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The Practice Of Statistics For Business And Economics 3rd Edition David S. Moore, George P. McCabe, Layth C. Alwan, Bruce A. Craig, William M. Duckworth - Solutions
Plans to study abroad. The survey described in the previous exercise also asked about items related to academics. In response to one of these questions, 42% of first-year students reported that they plan to study abroad.(a) Based on the information available, what is the value of the count of
Students doing community service. In a sample of 159,949 first-year college students, the National Survey of Student Engagement reported that 39% participated in community service or volunteer work.10(a) Find the margin of error for 99% confidence.(b) Here are some facts from the report that
Women athletes and gambling. In the study described in the previous exercise, 1447 out of a total of 3469 female studentathletes reported participation in some gambling activity.(a) Use the large-sample methods to find an estimate of the true proportion with a 95% confidence interval.(b) The margin
Gambling and college athletics. Gambling is an issue of great concern to those involved in intercollegiate athletics.Because of this, the National Collegiate Athletic Association(NCAA) surveyed student-athletes concerning their gamblingrelated behaviors.9 There were 5594 Division I male athletes in
Guitar Hero and Rock Band. Refer to the previous exercise.(a) How would the result that you reported in part (c) of the previous exercise change if only 25% of the respondents said that they did not currently play a musical instrument?(b) Do the same calculations if the percent was 75%.(c) The main
Guitar Hero and Rock Band. An electronic survey of 7061 reported that 67% of players of Guitar Hero and Rock Band who do not currently play a musical instrument said that they are likely to begin playing a real musical instrument in the next two years.8 The reports describing the survey do not give
Most desirable mates. A poll of 5000 residents in Brazil, Canada, China, France, Malaysia, South Africa, and the United States asked about what profession they would prefer their marriage partner to have. The choice receiving the highest percent, 805 of the responses, was doctors, nurses, and other
Country food and Inuits. Country food includes seal, caribou, whale, duck, fish, and berries and is an important part of the diet of the aboriginal people called Inuits who inhabit Inuit Nunaat, the northern region of what is now called Canada. A survey of Inuits in Inuit Nunaat reported that 3274
Draw some pictures. Consider the binomial setting with n = 50 and p = 0.4.(a) The sample proportion ˆp will have a distribution that is approximately Normal. Give the mean and the standard deviation of this Normal distribution.(b) Draw a sketch of this Normal distribution. Mark the location of the
What’s wrong? Explain what is wrong with each of the following.(a) The margin of error for a confidence interval used for an opinion poll takes into account that fact that people who did not answer the poll questions may have had different responses from those who did answer the questions.(b) If
What’s wrong? Explain what is wrong with each of the following.(a) You can use a significance test to evaluate the hypothesis H0: ˆp = 0.6 versus the two-sided alternative.(b) The large-sample significance test for a population proportion is based on a t statistic.(c) Alarge-sample 95%
More information is needed. Refer to the previous exercise. Suppose that, after reviewing the results of the previous survey, you proceeded with preliminary development of the product. Now you are at the stage where you need to decide whether or not to make a major investment to produce and market
Is there interest in a new product? One of your employees has suggested that your company develop a new product. You decide to take a random sample of your customers and ask whether or not there is interest in the new product. The response is on a 1 to 5 scale, with 1 indicating “definitely would
Yes or no? In Example 8.4 we performed a significance test to compare your product with your competitor’s. Successwas defined as the outcome where your product provided better protection. Now, take the viewpoint of your competitor and define success as the outcome where your competitor’s
The effect of n. In Example 8.4, consider what would have happened if you had paid for twice as many subjects to be tested. Assume that the results would be the same as what you obtained for 20 subjects; that is 65% had better UVA and UVB protection with your product. Perform the significance test
The effect of X. In Example 8.4, suppose that your product provided better UVA and UVB protection for 15 of the 20 subjects. Perform the significance test and summarize the results.
What does the confidence interval tell us? Inspect the outputs in Figure 8.3 and report the confidence interval for the percent of people who would get better sun protection from your product than from your competitor’s. Be sure to convert from proportions to percents and to round appropriately.
Draw a picture. Draw a picture of a standard Normal curve and shade the tail areas to illustrate the calculation of the P-value for Example 8.4.
Construct an example. Make up an example where the large-sample method and the plus four method give very different intervals. Do not use a case where either ˆp = 0 or ˆp = 1.
New-product sales. Yesterday, your top salesperson called on 6 customers and obtained orders for your new product from all 6. Suppose that it is reasonable to view these 6 customers as a random sample of all of her customers.(a) Give the plus four estimate of the proportion of her customers who
Use plus-four for adultswhoplay video games. Refer to Example 8.3 (page 460).Compute the plus four 95% confidence interval and compare this interval with the one given in that example.
How often do they play? Refer to Exercise 8.2 (page 459).(a) Find SEˆp, the standard error of ˆp.(b) Give the 95% confidence interval for p in the form of estimate plus or minus the margin of error.(c) Give the confidence interval as an interval of percents.
Bank acquisitions. Refer to Exercise 8.1 (page 459).(a) Find SEˆp, the standard error of ˆp.(b) Give the 95% confidence interval for p in the form of estimate plus or minus the margin of error.(c) Give the confidence interval as an interval of percents.
How often do they play? In the PEW survey described in Case 8.1, those who played video games were asked howoften they played. In this subpopulation, 223 adults said that they played every day or almost every day.(a) What is the sample size n for the subpopulation of U.S. adults who play video
Bank acquisitions. The American Bankers Association Community Bank Competitiveness Survey for 2008 had responses from 760 community banks. Of these, 283 reported that they expected to acquire another bank within five years.3(a) What is the sample size n for this survey?(b) What is the count X?
Sample size and margin of error. The margin of error for the one-sample t confidence interval depends on the confidence level, the standard deviation, and the sample size. Fix the confidence level at 95% and the standard error at s = 1 to examine the effect of the sample size n. Find the margin of
t approaches z. As the degrees of freedom increase, the t distributions get closer and closer to the N(0, 1), or z, distribution.One way to see this is to look at how the critical value t∗for a 95% confidence interval changes with the degrees of freedom.Make a plot with degrees of freedom from 2
Ego strengths of MBA graduates: power. In Exercise 7.111 (page 446) you found the power for a study designed to compare the “ego strengths” of two groups of MBA students.Now you must design a study to compare MBA graduates who reached partner in a large consulting firm with those who joined the
Occupation and diet, continued. Use the data in the previous exercise to give two confidence intervals:(a) A 90% confidence interval for the mean daily alcohol consumption of London double-decker bus conductors.(b) An 80% confidence interval for the difference in mean daily alcohol consumption
Occupation and diet. Do various occupational groups differ in their diets? A British study of this question compared 98 drivers and 83 conductors of London double-decker buses.The conductors’ jobs require more physical activity. The article reporting the study gives the data as “mean daily
Testing job applicants. The one-hole test is used to test the manipulative skill of job applicants. This test requires subjects to grasp a pin, move it to a hole, insert it, and return for another pin. The score on the test is the number of pins inserted in a fixed time interval. One study compared
Sign test for telephone expenditures.Example 7.1 (page 398) gives data on the monthly expenditures for landline telephone service for 8 households. Is there evidence that the median monthly expenditure is less than $49? State the hypotheses, carry out the sign test, and report your
Competitive prices? A retailer entered into an exclusive agreement with a supplier who guaranteed to provide all products at competitive prices. The retailer eventually began to purchase supplies from other vendors who offered better prices.The original supplier filed a legal action claiming
Brain training. The assessment of computerized braintraining programs is a rapidly growing area of research. Researchers are now focusing on who this training benefits most, what brain functions are most susceptible to improvement, and which products are most effective. A recent study looked at 487
Insulation failures. A manufacturer of electric motors tests insulation at a high temperature (250◦C) and records the number of hours until the insulation fails. The data for 5 specimens are41 DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA
Recovery from wrinkles. Of course, the reason for durable press treatment is to reduce wrinkling. “Wrinkle recovery angle” measures how well a fabric recovers from wrinkles.Higher is better. Here are data on the wrinkle recovery angle (in degrees) for the same fabric specimens discussed in the
Find a confidence interval. Continue yourwork from the previous exercise.Afabric manufacturerwants to knowhowlarge a strength advantage fabrics treated by the Permafresh method have over fabrics treated by the Hylite process. Give a 95% confidence interval for the difference in mean breaking
Durable press and breaking strength. “Durable press”cotton fabrics are treated to improve their recovery from wrinkles after washing. Unfortunately, the treatment also reduces the strength of the fabric. A study compared the breaking strength of fabric treated by two commercial durable press
The manufacture of dyed clothing fabrics. Different fabrics respond differently when dyed. This matters to clothing manufacturers, who want the color of the fabric to be just right.Fabrics made of cotton and of ramie are dyed with the same“procion blue” die applied in the same way. A
Air in poultry-processing plants: summer versus winter. The air in poultry-processing plants often contains fungus spores. If the ventilation is inadequate, this can affect the health of the workers. The problem is most serious during the summer and least serious during the winter. To measure the
Alcohol content of wine. The alcohol content of wine depends on the grape variety, theway in which the wine is produced from the grapes, the weather, and other influences. Here are data on the percent of alcohol in wine produced from the same grape variety in the same year by 48 winemakers in the
Another personality trait of hotel managers. Continue your study from the previous exercise. The mean BSRI femininity score in the general male population is μ = 5.19. (It does seem odd that the mean femininity score is higher than the mean masculinity score, but such is the world of personality
Personalities of hotel managers. Successful hotel managers must have personality characteristics often thought of as feminine (such as “compassionate”) as well as those often thought of as masculine (such as “forceful”). The Bem Sex-Role Inventory(BSRI) is a personality test that gives
Air in poultry-processing plants. The air in poultryprocessing plants often contains fungus spores. If the ventilation is inadequate, this can affect the health of the workers. The problem is most serious during the summer. To measure the presence of spores, air samples are pumped to an agar plate
Evaluate the restaurant study. Refer to Exercise 7.119.Subjects who provided the evaluation data were shoppers who entered a mall in Seoul, South Korea, between the hours of 1:00 and 6:00 P.M., on Monday, Wednesday, and Saturday during two weeks. A total of 950 questionnaires were distributed, and
Evaluate the dress study. Refer to Exercise 7.118. Participants in the study viewed a videotape of awoman described as a 28-year-old senior manager for a Chicago advertising firm who had been working for this firm for 7 years. The same woman was used for each of the two conditions, but she wore
Perceived quality of high- and low-performing restaurants.A study classified 394 quick-service restaurants (QSR)into high-performing and low-performing groups based on their total sales. Each restaurant was rated on a collection of perceived measures of quality by a large number of diners using a 1
Does dress affect competence and intelligence ratings?Researchers performed a study to examine whether or notwomen are perceived as less competent and less intelligent when they dress in a sexy manner versus a business-like manner. Competence was rated from 1 (not at all) to 7 (extremely), and a 1
Study design information. In the previous study, diners were seated alone or in groups of two, three, four, and, in one case, nine (for a total of n = 16 tables). Also, each table, not each patron, was randomly assigned a particular wine label. Does this information alter how you might do the
The wine makes the meal? In a recent study, 39 diners were given a free glass of Cabernet Sauvignon to accompany a French meal.32 Although the wine was identical, half the bottle labels claimed the wine was from California and the other half claimed it was from North Dakota. The table below
Interpreting software output. You use statistical software to perform a significance test of the null hypothesis that two means are equal. The software reports P-values for the two-sided alternative. Your alternative is that the first mean is less than the second mean.(a) The software reports t =
Number of critical food violations. The results of a major city’s restaurant inspections are available through its online newspaper.31 Critical food violations are those that put patrons at risk of getting sick and must be immediately corrected by the restaurant. An SRS of n = 200 inspections
t is robust. A manufacturer of small appliances employs a market research firm to estimate retail sales of its products.Here are last month’s sales of electric can openers from an SRS of 50 stores in the Midwest sales region: DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA
LSAT scores. The scores of four roommates on the Law School Admission Test are 156 122 140 135 Find the mean, the standard deviation, and the standard error of the mean. Is it appropriate to calculate a confidence interval based on these data? Explain why or why not.
Ego strength: power. You want to compare the ego strengths of MBA students who plan to seek work at consulting firms and those who favor manufacturing firms. Based on the data from Exercise 7.89 (page 438), you will use σ = 0.7 for planning purposes. The pooled two-sample t test with α = 0.01
Margins of error. For each of the sample sizes considered in the previous two exercises, estimate the margin of error for the 95% confidence interval for the difference in seed counts.Display these results with a graph or a sketch.
Power, continued. Repeat the power calculation in the previous exercise, for 25, 30, 35, and 40 scoops from each plant.Summarize your power study. A graph of the power against sample size will help.
Comparison of packaging plants: power. Exercise 7.75(page 435) summarizes data on the number of seeds in one-pound scoops from two different packaging plants. Suppose that you are designing a new study for their next improvement effort. Based on information from the company, you want to identify a
Study habits of men and women. Return to the SSHA data in Exercise 7.93 (page 438). SSHA scores are generally less variable among women than among men. We want to know whether this is true for this college.(a) State H0 and Ha. Note that Ha is one-sided.(b) Because Table E contains only upper
Wheat prices. Example 7.14 (page 425) describes a USDA survey used to estimate wheat prices in July and September.Calculate the two sample standard deviations and perform the test for equality of standard deviations and summarize your conclusion.
Vitamin C loss in storage. Exercise 7.85 (page 437)presents data on the loss of vitamin C when bread is stored. Two loaves were measured immediately after baking and another two loaves were measured after three days of storage. These are very small sample sizes.(a) Use Table E to find the value
Revisiting the cholesterol comparison. Compare the standard deviations of total cholesterol in Exercise 7.73(page 435). Give the test statistic, the degrees of freedom, and the P-value. Write a short summary of your analysis, including comments on the assumptions for the test.
Comparison of standard deviations. Here are some summary statistics from two independent samples from Normal distributions:Sample n s2 1 10 3.2 2 16 11.5 You want to test the null hypothesis that the two population standard deviations are equal versus the two-sided alternative at the 5%
Power and the standard deviation. If the true population standard deviation were 0.7 instead of the 0.5928 hypothesized in Example 7.19,would the power increase or decrease? Explain.
Power and μ1 −μ2. If you repeat the calculation in Example 7.19 for other values of μ1 − μ2 that are smaller than 1.15, would you expect the power to increase or decrease? Explain.
Statistical significance? The F statistic for equality of standard deviations based on samples of sizes n1 = 15 and n2 = 7 takes the value F = 5.12.(a) Is this significant evidence of unequal population standard deviations at the 5%level?(b) Use Table E to give an upper and a lower bound for the
The F statistic. The F statistic F = s2 1/s2 2 is calculated from samples of size n1 = 10 and n2 = 16. (Remember that n1 is the numerator sample size.)(a) What is the upper 5% critical value for this F?(b) In a test of equality of standard deviations against the two-sided alternative, this
The advantage of pooling. Suppose that in the setting of the previous exercise you are interested in 95% confidence intervals for the difference rather than significance testing.Find the widths of the intervals for the two procedures (assuming or not assuming equal standard deviations). How do they
The advantage of pooling. For the analysis of wheat prices in Example 7.14 (page 425), there are only five observations per month. When sample sizes are small, we have very little information to make a judgment about whether the population standard deviations are equal. The potential gain from
Pooled procedures. Exercise 7.60 (page 423) compares a new type of computer monitor with a standard design. Reanalyze the data using the pooled procedure. Does the conclusion depend on the choice of method? The standard deviations are quite different for these data, so we do not recommend use of
Satterthwaite approximation. Example 7.11 (page 421)reports an analysis comparing product preference for a group of primed and a group of nonprimed consumers. Starting from the computer’s results for xi and si , verify that the Satterthwaite approximation for the degrees of freedom is 39.5.
Summer earnings of college students. College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One college studied this question by asking a sample of students how much they earned.27 Omitting students who were not employed, 1324
Study habits. The Survey of Study Habits and Attitudes(SSHA) is a psychological test designed to measure the motivation, study habits, and attitudes toward learning of college students.These factors, along with ability, are important in explaining success in school. Scores on the SSHA range from 0
Compare two marketing strategies. A bank compares two proposals to increase the amount that its credit card customers charge on their cards. (The bank earns a percentage of the amount charged, paid by the stores that accept the card.) Proposal A offers to eliminate the annual fee for customers who
Sales of small appliances. Amarket research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. Suppose that an SRS of 70 stores this month shows mean sales of
Study design matters! In the previous exercise you analyzed data on the ego strength of high-fitness and low-fitness participants in a campus fitness program. Suppose that instead you had data on the ego strengths of the same men before and after six months in the program. You wonder if the program
Fitness and ego. Employers sometimes seem to prefer executives who appear physically fit, despite the legal troubles that may result. Employers may also favor certain personality characteristics. Fitness and personality are related. In one study, middle-aged college faculty who had volunteered for
Are the samples too small? Exercises 7.85 and 7.87 are based on samples of just two loaves of bread. Some people claim that significance tests with very small samples never lead to rejection of the null hypothesis. Discuss this claim using the results of these two exercises.
Another ingredient. The researchers of Exercise 7.85 also measured the amount of vitamin E (in mg/100 g of flour) in the same four loaves. Here are the data: DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA
Study design matters! The researchers in the previous exercise might have measured only two loaves of bread, first immediately after baking and again after three days. Suppose that the data given had come from this study design. (The values are for the first loaf and second loaf, from left to
Effect of storage on a product. Does bread lose vitamins when stored? Researchers prepared four loaves of bread with flour fortified with a known amount of vitamins. After baking, they measured the vitamin C content of two loaves. The other two loaves were baked at the same time but were stored for
Healthy companies versus failed companies.Examples 7.16 and 7.17 (pages 431–432) compare healthy and failed companies under the special assumption that the two populations of firms have the same standard deviation. In practice, we prefer not to make this assumption, so let’s analyze the data
Compare two groups of consumers. The results in the previous exercise were based on two national surveys with a very large number of individuals. Here is a study that also looked at beverage consumption but with much smaller samples. One part of this study compared 20 children who were 7 to 10
Change in portion size. A recent study of food portion sizes reported that over a 17-year period, the average size of a soft drink consumed by Americans aged 2 years and older increased from 13.1 ounces (oz) to 19.9 oz. The authors state that the difference is statistically significant with P <
Not all dust is the same. Not all dust particles that are in the air around us cause problems for our lungs. Some particles are too large and stick to other areas of our body before they can get to our lungs. Others are so small that we can breathe them in and out and they will not deposit in our
Dust exposure at work. Exposure to dust at work can lead to lung disease later in life. One study measured the workplace exposure of tunnel constructionworkers.22 Part of the study compared 115 drill and blast workers with 220 outdoor concrete workers. Total dust exposure was measured in milligram
Self-control and food. Self-efficacy is a general concept that measures how well we think we can control different situations.In the study described in the previous exercise, the participants were asked, “How sure are you that you can eat foods low in fat over the next month?” The response was
A multimedia program designed to change behavior.A multimedia program designed to improve dietary behavior among low-income women was evaluated by comparing women who were randomly assigned to intervention and control groups.The intervention was a 30-minute session in a computer kiosk in the food
Drive-thru speaker clarity. QSR Magazine.com surveyed 689 adults on their drive-thru window experiences at quickservice restaurants.20 One question was “Thinking about your most recent drive-thru experience, please rate how satisfied you were with the clarity of communication through the
More on counts of seeds. Refer to the previous exercise.(a) When would a one-sided alternative hypothesis be appropriate in this setting? Explain.(b) What alternative hypothesiswould we be testing if we halved the P-value from the previous exercise?
Counts of seeds in one-pound scoops. Refer to Exercise 7.27 (page 414). As part of the Six Sigma quality improvement effort, the company wants to compare scoops of seeds from two different packaging plants. An SRS of 50 one-pound scoops of seeds was collected from Plant 1746 and an SRS of 19
More on blood lipid levels. Refer to the previous exercise.LDL is also known as “bad” cholesterol. Suppose the researcherswanted to test the hypothesis that LDL levels are higher in sedentary males than in sedentary females. Describe appropriate null and alternative hypotheses, and carry out
Comparison of blood lipid levels in males and females.Coronary heart disease (CHD) begins in young adulthood and is the fifth leading cause of death among adults aged 20 to 24 years.However, studies of serum cholesterol levels among college students are scarce. One study at a southern university
Sadness and spending. The “misery is not miserly” phenomenon refers to a sad person’s spending judgment going haywire. In a recent study, 31 young adults were given $10 and randomly assigned to either a sad or a neutral group. The participants in the sad group watched a video about the death
Effect of the confidence level. Assume x1 = 120, x2 = 110, s1 = 12, s2 = 11, n1 = 50, and n2 = 50. Find a 95% confidence interval for the difference in the corresponding values of μ. Does this interval include more or fewer values than a 99% confidence interval? Explain your answer.
Determining significance. For each of the following, answer the question and give a short explanation of your reasoning.(a) Asignificance test for comparing two means gave t = −2.16 with 11 degrees of freedom. Can you reject the null hypothesis that the μ’s are equal versus the two-sided
Understanding concepts. For each of the following, answer the question and give a short explanation of your reasoning.(a) A 95% confidence interval for the difference between two means is reported as (0.6, 1.3). What can you conclude about the results of a significance test of the null hypothesis
What’s wrong? In each of the following situations explain what is wrong and why.(a) A researcher wants to test H0: x1 = x2 versus the two-sided alternative Ha: x1 = x2.(b) A study recorded the credit card IQ scores of 100 college freshmen. The scores of the 48 males in the study were compared
Pooled equals unpooled? The software outputs in Figure 7.8 give the same value for the pooled and unpooled t statistics. Do some simple algebra to show that this is always true when the two sample sizes n1 and n2 are the same. In other cases, the two t statistics usually differ.
Using software. Figure 7.8 (pages 427 and 428) gives the outputs from five software systems for comparing prices received by wheat producers in July and September for small samples of 5 producers in each month. Some of the software reports both pooled and unpooled analyses. Which outputs give the
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