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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
9.28 Perform the significance test Refer to the previous exercise. Find the chi-square test statistic and its P-value and write a short summary of your conclusions.
9.27 Is the die fair? You suspect that a die has been altered so that the outcomes of a roll, the numbers 1 to 6, are not equally likely. You toss the die 500 times and obtain the following results:Outcome 1 2 3 4 5 6 Count 69 84 99 78 98 72 Compute the expected counts that you would need to use in
9.26 Is there a random distribution of trees? In Example 6.1(page 329), we examined data concerning the longleaf pine trees in the Wade Tract and concluded that the distribution of trees in the tract was not random. Here is another way to examine the same question. First, we divide the tract into
9.25 Repeat your analysis. In part (a) of Exercise 9.23, you had to decide which variable was the explanatory variable and which variable was the response variable when you computed the proportions to be compared.a. Did you use harassed online or harassed in person as the explanatory variable?
9.24 Data for the boys. Refer to the previous exercise. Here are the corresponding data for boys:Harassed in person Harassed online Yes No Yes 183 154 No 48 578 Using these data, repeat the analyses that you performed for the girls in Exercise 9.23. How do the results for the boys differ from those
9.23 Sexual harassment online or in person. In the study described in Exercise 9.11, the students were also asked whether or not they were harassed in person and whether or not they were harassed online. Here are the data for the girls:Harassed in person Harassed online Yes No Yes 321 200 No 40
9.22 Translate each problem into a r×c table. In each of the following scenarios, translate the problem into one that can be analyzed using a r×c table. Give the values of r andc, the table, and its entries.a. A sample of undergraduate students were asked whether or not they were in favor of
9.21 More on the goodness of fit to a Poisson distribution. Refer to the previous exercise.Repeat the analysis using 41, 35, and 24 as the observed counts. What do you conclude?
9.20 Goodness of fit to a Poisson distribution. Refer to Example 5.30 (page 316), where a Poisson distribution is described as a model for the number of Wi-Fi slowdowns per day. The mean number of slowdowns is 3.7. In this setting, the probability for 0, 1, or 2 slowdowns is 0.28543, the
9.19 Interpret the results of the coin tossing analysis. Refer to Exercises 9.15 and 9.17. Write a short summary of your analysis of John Kerrich’s coin tossing, including the results of the chi-square test.
9.18 More on the goodness of fit to a standard Normal distribution. Refer to Exercise 9.16. Use software to generate a sample of 300 Normal random variables with mean 10 and standard deviation 5.Choose a set of intervals and perform the goodness-of-fit test.
9.17 Test the hypothesis that the coin fair. Refer to Exercise 9.15. Find the chi-square statistic and the P-value.
9.16 Goodness of fit to a standard Normal distribution. Computer software generated 300 random numbers that should look as if they are from the standard Normal distribution. They are categorized into five groups: (1) less than or equal to−0.7 , (2) greater than−0.7 and less than or equal to
9.15 Is the coin fair? In Example 4.3 (page 207), we learned that the South African statistician John Kerrich tossed a coin 10,000 times while imprisoned by the Germans during World War II. The coin came up heads 5067 times.a. Formulate the question about whether or not the coin was fair as a
9.14 What’s wrong? Each of the following statements contains an error. Describe each error and explain why the statement is wrong.a. A goodness-of-fit test can be used to compare the observed distribution of a categorical variable with a distribution specified by an alternative hypothesis.b. The
9.13 Sexual harassment in middle and high schools. Refer to Exercise 9.11. Use the output in Figure 9.9 to find the chi-square statistic, the degrees of freedom, and the P value. What do you conclude from this analysis?
9.12 What’s wrong? Each of the following statements contains an error. Describe each error and explain why the statement is wrong.a. A chi-square statistic is used to test the null hypothesis that two categorical variables are dependent.b. Marginal distributions can be used to explain the
9.11 Sexual harassment in middle and high schools. A nationally representative survey of students in grades 7 to 12 asked about the experience of these students with respect to sexual harassment. One question asked how many times the student had witnessed sexual harassment in school. The two-way
9.10 Survival and class on the Titanic. On April 15, 1912, on her maiden voyage, the Titanic collided with an iceberg and sank. The ship was luxurious but did not have enough lifeboats for the 2224 passengers and crew. As a result of the collision, 1502 people died. The ship had three classes of
9.9 Two views of the significance test for physical education requirements. Refer to Exercise 9.2.Show that the chi-square statistic that you found in Exercise 9.8 is the square of the z statistic that you found in Exercise 8.41 (page 482).
9.8 Significance test for physical education requirements. Refer to Exercise 9.2. Find the chi-square statistic, the degrees of freedom, and the P-value. What do you conclude?
9.7 Significance test for eight is enough. Refer to Exercise 9.1. Find the chi-square statistic, the degrees of freedom, and the P-value. What do you conclude?
9.6 Expected counts for physical education requirements. Refer to Exercise 9.2. Find the expected counts.
9.5 Expected counts for eight is enough. Refer to Exercise 9.1. Find the expected counts.
9.4 Conditional distribution for physical education requirements. Refer to Exercise 9.2. Which conditional distribution do you prefer to explain the results of your analysis? Give a reason for your 5answer.
9.3 Conditional distribution for eight is enough. Refer to Exercise 9.1. Which conditional distribution would you choose to explain the relationship between the two variables? Write a summary that includes your interpretation of the relationship based on this conditional distribution.
9.2 Physical education requirements. In Exercise 8.41 (page 482), you analyzed data from a study that included 354 higher education institutions: 225 private and 129 public. Among the private institutions, 60 required a physical education course, while among the public institutions, 101 required a
9.1 Eight is enough. A healthy body needs good food, and healthy teeth are needed to chew our food so that it can nourish our bodies. The U.S. Army has recognized this fact and requires recruits to pass a dental examination. If you wanted to be a soldier in the Spanish American War, which took
8.76 Wallets in Poland. The wallet study also collected data in Poland, with 200 wallets in each of the two conditions. For the wallets with no money, 130 were returned; for wallets with money, 138 were returned. For this study, the wallets with money contained 25 Polish Zloty. Summarize your work
8.75 Wallets with money in Canada. Refer to Example 8.11, where we examined U.S. data for a study of returns of lost wallets with no money and with money. Data were also collected for people in other countries. For Canada, 200 wallets were used for each condition. The wallets with money contained
8.74 Statistics and the law. Castaneda v. Partida is an important court case in which statistical methods were used as part of a legal argument. When reviewing this case, the Supreme Court used the phrase“two or three standard deviations” as a criterion for statistical significance.This Supreme
8.73 A corporate liability trial. A major court case on the health effects of drinking contaminated water took place in the town of Woburn, Massachusetts. A town well in Woburn was contaminated by industrial chemicals. During the period that residents drank water from this well, there were 16 birth
8.72 Calculating sample sizes for the two-sample problem. For a single proportion, the margin of error of a confidence interval is largest for any given sample size n and confidence level C when p^=0.5. This led us to use p*=0.5 for planning purposes. The same kind of result is true for the
8.71 Sample size and the margin of error. In Section 8.1, we studied the effect of the sample size on the margin of error of the confidence interval for a single proportion. In this exercise, we perform some calculations to observe this effect for the two-sample problem. Suppose that p^1=0.8 and
8.70 Sample size and the P-value. In this exercise, we examine the effect of the sample size on the significance test for comparing two proportions. In each case, suppose that p^1=0.70 and p^2=0.50, and take n to be the common value of n1 and n2. Use the z statistic to test H0: p1=p2 versus the
8.69 Examine the effect of the sample size. Refer to the previous exercise.Assume a variety of different scenarios where the sample size changes, but the proportion in the sample who work 10 or more hours a week during the school year remains the same. Write a short report summarizing your results
8.68 Student employment during the school year. A study of 1425 undergraduate students reported that 930 work 10 or more hours a week during the school year. Give a 95% confidence interval for the proportion of all undergraduate students who work 10 or more hours a week during the school year.
8.67 We did not know the sample size. Refer to the previous two exercises.We did not report the sample size for the earlier study, but it is reasonable to assume that it is close to the sample size for the later study.a. Suppose that the sample size for the earlier study was only 800. Redo the
8.66 Do the significance test for the change. Refer to the previous exercise.Perform the significance test for comparing the two proportions. Report your test statistic, the P-value, and summarize your conclusion.
8.65 Changes in credit card usage by undergraduates. In Exercise 8.18(page 466), we looked at data from a survey of 1430 undergraduate students and their credit card use. In the sample, 43% said that they had four or more credit cards. A similar study of a different sample of undergraduates
8.64 Too many errors. Refer to the previous exercise. The chance that each of the six intervals that you calculated includes the true proportion for that genre is approximately 95%. In other words, the chance that your interval misses the true value is approximately 5%.a. Explain why the chance
8.63 Video game genres. A survey of 1102 teens collected data about video game use by teens. According to the survey, the following are the most popular game genres:Genre Examples Percent who play Racing NASCAR, Mario Kart, Burnout 74 Puzzle Bejeweled, Tetris, Solitaire 72 Sports Madden, FIFA, Tony
8.62 Facebook versus Twitter. Refer to Exercises 8.60 and 8.61. Can you use the data provided in these two exercises to compare the proportion of Facebook users with the proportion of Twitter users? If your answer is Yes, do the comparison. If your answer is No, explain why you cannot make the
8.61 Twitter users. Refer to the previous exercise. The same survey reported that 16% of Internet users used Twitter. Answer the questions in the previous exercise for Twitter use.29
8.60 Facebook users. A Pew survey of 1802 Internet users found that 67%used Facebook.a. How many of those surveyed used Facebook?b. Give a 95% confidence interval for the proportion of Internet users who used Facebook.c. Convert the confidence interval that you found in part (b) to a confidence
8.59 Changing majors during college. In a simple random sample of 975 students from a large public university, it was found that 463 of the students changed majors during their college years.a. Give a 95% confidence interval for the proportion of students at this university who change majors.b.
8.58 Confidence interval or significance test? Refer to Exercises 8.55, 8.56, and 8.57. Do you prefer to use the confidence interval or the significance test for this comparison? Give reasons for your answer.28
8.57 Use a significance test for the comparison. Refer to Exercise 8.55.Use a significance test to make the comparison. Interpret the result of your test. Be sure to include a justification for the use of the large-sample procedure for this comparison.
8.56 Use a confidence interval for the comparison. Refer to the previous exercise. Use a 95% confidence interval for the comparison and explain what the confidence interval tells us. Be sure to include a justification for the use of the large-sample procedure for this comparison.
8.55 Is the calcium intake adequate? Young children need calcium in their diet to support the growth of their bones. The Institute of Medicine provides guidelines for how much calcium should be consumed by people of different ages. One study examined whether or not a sample of children consumed 25
8.54 Where do you get your news? A report produced by the Pew Research Center’s Project for Excellence in Journalism summarized the results of a survey on how people get their news. Of the 2342 people in the survey who own a desktop or laptop, 1639 reported that they get their news from the
8.53 The future of gamification. Gamification is an interactive design that includes rewards such as points, payments, and gifts. A Pew survey of 1021 technology stakeholders and critics was conducted to predict the future of gamification. A report on the survey said that 42% of those surveyed
8.52 Find the relative risk. Refer to Exercise 8.35. For each scenario, find the relative risk. Be sure to give a justification for your choice of proportions to use in the numerator and the denominator of the ratio. Use the scenarios to explain the meaning of the relative risk.
8.51 Find the power. Consider testing the null hypothesis that two proportions are equal versus the twosided alternative withα=0.05 , 80% power, and equal sample sizes in the two groups.a. For each of the following situations, find the required sample size: (i)p1=0.1 and p2=0.2 , (ii)p1=0.2 and
8.50 Can we compare gaming on consoles with gaming on computers? Refer to Exercises 8.45 to 8.48. Do you think that you can use the large-sample confidence intervals for a difference in proportions to compare teens’ use of computers with teens’ use of consoles? Write a short paragraph giving
8.49 Find the sample size. You are planning a study in which you will use a 95% confidence interval to report the difference between two proportions. Find the sample size needed for a margin of error of 0.2 if you do not have good guess at the values of the two proportions. How would your answer
8.48 Significance test for gaming on consoles. Refer to the previous exercise. Test the null hypothesis that the two proportions are equal. Report the test statistic with the P-value and summarize your conclusion.
8.47 Gamers on computers. The report described in Exercise 8.45 also presented data from the same surveys for gaming on computers (desktops or laptops). These devices were used by 73% of adult 24 gamers and by 76% of teen gamers. Answer the questions given in Exercise 8.45 for gaming on computers.
8.46 Significance test for gaming on computers. Refer to the previous exercise. Test the null hypothesis that the two proportions are equal. Report the test statistic with the P-value and summarize your conclusion.
8.45 Adult gamers versus teen gamers. A Pew Internet Project Data Memo presented data comparing adult gamers with teen gamers with respect to the devices on which they play. The data are from two surveys. The adult survey had 1063 gamers, while the teen survey had 1064 gamers. The memo reports that
8.44 Significance test for exergaming in Canada. Refer to Exercise 8.42. Use a significance test to compare the proportions. Write a short statement interpreting this result.
8.43 Confidence interval for exergaming in Canada. Refer to the previous exercise. Find the 95%confidence interval for the difference in proportions. Write a short statement interpreting this result.
8.42 Exergaming in Canada. Exergames are active video games such as rhythmic dancing games, virtual bicycles, balance board simulators, and virtual sports simulators that require a screen and a console. A study of exergaming practiced by students from grades 10 and 11 in Montreal, Canada, examined
8.41 Physical education requirements. In the 1920s, about 97% of U.S. colleges and universities required a physical education course for graduation. Today, about 40% require such a course. A recent study of physical education requirements included 354 institutions: 225 private and 129 public. Among
8.40 Teeth and military service. In 1898 the United States and Spain fought a war over the U.S.intervention in the Cuban War of Independence. At that time, the U.S. military was concerned about the nutrition of its recruits. Many did not have a sufficient number of teeth to chew the food provided
8.39 Perform the significance test. Refer to Exercise 8.35. For each scenario, perform the large-sample significance test and use the scenario to explain the meaning of the significance test.20
8.38 Apply the significance test guidelines. Refer to Exercise 8.35. For each of the scenarios, determine whether or not the guidelines for using the large-sample significance test are satisfied. Explain your answers.
8.37 Find the 95% confidence interval. Refer to Exercise 8.35. For each scenario, find the largesample 95% confidence interval for the difference in proportions and use the scenario to explain the meaning of the confidence interval.
8.36 Apply the confidence interval guidelines. Refer to the previous exercise. For each of the scenarios, determine whether or not the guidelines for using the large-sample method for a 95%confidence interval are satisfied. Explain your answers.
8.35 Identify the key elements. For each of the following scenarios, identify the populations, the counts, and the sample sizes; compute the two proportions and find their difference.a. A study of tipping behaviors examined the relationship between the color of the shirt worn by the server and
8.34 What’s wrong? For each of the following, explain what is wrong and why.a. A z statistic is used to test the null hypothesis that p^1=p^2 .b. If two sample proportions are equal, then the sample counts are equal.c. A 95% confidence interval for the difference in two proportions includes
8.33 What’s wrong? For each of the following statements, explain what is wrong and why.a. The margin of error for a confidence interval used for an opinion poll takes into account the fact that people who did not answer the poll questions would have given the same responses as those who did
8.32 Sample size for tossing a coin. Refer to Exercise 8.25, where we analyzed the 10,000 coin tosses made by John Kerrich. Suppose that you want to design a study that would test the hypothesis that a coin is fair versus the alternative that the probability of a head is 0.52. Using a two-sided
8.31 Sample size for coffee. Refer to Exercise 8.24, where we analyzed data from a matched pairs study that compared preferences for instant versus fresh-brewed coffee. Suppose that you want to design a similar study. The null hypothesis is that instant and fresh-brewed are equally likely to be
8.30 Are the customers dissatisfied? An automobile manufacturer would like to know what proportion of its customers are dissatisfied with the service received from their local dealer. The customer relations department will survey a random sample of customers and compute a 95% confidence interval
8.29 Find more sample sizes. The evaluation in the previous exercise will also have questions that have not been asked before, so you do not have previous information about the possible value of p.Repeat the preceding calculation for the following values of p*: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7,
8.28 Sample size needed for an evaluation. You are planning an evaluation of a semester-long alcohol awareness campaign at your college. Previous evaluations indicate that about 25% of the students surveyed will respond Yes to the question “Did the campaign alter your behavior toward alcohol
8.27 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
8.26 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
8.25 Tossing a coin 10,000 times! The South African mathematician John Kerrich, while a prisoner of war during World War II, tossed a coin 10,000 times and obtained 5067 heads.15a. Is this significant evidence at the 5% level that the probability that Kerrich’s coin comes up heads is not 0.5? Use
8.24 Instant versus fresh-brewed coffee. A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order, and states which they prefer. Of the 50 subjects who participate in the study, 32 preferred
8.23 Long sermons. The National Congregations Study collected data in a one-hour interview with a key informant—that is, a minister, priest, rabbi, or other staff person or leader. One question concerned the length of the typical sermon. For this question, 390 out of 1191 congregations reported
8.22 Can we use the z test? In each of the following cases, state whether or not the Normal approximation to the binomial should be used for a significance test on the population proportion p.Explain your answers.a. n=20 and H0: p=0.3 .b. n=70 and H0: p=0.2 .c. n=100 and H0: p=0.08 .d. n=150 and
8.21 Do students report Internet sources? The National Survey of Student Engagement found that 87% of students report that their peers at least “sometimes” copy information from the Internet in their papers without reporting the source. Assume that the sample size is 430,000.a. Find the margin
8.20 How would the confidence interval change? Refer to the previous exercise.a. Would a 90% confidence interval be wider or narrower than the one that you found in the previous exercise? Verify your answer by computing the interval.b. Would a 97% confidence interval be wider or narrower than the
8.19 How many credit cards? The summary of the survey described in the previous exercise reported that 43% of undergraduates had four or more credit cards. Give a 95% confidence interval for the proportion of all college students who had four or more credit cards.
8.18 Student credit cards. In a survey of 1430 undergraduate students, 1087 reported that they had one or more credit cards. Give a 95% confidence interval for the proportion of all college students who had at least one credit card.
8.17 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 planned to study abroad.a. Based on the information available, how many students planned to
8.16 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.a. Find the margin of error for 99% confidence.b. Here are some facts from the report that
8.15 p^ and the Normal distribution. Consider the binomial setting with n=45 . You are testing the null hypothesis that p=0.7 versus the two-sided alternative with a 5% chance of rejecting the null hypothesis when it is true.a. Find the values of the sample proportion p^ that will lead to rejection
8.14 Bullying. Refer to the previous exercise. The survey also reported that 93% of the parents surveyed said that bullying contributes to violence in the United States. Answer the questions in the previous exercise for this item on the survey.
8.13 Violent video games. A survey of 1050 parents who have a child under the age of 18 living at home asked about their opinions regarding violent video games. A report describing the results of the survey stated that 89% of parents say that violence in today’s video games is a problem.a. What
8.12 Soft drink consumption in New Zealand. A survey commissioned by the Southern Cross Healthcare Group reported that 16% of New Zealanders consume five or more servings of soft drinks per week. The data were obtained through an online survey of 2006 randomly selected New Zealanders over 15 years
8.11 Country food and Inuits. Country food includes seals, caribou, whales, ducks, fish, and berries and is an important part of the diet of the aboriginal people called Inuits who inhabit Inuit Nunangat, the northern region of what is now called Canada. A survey of Inuits in Inuit Nunangat
8.10 Draw some pictures. Consider the binomial setting with n=200 and p=0.4 .a. The sample proportion p^ 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
8.9 Find the sample size. You are planning a survey similar to the one about the use of smart watches and fitness trackers described in Exercise 8.1. You will report your results with a large-sample 95%confidence interval. How large a sample do you need to be sure that the margin of error will not
8.8 What’s wrong? For each of the following statements, explain what is wrong and why.a. You can use a significance test to evaluate the hypothesis H0: p^=0.4 versus the two-sided alternative.b. The large-sample significance test for a population proportion is based on a t statistic.c. An
8.7 Whole grain versus regular grain? A study of young children was designed to increase their intake of whole-grain, rather than regular-grain, snacks. At the end of the study, the 82 children who participated in the study were presented with a choice between a regular-grain snack and a
8.6 Analysis of the service recommendation data. Refer to the previous exercise.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
8.5 Would you recommend the service to a friend? An automobile dealership asks all its customers who used its service department in a given two-week period if they would recommend the service to a friend. A total of 200 customers used the service during the two-week period, and 180 said that they
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