BSC Expected ValueExercise 1 includes results from a

Problem 1BSC Notation? In analyzing hits by V-l buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 576 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In applying Formula 5-9, identify the values of ?µ, x,? and ?e.? Also, briefly describe what each of those symbols represents.

Problem 2 BSC Expected Value?Exercise 1 includes results from a survey of 1005 randomly selected subjects. Consider the claim that when respondents select days of the week, the seven different days have the same chance of being selected. If that claim is true for the 1005 respondents, what is the expected value for each of the seven days? Identify the values of?O?and?E?for Sunday.

Problem 3BSC x2? Value? Without performing actual calculations, examine the frequencies in the table given with Exercise 1. Do you expect the value of the ?x2? test statistic to be large or small? Do you expect the P? ?-value to be large or small? Explain. Exercise 1 Quality Family Time? The table below lists days of the week selected by a random sample of 1005 subjects who were asked to identify the day of the week that is best for quality family time (based on results from a Pillsbury survey reported in ?USA Today?). Consider the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected. If we test that claim using the goodness-of-fit test described in this section, what is it that we actually test?

Problem 4BSC Goodness-of-Fit Test? For the goodness-of-fit test described in Exercise 1, identify the number of degrees of freedom and the critical value of ?x1,? assuming a 0.05 significance level. Exercise 1 Quality Family Time? The table below lists days of the week selected by a random sample of 1005 subjects who were asked to identify the day of the week that is best for quality family time (based on results from a Pillsbury survey reported in ?USA Today?). Consider the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected. If we test that claim using the goodness-of-fit test described in this section, what is it that we actually test?

Problem 5BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Quality Family Time? The accompanying STATDISK display shows results from the claim and data given in Exercise 1. Test that claim. Exercise 1 Quality Family Time? The table below lists days of the week selected by a random sample of 1005 subjects who were asked to identify the day of the week that is best for quality family time (based on results from a Pillsbury survey reported in ?USA Today).? Consider the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected. If we test that claim using the goodness-of-fit test described in this section, what is it that we actually test?

Problem 6BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Last Digits of Heights? Example 1 in this section involved an analysis of the last digits of weights from a random sample of 100 Californians. Using those same subjects, the last digits of their heights are listed in the table below (based on data from the California Department of Public Health). Use a 0.05 significance level to test the claim that the sample is from a population of heights in which the last digits do ?not? occur with the same frequency. The accompanying Minitab display results from the data in the table. L a s t D i g i t F r e q u e n c y Example 1? Last Digits of Weights

Problem 7BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Testing a Slot Machine? The author purchased a slot machine (Bally Model 809) and tested it by playing it 1197 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on. When testing the claim that the observed outcomes agree with the expected frequencies, the author obtained a test statistic of ???2 = 8.185. Use a 0.05 significance level to test the claim that the actual outcomes agree with the expected frequencies. Does the slot machine appear to be functioning as expected?

Problem 8BSC Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Flat Tire and Missed Class ?A classic story involves four carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn’t have a flat tire, would they be able to identify the same tire? The author asked 41 other students to identify the tire they would select. The results are listed in the following table (except for one student who selected the spare). Use a 0.05 significance level to test the author’s claim that the results fit a uniform distribution. What does the result suggest about the ability of the four students to select the same tire when they really didn’t have a flat?

Problem 9BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. NYC Homicides? For a recent year, the following are the numbers of homicides that occurred each month in New York City: 38, 30, 46, 40, 46, 49, 47, 50, 50, 42, 37, 37. Use a 0.05 significance level to test the claim that homicides in New York City are equally likely for each of the 12 months. Is there sufficient evidence to support the police commissioner’s claim that homicides occur more often in the summer when the weather is better?

Problem 10BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Baseball Player Births? In his book ?Outliers,? author Malcolm Gladwell argues that more baseball players have birthdates in the months immediately following July 31, because that was the cutoff date for nonschool baseball leagues. Here is a sample of frequency counts of months of birthdates of American-born major league baseball players starting with January: 387, 329, 366, 344, 336, 313, 313, 503, 421, 434, 398, 371. Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that American-born major league baseball players are born in different months with the same frequency? Do the sample values appear to support Gladwell’s claim?

Problem 11BSC Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Loaded Die?The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27, 31, 42, 40, 28, 32. Use a 0.05 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?

Problem 12BSC Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Births?Records of randomly selected births were obtained and categorized according to the day of the week that they occurred (based on data from the National Center for Health Statistics). Because babies are unfamiliar with our schedule of weekdays, a reasonable claim is that births occur on the different days with equal frequency. See the table that follows. Use a 0.01 significance level to test that claim. Can you provide an explanation for the result?

Problem 13BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Kentucky Derby? The table below lists the frequency of wins for different post positions in the Kentucky Derby horse race (current as of this writing). A post position of 1 is closest to the inside rail, so that horse has the shortest distance to run. (Because the number of horses varies from year to year, only the first 10 post positions are included.) Use a 0.05 significance level to test the claim that the likelihood of winning is the same for the different post positions. Based on the result, should bettors consider the post position of a horse racing in the Kentucky Derby? P o s t P o s i t i o n W i n s

Problem 14BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Win 4 Lottery? The author recorded all digits selected in New York’s Win 4 Lottery for two drawings held each day in a recent year. The frequencies of the digits from 0 through 9 are 280, 303, 331, 289, 285, 294, 283, 274, 297, and 284. Use a 0.05 significance level to test the claim of lottery officials that the digits are selected in a way that they are equally likely.

Problem 16BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Police Calls? Repeat the preceding exercise using these observed frequencies for police calls received during the month of March: Monday (208); Tuesday (224); Wednesday (246); Thursday (173); Friday (210); Saturday (236); Sunday (154). What is a fundamental error with this analysis?

Problem 15BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Police Calls? The police department in Madison, Connecticut, released the following numbers of calls for the different days of the week during a recent February that had 28 days: Monday (114); Tuesday (152); Wednesday (160); Thursday (164); Friday (179); Saturday (196); Sunday (130). Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. Is there anything notable about the observed frequencies?

Problem 17BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. World Series Games? The table below lists the numbers of games played in the baseball World Series as of this writing. That table also includes the expected proportions for the numbers of games in a World Series, assuming that in each series, both teams have about the same chance of winning. Use a 0.05 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions. Games Played Actual World Series Contests Expected Proportion

Problem 18BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. American Idol? The contestants on the TV show A? merican Idol? try to win a singing contest. At one point, the Web site ?WhatNotToSing.com? listed the actual numbers of eliminations for different orders of singing, and the expected number of eliminations was also listed. The results are in the table below. Use a 0.05 significance level to test the claim that the actual eliminations agree with the expected numbers. Does there appear to be support for the claim that the leadoff singers appear to be at a disadvantage? 7 t h r Singi o ng u Order g h 1 2 Elimi natio 9 ns Expe 1 cted 3 Elimi . natio 5 ns

Problem 19BSC Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. M&M Candies?Mars, Inc. claims that its M&M plain candies are distributed with the following color percentages: 16% green, 20% orange, 14% yellow, 24% blue, 13% red, and 13% brown. Refer to Data Set 20 in Appendix B and use the sample data to test the claim that the color distribution is as claimed by Mars, Inc. Use a 0.05 significance level.

Problem 20BSC In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Do World War II Bomb Hits Fit a Poisson Distribution? In analyzing hits by V-l buzz bombs in World War II, South London was subdivided into regions, each with an area of 0.25 km2. Shown below is a table of actual frequencies of hits and the frequencies expected with the Poisson distribution. (The Poisson distribution is described in Section 5-5.) Use the values listed and a 0.05 significance level to test the claim that the actual frequencies fit a Poisson distribution. Number of Bomb Hits Actual Number of Regions Expected Number of Regions (from Poisson Distribution)

Problem 21BSC Benford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercise?, ?test for goodness-offit with Benford’s law. L e a d i n g D i g i t B e n f o r d ’ s L a w : D i s t r i b u t i o n o f L e a d i n g D i g i t s Detecting Fraud? When working for the Brooklyn district attorney, investigator Robert Burton analyzed the leading digits of the amounts from 784 checks issued by seven suspect companies. The frequencies were found to be 0, 15, 0, 76, 479, 183, 8, 23, and 0, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford’s law, the check amounts appear to result from fraud. Use a 0.01 significance level to test for goodness-of-fit with Benford’s law. Does it appear that the checks are the result of fraud?

Problem 22BSC Benford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercise?, ?test for goodness-offit with Benford’s law. L e a d i n g D i g i t B e n f o r d ’ s L a w : D i s t r i b u t i o n o f L e a d i n g D i g i t s Author’s Check Amounts? Exercise 1 lists the observed frequencies of leading digits from amounts on checks from seven suspect companies. Here are the observed frequencies of the leading digits from the amounts on checks written by the author: 68, 40, 18, 19, 8, 20, 6, 9, 12. (Those observed frequencies correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.) Using a 0.05 significance level, test the claim that these leading digits are from a population of leading digits that conform to Benford’s law. Do the author’s check amounts appear to be legitimate? Exercise 1 Detecting Fraud? When working for the Brooklyn district attorney, investigator Robert Burton analyzed the leading digits of the amounts from 784 checks issued by seven suspect companies. The frequencies were found to be 0, 15, 0, 76, 479, 183, 8, 23, and 0, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford’s law, the check amounts appear to result from fraud. Use a 0.01 significance level to test for goodness-of-fit with Benford’s law. Does it appear that the checks are the result of fraud?

Problem 23BSC Benford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercise?, ?test for goodness-offit with Benford’s law. L e a d i n g D i g i t B e n f o r d ’ s L a w : D i s t r i b u t i o n o f L e a d i n g D i g i t s Tax Cheating?? Frequencies of leading digits from 1RS tax files are 152, 89, 63, 48, 39, 40, 28, 25, and 27 (corresponding to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively, based on data from Mark Nigrini, who sells software for Benford data analysis). Using a 0.05 significance level, test for goodness-of-fit with Benford’s law. Does it appear that the tax entries are legitimate?

Problem 24BSC Benford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercise?, ?test for goodness-offit with Benford’s law. L e a d i n g D i g i t B e n f o r d ’ s L a w : D i s t r i b u t i o n o f L e a d i n g D i g i t s Author’s Computer Files? The author recorded the leading digits of the sizes of the files stored on his computer, and the leading digits have frequencies of 45, 32, 18, 12, 9, 3, 13, 9, and 9 (corresponding to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively). Using a 0.05 significance level, test for goodness-of-fit with Benford’s law.

Problem 25BSC Testing Goodness-of-Fit with a Normal Distribution? Refer to Data Set 1 in Appendix B for the 40 heights of females. G r L 1 1 e e 5 6 a s 5 2 H t s . . e e T 4 0 i r h 1 0 g T a 0 5 h h n - - t a 1 1 1 ( n 5 6 6 c 1 5 2 8 m . . . 6 ) 8 4 0 6 . 1 0 0 6 0 5 1 0 1 F r e q u e n c y a. Enter the observed frequencies in the preceding table. b. Assuming a normal distribution with mean and standard deviation given by the sample mean and standard deviation, use the methods of Chapter 6 to find the probability of a randomly selected height belonging to each class. c. Using the probabilities found in part (b), find the expected frequency for each category. d. Use a 0.01 significance level to test the claim that the heights were randomly selected from a normally distributed population. Does the goodness-of-fit test suggest that the data are from a normally distributed population?

Problem 9BSC In Exercise, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. NYC Homicides For a recent year, the following are the numbers of homicides that occurred each month in New York City: 38, 30, 46, 40, 46, 49, 47, 50, 50, 42, 37, 37. Use a 0.05 significance level to test the claim that homicides in New York City are equally likely for each of the 12 months. Is there sufficient evidence to support the police commissioner’s claim that homicides occur more often in the summer when the weather is better?

Problem 11BSC Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Loaded Die The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27, 31, 42, 40, 28, 32. Use a 0.05 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?

Problem 10BSC In Exercise, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Baseball Player Births In his book Outliers, author Malcolm Gladwell argues that more baseball players have birthdates in the months immediately following July 31, because that was the cutoff date for non school baseball leagues. Here is a sample of frequency counts of months of birthdates of American-born major league baseball players starting with January: 387, 329, 366, 344, 336, 313, 313, 503, 421, 434, 398, 371. Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that American-born major league baseball players are born in different months with the same frequency? Do the sample values appear to support Gladwell’s claim?

Problem 3BSC x2 Value Without performing actual calculations, examine the frequencies in the table given with Exercise 1. Do you expect the value of the x2 test statistic to be large or small? Do you expect the P-value to be large or small? Explain.

Problem 4BSC Goodness-of-Fit Test For the goodness-of-fit test described in Exercise 1, identify the number of degrees of freedom and the critical value of x1, assuming a 0.05 significance level.

Statistical Literacy and Critical Thinking Quality Family Time The accompanying STATDISK display shows results from the claim and data given in Exercise 1. Test that claim. STATDISK

Problem 21BSC Benford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercise, test for goodness-offit with Benford’s law. Leading Digit 1 2 3 4 5 6 7 8 9 Benford’s Law: Distribution of Leading Digits 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6% Detecting Fraud When working for the Brooklyn district attorney, investigator Robert Burton analyzed the leading digits of the amounts from 784 checks issued by seven suspect companies. The frequencies were found to be 0, 15, 0, 76, 479, 183, 8, 23, and 0, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford’s law, the check amounts appear to result from fraud. Use a 0.01 significance level to test for goodness-of-fit with Benford’s law. Does it appear that the checks are the result of fraud?

Problem 22BSC Benford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercise, test for goodness-offit with Benford’s law. Leading Digit 1 2 3 4 5 6 7 8 9 Benford’s Law: Distribution of Leading Digits 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6% Author’s Check Amounts Exercise 1 lists the observed frequencies of leading digits from amounts on checks from seven suspect companies. Here are the observed frequencies of the leading digits from the amounts on checks written by the author: 68, 40, 18, 19, 8, 20, 6, 9, 12. (Those observed frequencies correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.) Using a 0.05 significance level, test the claim that these leading digits are from a population of leading digits that conform to Benford’s law. Do the author’s check amounts appear to be legitimate? Exercise 1 Detecting Fraud When working for the Brooklyn district attorney, investigator Robert Burton analyzed the leading digits of the amounts from 784 checks issued by seven suspect companies. The frequencies were found to be 0, 15, 0, 76, 479, 183, 8, 23, and 0, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford’s law, the check amounts appear to result from fraud. Use a 0.01 significance level to test for goodness-of-fit with Benford’s law. Does it appear that the checks are the result of fraud?

Problem 23BSC Benford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercise, test for goodness-offit with Benford’s law. Leading Digit 1 2 3 4 5 6 7 8 9 Benford’s Law: Distribution of Leading Digits 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6% Tax Cheating? Frequencies of leading digits from 1RS tax files are 152, 89, 63, 48, 39, 40, 28, 25, and 27 (corresponding to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively, based on data from Mark Nigrini, who sells software for Benford data analysis). Using a 0.05 significance level, test for goodness-of-fit with Benford’s law. Does it appear that the tax entries are legitimate?

Statistical Literacy and Critical Thinking Last Digits of Heights Example 1 in this section involved an analysis of the last digits of weights from a random sample of 100 Californians. Using those same subjects, the last digits of their heights are listed in the table below (based on data from the California Department of Public Health). Use a 0.05 significance level to test the claim that the sample is from a population of heights in which the last digits do not occur with the same frequency. The accompanying Minitab display results from the data in the table. MINITAB

Problem 7BSC In Exercise, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Testing a Slot Machine The author purchased a slot machine (Bally Model 809) and tested it by playing it 1197 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on. When testing the claim that the observed outcomes agree with the expected frequencies, the author obtained a test statistic of ?2 = 8.185. Use a 0.05 significance level to test the claim that the actual outcomes agree with the expected frequencies. Does the slot machine appear to be functioning as expected?

Problem 8BSC Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Flat Tire and Missed Class A classic story involves four carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn’t have a flat tire, would they be able to identify the same tire? The author asked 41 other students to identify the tire they would select. The results are listed in the following table (except for one student who selected the spare). Use a 0.05 significance level to test the author’s claim that the results fit a uniform distribution. What does the result suggest about the ability of the four students to select the same tire when they really didn’t have a flat?

Problem 24BSC Benford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercise, test for goodness-offit with Benford’s law. Leading Digit 1 2 3 4 5 6 7 8 9 Benford’s Law: Distribution of Leading Digits 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6% Author’s Computer Files The author recorded the leading digits of the sizes of the files stored on his computer, and the leading digits have frequencies of 45, 32, 18, 12, 9, 3, 13, 9, and 9 (corresponding to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively). Using a 0.05 significance level, test for goodness-of-fit with Benford’s law.

Testing Goodness-­of-­Fit with a Normal Distribution Refer to Data Set 1 in Appendix B for the 40 heights of females. a. Enter the observed frequencies in the table above. b. Assuming a normal distribution with mean and standard deviation given by the sample mean and standard deviation, use the methods of Chapter 6 to find the probability of a randomly selected height belonging to each class. c. Using the probabilities found in part (b), find the expected frequency for each category. d. Use a 0.01 significance level to test the claim that the heights were randomly selected from a normally distributed population. Does the goodness­-of-fit test suggest that the data are from a normally distributed population?

Problem 12BSC Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Births Records of randomly selected births were obtained and categorized according to the day of the week that they occurred (based on data from the National Center for Health Statistics). Because babies are unfamiliar with our schedule of weekdays, a reasonable claim is that births occur on the different days with equal frequency. See the table that follows. Use a 0.01 significance level to test that claim. Can you provide an explanation for the result?

Problem 13BSC In Exercise, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Kentucky Derby The table below lists the frequency of wins for different post positions in the Kentucky Derby horse race (current as of this writing). A post position of 1 is closest to the inside rail, so that horse has the shortest distance to run. (Because the number of horses varies from year to year, only the first 10 post positions are included.) Use a 0.05 significance level to test the claim that the likelihood of winning is the same for the different post positions. Based on the result, should bettors consider the post position of a horse racing in the Kentucky Derby? Post Position 1 2 3 4 5 6 7 8 9 10 Wins 19 14 11 15 14 7 8 12 5 11

Problem 14BSC In Exercise, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Win 4 Lottery The author recorded all digits selected in New York’s Win 4 Lottery for two drawings held each day in a recent year. The frequencies of the digits from 0 through 9 are 280, 303, 331, 289, 285, 294, 283, 274, 297, and 284. Use a 0.05 significance level to test the claim of lottery officials that the digits are selected in a way that they are equally likely.

Problem 1BSC Notation In analyzing hits by V-l buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 576 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In applying Formula 5-9, identify the values of µ, x, and e. Also, briefly describe what each of those symbols represents.

Problem 2BSC Expected Value Exercise 1 includes results from a survey of 1005 randomly selected subjects. Consider the claim that when respondents select days of the week, the seven different days have the same chance of being selected. If that claim is true for the 1005 respondents, what is the expected value for each of the seven days? Identify the values of OandE for Sunday.

Problem 18BSC In Exercise, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. American Idol The contestants on the TV show American Idol try to win a singing contest. At one point, the Web site WhatNotToSing.com listed the actual numbers of eliminations for different orders of singing, and the expected number of eliminations was also listed. The results are in the table below. Use a 0.05 significance level to test the claim that the actual eliminations agree with the expected numbers. Does there appear to be support for the claim that the leadoff singers appear to be at a disadvantage? Singing Order 1 2 3 4 5 6 7 through 12 Eliminations 20 12 9 8 6 5 9 Expected Eliminations 12.9 12.9 9.9 7.9 6.4 5.5 13.5

Problem 19BSC Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. M&M Candies Mars, Inc. claims that its M&M plain candies are distributed with the following color percentages: 16% green, 20% orange, 14% yellow, 24% blue, 13% red, and 13% brown. Refer to Data Set 20 in Appendix B and use the sample data to test the claim that the color distribution is as claimed by Mars, Inc. Use a 0.05 significance level.

Problem 20BSC In Exercise, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Do World War II Bomb Hits Fit a Poisson Distribution? In analyzing hits by V-l buzz bombs in World War II, South London was subdivided into regions, each with an area of 0.25 km2. Shown below is a table of actual frequencies of hits and the frequencies expected with the Poisson distribution. (The Poisson distribution is described in Section 5-5.) Use the values listed and a 0.05 significance level to test the claim that the actual frequencies fit a Poisson distribution. Number of Bomb Hits 0 1 2 3 4 or more Actual Number of Regions 229 211 93 35 8 Expected Number of Regions (from Poisson Distribution) 227.5 211.4 97.9 30.5 8.7

Problem 15BSC In Exercise, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Police Calls The police department in Madison, Connecticut, released the following numbers of calls for the different days of the week during a recent February that had 28 days: Monday (114); Tuesday (152); Wednesday (160); Thursday (164); Friday (179); Saturday (196); Sunday (130). Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. Is there anything notable about the observed frequencies?

Problem 16BSC In Exercise, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Police Calls Repeat the preceding exercise using these observed frequencies for police calls received during the month of March: Monday (208); Tuesday (224); Wednesday (246); Thursday (173); Friday (210); Saturday (236); Sunday (154). What is a fundamental error with this analysis?

Problem 17BSC In Exercise, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. World Series Games The table below lists the numbers of games played in the baseball World Series as of this writing. That table also includes the expected proportions for the numbers of games in a World Series, assuming that in each series, both teams have about the same chance of winning. Use a 0.05 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions. Games Played 4 5 6 7 Actual World Series Contests 20 23 23 37 Expected Proportion 2/16 4/16 5/16 5/16