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introduction to operations research
Introduction To The Practice Of Statistics 10th Edition David S. Moore, George P. McCabe, Bruce A. Craig - Solutions
8.4 Analysis of the science knowledge data. Refer to Exercise 8.2.a. Report the sample proportion, the standard error of the sample proportion, and the margin of error for 95% confidence.b. Are the guidelines for when to use the large-sample confidence interval for a population proportion satisfied
8.3 Analysis of the smart watch or fitness tracker data. Refer to Exercise 8.1.a. Report the sample proportion, the standard error of the sample proportion, and the margin of error for 95% confidence.b. Are the guidelines for when to use the large-sample confidence interval for a population
8.2 What do you know about science? A Pew Internet poll tested 4464 U.S. adults about their knowledge of science. One of the questions asked how far a car will travel in 45 minutes if it travels at a constant speed of 40 miles per hour. Possible answers presented were 25 miles, 30 miles, 35 miles,
8.1 Do you use a smart watch or fitness tracker? A Pew Internet poll asked 4272 U.S. adults about their use of smart watches and fitness trackers. A summary of the results reported that 897 adults regularly wear a smart watch or fitness tracker.a. Identify the sample size and the count.b. Calculate
7.112 Self-concept and school performance. Refer to the previous exercise. Although self-concept in this study was measured on a scale with values in the data set ranging from 20 to 80, many prefer to think of this kind of variable as having only two possible values: low self-concept or high
7.111 Do women perform better in school? Some research suggests that women perform better than men in school, but men score higher on standardized tests. Table 1.2(page 24) presents data on a measure of school performance, grade point average (GPA), and a standardized test, IQ, for 78 seventh-grade
7.110 Alcohol consumption and body composition. Individuals who consume large amounts of alcohol do not use the calories from this source as efficiently as calories from other sources. One study examined the effects of moderate alcohol consumption on body composition and the intake of other foods.
7.109 Food intake and NEAT. Nonexercise activity thermogenesis (NEAT) provides a partial explanation for the results you found in the previous analysis. NEAT is energy burned by fidgeting, maintenance of posture, spontaneous muscle contraction, and other activities of daily living. In the study of
7.108 Food intake and weight gain. If we increase our food intake, we generally gain weight. Nutrition scientists can calculate the amount of weight gain that would be associated with a given increase in calories. In one study, 16 nonobese adults, aged 25 to 36 years, were fed 1000 calories per day
7.107 Approximating power. When software is not available to compute probabilities from the non-central t distribution, one can approximate the power by assuming the standard deviationσ is known and using the Normal distribution. Let’s compare the exact and approximate power calculations for a
7.106 Sign test for assessment of a foreign-language institute. Use the sign test to assess whether the summer institute of of the previous exercise improves French listening skills. State the hypotheses, give the P-value using the binomial table (Table C), and report your conclusion.
7.105 Assessment of a foreign-language institute. The National Endowment for the Humanities sponsors summer institutes to improve the skills of high school teachers of foreign languages. One such institute hosted 20 French teachers for four weeks. At the beginning of the period, the teachers were
7.104 Food costs. The Consumer Expenditure Survey provides information on the buying habits of U.S. consumers. In the latest report, the average annual amount a person under the age of 25 spent on food was $4876, with a standard error of $248.a. Assuming a sample size of n=2000, calculate a 90%
7.103 Conditions for inference. Suppose that your state contains 85 school corporations, and each corporation reports its expenditures per pupil. Is it proper to apply the onesample t method to these data to give a 95% confidence interval for the average expenditure per pupil in your state? Explain
7.102 Does flipping a classroom work? One approach to active learning is a “flipped classroom.” This commonly involves students watching video lectures outside of class and working on problem-solving activities in class. Research has primarily focused on comparing teaching approaches using
7.101 Different methods of teaching reading. In the READ data set, the response variable Post3 is to be compared for three methods of teaching reading. The Basal method is the standard, or control, method, and the two new methods are DRTA and Strat. We can use the methods of this chapter to compare
7.100 Sample size calculation. Example 7.13 (page 412) tells us that the mean height of 10-year-old girls is N(56.9, 2.8) and for boys it is N(56.0, 3.5). The null hypothesis that the mean heights of 10-year-old boys and girls are equal is clearly false. The difference in mean heights is
7.99 Behavior of pet owners. On the morning of March 5, 1996, a train with 14 tankers of propane derailed near the center of the small Wisconsin town of Weyauwega. Six of the tankers were ruptured and burning when the 1700 residents were ordered to evacuate the town. Researchers study disasters
7.98 Weight-loss programs. In a study of the effectiveness of weight-loss programs, 47 subjects who were at least 20% overweight took part in a group support program for 10 weeks. Private weighings determined each subject’s weight at the beginning of the program and six months after the
7.97 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
7.96 Transforming the response. Refer to Exercises 7.93 and 7.95. The researchers state that they took the natural log of the willingness to pay variable in order to “normalize the distribution” prior to analysis. Thus, their test results are based on log dollar measurements. For the t
7.95 More on snobby salespeople. Refer to Exercise 7.93. Researchers also asked a different 180 women to read the same hypothetical shopping experience, but now they entered a mass market (e.g., Gap, American Eagle, H&M). Here are those results (in dollars) for the two conditions:Chain n x¯ s
7.94 A comparison of female high school students. A study was performed to determine the prevalence of the female athlete triad (low energy availability, menstrual dysfunction, and low bone mineral density) in high school students. A total of 80 high school athletes and 80 sedentary students were
7.93 Can snobby salespeople boost retail sales? Researchers asked 180 women to read a hypothetical shopping experience where they entered a luxury store (for example, Louis Vuitton, Gucci, Burberry) and asked a salesperson for directions to the items they sought.For half the women, the salesperson
7.92 Analysis of tree size using the complete data set. The data used in Exercises 7.19 (page 407), 7.57, and 7.58 (page 432) were obtained by taking simple random samples from the 584 longleaf pine trees that were measured in the Wade Tract.The entire data set is given in the WADE data set. Find
7.91 Can mockingbirds learn to identify specific humans? A central question in urban ecology is why some animals adapt well to the presence of humans and others do not. The following results summarize part of a study of the northern mockingbird(Mimus polyglottos) that took place on a campus of a
7.90 Incomplete follow-up. Refer to the previous exercise. The researchers report that 19 participants(n=13 digital and n=6 control) did not complete training and thus were not included in the analysis. Does this information in any way alter your conclusions in the previous exercise? Explain your
7.89 The efficacy of digital mindfulness training. There is growing evidence that inperson mindfulness training can reduce stress. Little is known, however, about the efficacy of self-guided digital training. To investigate this, a group of researchers randomized 69 participants to either a digital
7.88 Average service time. Another benchmark that was measured in the QSRMagazine.com drive-thru study, described in Exercise 7.49 (page 430), was the service time. A summary of the results (in seconds) for two of the chains is shown below:Chain n x¯ s Taco Bell 165 240.38 36.3 McDonald’s 165
7.87 Two-sample t test versus matched pairs t test, continued. Refer to the previous exercise. Perhaps an easier way to see the major difference in the two analysis approaches for these data is by computing 95% confidence intervals for the mean difference.a. Compute the 95% confidence interval
7.86 Two-sample t test versus matched pairs t test. Consider the following data set.The data were actually collected in pairs, and each row represents a pair.Group 1 Group 2 48.86 48.88 50.60 52.63 51.02 52.55 47.99 50.94 54.20 53.02 50.66 50.66 45.91 47.78 48.79 48.44 47.76 48.92 51.13 51.63a.
7.85 Number of critical food violations. The results of a major city’s restaurant inspections are available through its online newspaper. Critical food violations are those that put patrons at risk of getting sick and must immediately be corrected by the restaurant. An SRS of 44 n=250 inspections
7.84 Identify the design. The following situations all require inference about a mean or means. Identify each as (1) a single sample, (2) matched pairs, or (3) two independent samples. Explain your answers.a. You want to estimate the average age of your store’s customers.b. You do an SRS survey
7.83 Which design? The following situations all require inference about a mean or means. Identify each as (1) a single sample, (2) matched pairs, or (3) two independent samples. Explain your answers.a. Your customers are college students. You are interested in comparing the interest in a new
7.82 Sample size and margin of error. The margin of error for a confidence interval forμ depends on the confidence level, the sample standard deviation s, and the sample size. Fix the confidence level at 95% and the sample standard deviation at s=1 to examine the effect of the sample size. Find
7.81 Degrees of freedom and t* . As the degrees of freedom increase, the t distributions get closer and closer to the z (N(0, 1))distribution. One way to see this is to look at how the value of t* for a 95% confidence interval changes with the degrees of freedom.a. Make a plot with degrees of
7.80 Converting a two-sided P-value. You use statistical software to perform a significance test of the null hypothesis that two means are equal. The software reports a P-value for the two-sided alternative. Your alternative is that the first mean is greater than the second mean.a. The software
7.79 LSAT scores. The scores of four senior roommates on the Law School Admission Test (LSAT) are 153 162 166 133 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.
For any two-sample t problems, try to use the degrees of freedom approximation provided by software. For exercises involving summarized data, this approximation is provided for you. If you instead use the conservative approximation, the smaller of n1−1 and n2−1 , be sure to clearly state this.
7.78 Planning a study to compare ad placement. Refer to Exercise 7.56 (page 431), where we compared trustworthiness ratings for ads from two different publications. Suppose that you are planning a similar study using two different publications that are not expected to show the differences seen when
7.77 More on planning a study to compare tree size. Refer to the previous exercise. Find the two standard deviations from Exercise 7.57. Do the same for the data in Exercise 7.58, which is a similar setting. These are somewhat smaller than the assumed value that you used in the previous exercise.
7.76 Planning a study to compare tree size. In Exercise 7.57 (page 432), DBH data for longleaf pine trees in two parts of the Wade Tract are compared. Suppose that you are planning a similar study in which you will measure the diameters of longleaf pine trees. Based on Exercise 7.57, you are
7.75 Changing the significance level. In Example 7.26 (page 440), we assessed the power of a new study of calcium on blood pressure, assuming n1=n2=45 subjects. The power was based onα=0.01 . Suppose that we wanted to use α=0.05 instead.a. Would the power increase or decrease? Explain your answer
7.74 Determining the sample size. In Example 7.25 (page 439), we determined the power of detectingμ=30 minutes when n=8 . Suppose your roommate wants the power to be at least 90% whenμ=30 . What is the minimum sample size needed for this desired power?
7.73 Power of the comparison of DXA machine operators. Suppose that the bone researchers in Exercise 7.29 (page 409) want to be able to detect an alternative mean difference of 0.002. Find the power for this alternative for a sample size of 20 patients. Make sure to explain the reasoning for your
7.72 Sample size calculations. You are designing a study to test the null hypothesis thatμ=50 versus the alternative that μ>50 .Assume that σ is 25.Suppose that it would be important to be able to detect the alternativeμ=54 . What sample size is needed to detect this alternative with power of
7.71 Accuracy of a laboratory scale, continued. Refer to the previous exercise. Suppose that instead of a confidence interval, the researchers want to perform a test (withα=0.05) that the scale is unbiased (μ=10) .a. What sample size n is necessary to have at least 90% power when the alternative
7.70 Accuracy of a laboratory scale. To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are Normally distributed, with unknown mean. (The mean is 10 grams if the scale has no bias.) The standard deviation of the scale
7.69 More on apartment rental rates. Refer to the previous exercise. Will the 95% confidence interval include approximately 95% of the rents of all unfurnished one-bedroom apartments in this area? Explain why or why not.
7.68 Apartment rental rates. You hope to rent an unfurnished one-bedroom apartment in Washington, DC, next year. You call a friend who lives there and ask him to give you an estimate of the mean monthly rate. Having taken a statistics course recently, the friend asks about your desired margin of
7.67 Starting salaries. In a recent survey by the National Association of Colleges and Employers, the average starting salary for college graduates with a computer and information sciences degree was reported to be $81,292. You are planning to do a survey of starting salaries for recent computer
7.66 What’s wrong? For each of the following statements, explain what is wrong and why.a. Doubling the sample size means the margin of error for a population meanμ is exactly cut in half.b. When testing H0: μ=50 versus the greater-than alternative, the power atμ=53 is larger than at μ=56 .c.
7.65 Revisiting the small-sample example. Refer to Example 7.19 (page 421). This is a case where the sample sizes are quite small. With only five observations per group, we have very little information to make a judgment about whether the population standard deviations are equal. The potential gain
7.64 Two-sample test of equivalence. In Section 7.1 (page 396), we were introduced to the one-sample test of equivalence. Using the same ideas, describe how to perform a two-sample test of equivalence.
7.63 Revisiting the diet and mood study. In Exercise 7.48 (page 430), the total mood disturbance score means were compared using the two-sample t procedures that do not assume equal standard deviations.Compare the means using a significance test and find the 95% confidence interval for the
7.62 Revisiting the sadness and spending study. In Exercise 7.47 (page 430), the purchase price of a water bottle was analyzed using the two-sample t procedure that does not assume equal standard deviations. Compare the means using a significance test and find the 95% confidence interval for the
7.61 Breast-feeding versus baby formula. A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, and the infants in another group were fed a standard baby formula without any iron supplements. Here are
7.60 An improper significance test. A friend has performed a significance test of the null hypothesis that two means are equal. His report states that the null hypothesis is rejected in favor of the alternative that the first mean is larger than the second. In a presentation on his work, he notes
7.59 Sales of a small appliance across months. A market 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 55 stores this
7.58 Size of trees in the eastern and western halves. Refer to the previous exercise. The Wade Tract can also be divided into eastern and western halves. Here are the DBHs of 30 randomly selected longleaf pine trees from each half:East 23.5 43.5 6.6 11.5 17.2 38.7 2.3 31.5 10.5 23.7 13.8 5.2 31.5
7.57 Size of trees in the northern and southern halves. The study of 584 longleaf pine trees in the Wade Tract in Thomas County, Georgia, had several purposes. Are trees in one part of the tract more or less like trees in any other part of the tract, or are there differences? In Example 6.1 (page
7.56 Does ad placement matter? Corporate advertising tries to enhance the image of the corporation. A study compared two ads from two sources, the Wall Street Journal and the National Enquirer. Subjects were asked to pretend that their company was considering a major investment in Performax, the
7.55 Why randomize? Refer to the previous exercise. A coworker suggested that you give the new hybrid computers to the next eight employees who need new computers and the standard laptop to the following eight. Explain why your randomized design is better.
7.54 New hybrid tablet and laptop? The purchasing department has suggested that your company switch to a new hybrid tablet and laptop. As CEO, you want data indicating that employees will like these new hybrids over the old laptops. You designate the next 16 employees needing new laptops to
7.53 Study design is important! Recall Exercise 7.50. You are concerned that day of the week may affect the number of hits. So to compare the two web page designs, you choose two successive weeks in the middle of a month. You flip a coin to assign one Monday to the first design and the other Monday
7.52 Beverage consumption. The results in the previous exercise were based on two national surveys with a very large number of individuals. Another study also looked at beverage consumption, but the 38 sample sizes were much smaller. One part of this study compared 20 children who were 7 to 10
7.51 Change in portion size. A study of food portion sizes reported that over a 17-year period, the average size of a soft drink consumed by Americans aged two years and older increased from 13.1 ounces (oz) to 19.9 oz. The authors state that the difference is statistically significant with P
7.50 Comparison of two web page designs. You want to compare the daily number of hits for two different website designs for your indie rock band. You assign the next 30 days to either Design A or Design B, 15 days to each.a. Would you use a one-sided or a two-sided significance test for this
7.49 Drive-thru customer service. QSRMagazine.com assessed 1503 drive-thru visits at quick-service restaurants. One benchmark assessed was customer service. Responses ranged from “Rude (1)” to“Very Friendly (5).” The following table breaks down the responses according to two of the chains
7.48 Diet and mood. Researchers were interested in comparing the long-term psychological effects of being on a high-carbohydrate, low-fat (LF) diet versus a high-fat, low-carbohydrate (LC) diet. A total of 106 overweight and obese participants were randomly assigned to one of these two
7.47 Sadness and spending. The “misery is not miserly” phenomenon refers to a person’s spending judgment going haywire when the person is sad. In a study, 31 young adults were given $10 and randomly assigned to either a sad group or a neutral group. The participants in the sad group watched a
7.46 Comparing means. Refer to Exercise 7.44. Suppose that you wanted to compare the average minutes per week spent on Facebook with the average minutes per week spent preparing for class.a. Provide an estimate of this difference.b. Explain why it is incorrect to use the two-sample t test to see if
7.45 Possible biases? Refer to the previous exercise. The researcher surveyed students at a four-year public university in the northeastern United States(N=3866) . Each student was emailed a link to the survey hosted on SurveyMonkey.com. The researcher stated:For the students who did not
7.44 Facebook use in college. Because of Facebook’s popularity among college students, there is a great deal of interest in the relationship between Facebook use and academic performance. One study collected information on n=1839 undergraduate students to look at the relationships among frequency
7.43 Trustworthiness and eye color. Why do we naturally tend to trust some strangers more than others? One group of researchers decided to study the relationship between eye color and trustworthiness. In their experiment, the researchers took photographs of 80 students (20 males with brown eyes, 20
7.42 When is 52 weeks not equal to a year? Refer to the previous exercise. The researchers also had 60 marketing students read an announcement about a construction project. The expected duration was either 1 year or 52 weeks. Each student was then asked to state the earliest and latest completion
7.41 When is 30/31 days not equal to a month? Time can be expressed on different levels of scale, including days, weeks, months, and years. Can the scale provided influence perception of time? For example, if you placed an order over the phone, would it make a difference if you were told the
7.40 Noise levels in fitness classes, continued. Refer to the previous exercise. In most countries, the workplace noise standard is 85 db (over eight hours). For every 3 dB increase above that, the amount of exposure time is halved. This means that the exposure time for a dB level of 91 is two
7.39 Noise levels in fitness classes. Fitness classes often have very loud music that could affect hearing.One study collected noise levels (decibels) in both high-intensity and low-intensity fitness classes across eight commercial gyms in Sydney, Australia.a. Create a histogram or Normal quantile
7.38 Physical demands of women’s rugby sevens matches. Rugby sevens is rapidly growing in popularity and became an Olympic sport in 2016. Matches are played on a full rugby field and consist of two seven-minute halves. Each team also consists of seven players. To better understand the demands of
7.37 More basic concepts. For each of the following, answer the question and give a short explanation of your reasoning.a. A significance test for comparing two means gave t=−1.97 with 10 degrees of freedom. Can you reject the null hypothesis that theμ ’s are equal versus the two-sided
7.36 Basic 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 (0.8, 2.3). What can you conclude about the results of a significance test of the null hypothesis that
7.35 What’s wrong? For each of the following statements, explain what is wrong and why.a. A researcher wants to test H0: x¯1=x¯2 versus the two-sided alternative Ha: x¯1≠x¯2 .b. A study recorded the IQ scores of 100 college freshmen. The scores of the 56 males in the study were compared
7.34 Insulation study. 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 five specimens are 446 326 372 377 310 The small sample size makes judgment from the data difficult, but engineering
7.33 Sign test for fuel efficiency comparison. Use the sign test to assess whether the computer calculates a higher mpg than the driver in Exercise 7.25. State the hypotheses, give the P-value using the binomial table (Table C), and report your conclusion.
7.32 Sign test for the comparison of operators. The differences in the TBBMC measures in Exercise 7.29 can also be analyzed using a sign test. Set up the appropriate null and alternative hypotheses, carry out the test, and summarize the results. How do these results compare with those that you
7.31 Sign test for potential insurance fraud. The differences in the repair estimates in Exercise 7.24 can also be analyzed using a sign test. Set up the appropriate null and alternative hypotheses, carry out the test, and summarize the results. How do these results compare with those that you
7.30 Equivalence of paper and computer-based questionnaires. Computers are commonly used to complete questionnaires because of the increased efficiency of data collection and reduction in coding errors. Studies, however, have shown that questionnaire format can influence responses, especially for
7.29 Comparing operators of a DXA machine. Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body bone mineral content (TBBMC). A highly skilled operator is required to take the measurements. Recently, a new DXA machine was
7.28 A customer satisfaction survey. Many organizations are doing surveys to determine the satisfaction of their customers. Attitudes toward various aspects of campus life were the subject of one such study conducted at Purdue University. Each item was rated on a 1 to 5 scale, with 5 being the
7.27 Significance test for the average number of picks. Refer to the previous exercise.a. Do these data provide evidence that the average number of picks in a one-pound bag is greater than 925? Using a significance level of 5%, state your hypotheses, the P-value, and your conclusions.b. Do these
7.26 Counts of picks in a one-pound bag. A guitar supply company must maintain strict oversight on the number of picks it packages for sale to customers. The company’s current advertisement specifies between 900 and 1000 picks in every bag. An SRS of 36 one-pound bags of picks was collected as
7.25 Fuel efficiency comparison t test. Refer to Exercise 7.18. In addition to the computer calculating miles per gallon, the driver also recorded the miles per gallon by dividing the miles driven by the number of gallons at fill-up. The driver wants to determine if these calculations are
7.24 Potential insurance fraud? Insurance adjusters are concerned about the high estimates they are receiving from Jocko’s Garage. To see if the estimates are unreasonably high, each of 10 damaged cars was taken to Jocko’s and to another garage, and the estimates (in dollars) were recorded.
7.23 Are the parents feeling extreme stress? Refer to the previous exercise. The researchers considered a score greater than 45 to represent extreme stress. Is there evidence that the average stress level for the parents in this study is above this level? Perform a test of significance usingα=0.10
7.22 Stress levels in parents of children with ADHD. In a study of parents who have children with attention-deficit/hyperactivity disorder (ADHD), parents were asked to rate their overall stress level using the Parental Stress Scale (PSS). This scale has 18 items that contain statements regarding
7.21 Corn seed prices. The U.S. Department of Agriculture (USDA) uses sample surveys to obtain important economic estimates. One USDA pilot study estimated from a sample of 30 farms the amount a farmer will pay per planted acre of corn. The mean price was reported as $674.96 with a standard error
7.20 Nutritional intake among Canadian high-performance male athletes. Recall Exercise 6.44(page 366). For one part of the study, n=114 male athletes from eight Canadian sports centers were surveyed. Their average caloric intake was 3077.0 kilocalories per day (kcal/d), with a standard deviation of
7.19 Tree diameter confidence interval. A study of 584 longleaf pine trees in the Wade Tract in Thomas County, Georgia, is described in Example 6.1 (page 329). For each tree in the tract, the researchers measured the diameter at breast height (DBH). This is the diameter of the tree at a height of
7.18 Fuel efficiency t test. Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon(mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas
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