bags from line 1 and a random sample of
A credit card company operates two customer service centers: one in Boise and one in Richmond. Callers to the service centers dial a single number, and a computer program routes callers to the center having the fewest calls waiting. As part of a customer service review program, the credit card
Most banks provide different types of accounts to benefit their customers. Most people will choose either a savings account or a current account to manage their money. A savings account is the most common type of deposit account with limited withdrawals compared to a current account, which aids
Two random samples were selected independently from populations having normal distributions. The following statistics were extracted from the samples:x1 = 42.3 x2 = 32.4a. If s1 = 3 and s2 = 2 and the sample sizes are n1 = 50 and n2 = 50, construct a 95% confidence interval for the difference
Construct a 95% percent confidence interval for the difference between two population means using the following sample data that have been selected from normally distributed populations with different population variances:Sample 1 Sample 2 473 386 406 379 349 359 346 395 346 438 391 328 398 401 411
Construct a 95% confidence interval estimate for the difference between two population means based on the following information:Population 1 Population 2 x1 = 355 x2 = 320 s1 = 34 s2 = 40 n1 = 50 n2 = 80
Construct a 90% confidence interval estimate for the difference between two population means given the following sample data selected from two normally distributed populations with equal variances:Sample 1 Sample 2 29 25 31 42 39 38 35 35 37 42 40 43 21 29 34 46 39 35
The following information is based on independent random samples taken from two normally distributed populations having equal variances:n1 = 24 n2 = 28 x1 = 130 x2 = 125 s1 = 19 s2 = 17.5 Based on the sample information, determine the 95%confidence interval estimate for the difference between the
The following information is based on independent random samples taken from two normally distributed populations having equal variances:n1 = 15 n2 = 13 x1 = 50 x2 = 53 s1 = 5 s2 = 6 Based on the sample information, determine the 90%confidence interval estimate for the difference between the two
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