Читать книгу Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP - Bhisham C. Gupta, Irwin Guttman - Страница 109

1 During a flu season, it is common that many workers cannot come to work because either they themselves are sick or they have to take care of their sick children. The following data give the number of employees of a company who did not come to work on 18 days during a flu season:7, 5, 10, 12, 6, 7, 8 10, 3, 16, 10, 9, 8, 10, 9, 8, 7, 6Construct a dot plot for these data. Comment on what you learn from the dot plot.

2 A saving and loan institution wants to find how many of their customers default their loan payments. The following data give the number of customers who did not make their payment on time at least once over the past 12 months:15, 20, 18, 16, 3, 19, 14, 17, 17, 16, 30, 15Construct a dot plot for these data. Comment on any patterns you observe in these data.

3 The following data give the number of machines in a shoe factory that had breakdowns during the past 21 shifts:3, 2, 1, 0, 2, 1, 4, 2, 0, 1, 2, 3, 1, 0, 4, 2, 1, 10, 2, 1, 2Construct a dot plot for these data. If you were the maintenance engineer, what would you learn from these data?

4 The following data classify a group of students who are attending a seminar on environmental issues by their class standing:Class standingFrequencyFreshmen16Sophomore18Junior20Senior15Graduate30Construct a bar chart for these data.Construct a pie chart for these data.

5 Suppose there are two fund‐raising concerts at a university. The following data give the number of students by their class standing who attended one or the other of the concerts:Class standingFrequency‐1Frequency‐1Freshmen1640Sophomore1830Junior2021Senior1520Graduate3015Construct a side‐by‐side bar chart for each of the concert and compare the two sets of data.Construct pie charts for each of the concerts. Do you think you can get the same information by using the two pie charts, as by using the side‐by‐side bar charts?

6 Refer to the data in Problem 15 of Section 2.4.Construct a frequency histogram for these data.Construct a relative‐frequency histogram for these data.

7 Suppose that in a midwestern state, a legislator running for governor proposes the following state budget (in millions of dollars) for the following year:Education900Medicaid400Other social programs500Road and bridges350Agriculture400Others250Use JMP, MINITAB, or R to do the following:Construct a bar chart for these data.Construct a pie chart for these data.Determine what percentage of the budget is used for all social programs.

8 The following data give the number of defective parts produced in 21 consecutive shifts of 1 wk15141816171327141510301481415171513141620Prepare a line graph of these data.Check if any peaks or dips appear in the line graph.As a quality manager of the company, what would you conclude from this line graph, and what will be your line of action to reduce the number of defective parts produced?

9 Consider the following stem‐and‐leaf diagram:StemLeaf32 5 740 3 6 8 951 2 2 7 863 5 6 6 9 971 5 5 7 8Reproduce the data set represented by the diagram.

10 The following data give the number of employees from 19 different sectors of a large company who were absent for at least two days from a certain training program:75101267810316109810769112Construct a dot plot for these data and comment on what you observe in these data.

11 To improve the quality of a crucial part used in fighter jets, a quality control engineer is interested in finding the type of defects usually found in that part. He labels these defects as A, B, C, D, and E based on severity of the defect. The following data show the type of defects found in the defective parts:BDABCDBEBEDBCBECDBEDBCBDBCDBABCBDEBEBECBDEBCEBEBCBDBPrepare a bar chart for these data, and comment on the types of defects encountered in the parts under study.

12 The following data give the salaries (in thousands of dollars) of 62 randomly selected engineers from different manufacturing companies located in different regions of the United States:654585689895586264545758851204556150140123655566768845506066554648985666185565577596714516667586869878992858877697686815414515419020585Prepare a box whisker plot for these data.Do these data contain any mild or extreme outliers?

13 The following data give the number of cars owned by 50 randomly selected families in a metropolitan area:35212431234232531243212145123234231232423213124232Construct a single‐valued frequency distribution table for these data.Compute the columns of relative frequencies and percentages.Construct a bar chart for these data.What percentage of the families own at least 3 cars?What percentage of the families own at most 2 cars?

14 The following data give the total cholesterol levels (mg/100 mL) of 100 US males between 35 to 65 years of age:177196150167175162195200167170179172176179177153177189185167151177191177175151173199167197188163174151183174177200182195160151177154150180170172153152194197192155174159193182175169180200194182188152196198171176200180161182188168165168160175193159183166198184172180195199156158152174151173166183194156Construct a frequency distribution table with classes [150, 160), [160, 170), What percentage of US males between 35 to 65 years of age do you estimate have cholesterol levels higher than 200 mg/100 mL?What percentage of US males between 35 to 65 years of age do you estimate have cholesterol levels less than 180 mg/100 mL?

15 We know that from a grouped data set we cannot retrieve the original data. Generate a new (hypothetical) data set from the frequency distribution table that you prepared in Problem 14. Reconstruct a frequency distribution table for the new set and comment on whether the two frequency tables should be different or not.

16 A group of dental professionals collected some data on dental health and concluded that 10% of the Americans have zero or one cavity, 50% have two or three cavities, 30% have four cavities, and rest of the 10% have five or more cavities. Construct a pie chart that describes the dental health of the American population.

17 Find the mean, median, and mode for the following sample data on credit hours for which students are registered in a given semester:7118127614171513

18 The following data give hourly wages of 20 workers randomly selected from a chipmaker company:1612181523292120212518272125221624262126Determine the mean, median, and mode for these data. Comment on whether these data are symmetric or skewed.

19 The following data give daily sales (in gallons) of gasoline at a gas station during April:414450380360470400411465390384398412416454459395430439449453464450380398410399416426430425Find the mean, median, and mode for these data. Comment on whether these data are symmetric, left skewed, or right skewed.Find the range, variance, standard deviation, and the coefficient of variation for these data.

20 The owner of the gas station of Problem 19 also owns another gas station. He decided to collect similar data for the second gas station during the same period. These data are given below.570590600585567570575580577583589585595570574576581583595591585583580597599600577573574579Find the range, variance, standard deviation, and coefficient of variation for these data.Compare the standard deviations for the two data sets.Do you think it will be more prudent to compare the coefficients of variation rather than the two standard deviations? Why or why not?Sometimes the observations in a given data set are too large numerically to compute the standard deviation easily. However, if these observations are small, particularly when we are using paper, pen, and a small calculator, then there is little problem in computing the standard deviation. If observations are large, all one has to do is to subtract a constant from each of the data points and then find the standard deviation for the new data. The standard deviation of the new data, usually called the coded data, is exactly the same as that of the original data. Thus, for example, in Problem 20, one can subtract 567 (the smallest data point) from each data point and then find the standard deviation of the set of the coded data. Try it.

21 Collect the closing price of two stocks over a period of 10 sessions. Calculate the coefficients of variation for the two data sets and then check which stock is more risky.

22 The following data give the number of physicians who work in a hospital and are classified according to their age:Age[35–40)[40–45)[45–50)[50–55)[55–60)[60–65]Frequency607568729055Find the mean and the standard deviation for this set of grouped data.

23 Prepare a frequency table for the data in Problem 9 of Section 2.4. Find the mean and the variance for the grouped and the ungrouped data. Then compare the values of the mean and variance of the grouped and the ungrouped data.

24 The following data give lengths (in mm) of a type of rods used in car engines.128118120124135130128116122120118125127123126124120132131119117124129131133115121122127127134128132135125120121126124123Determine the quartiles () for this data.Find the IQR for these data.Determine the value of the 70th percentile for these data.What percentage of the data falls between and ?

25 Compute , , and for the data in Problem 24. Then,Find the number of data points that fall in the intervals , , and Verify whether the empirical rule holds for these data.

26 A car manufacturer wants to achieve 35 miles/gal on a particular model. The following data give the gas mileage (rounded to the nearest mile) on 40 randomly selected brand‐new cars of that model. Each car uses regular unleaded gasoline:34333632333435373233323134373233333634 3135363533323234353430343735323134323332 33Find the mean and the standard deviation for these data.Check whether the empirical rule holds for these data.

27 Refer to the data in Problem 26. Determine the following:The values of the three quartiles , and .The IQR for these data.Construct a box‐plot for these data and verify if the data contains any outliers.

28 The following data give the test scores of 57 students in an introductory statistics class:687892808779748586889197717281866040767720998079898787808395929887869596757679808581777684828356686991886975745961Find the values of three quartiles , and .Find the IQR for these data.Construct the box plot for these data and check whether the data is skewed.Do these data contain any outliers?

29 The following data give the overtime wages (in dollars) earned on a particular day by a group of 40 randomly selected employees of a large manufacturing company:30354550253036384240463630352446425040403534343028323026283640424038383645403642Find the IQR for these data.Count what percentage of the data falling between the first and the third quartiles.Do you think the result in part (b) agrees with your expectations?

30 The following data give the time (in minutes) taken by 20 students to complete a class test:5563705862715070606559626671587075706568Find the mean, median, and mode for these data.Use values of the mean, median, and mode to comment on the shape of the frequency distribution of these data.

31 The following data give the yearly suggested budget (in dollars) for undergraduate books by 20 randomly selected schools from the whole United States:690650800750675725700690650900850825910780860780850870750875Find the mean and the standard deviation for these data.What percentage of schools has their budget between and ?

32 A data set has a mean of 120 and a standard deviation of 10. Using the empirical rule, find what percentage of data values fall:Between 110 and 130.Between 100 and 140.Between 90 and 150.

33 Suppose that the manager of a pulp and paper company is interested in investigating how many trees are cut daily by one of its contractors. After some investigation, the manager finds that the number of trees cut daily by that contractor forms a bell shaped distribution with mean 90 and standard deviation 8. Using the empirical rule, determine the percentage of the days he cutsBetween 82 and 98 trees.Between 66 and 114 trees.More than 106 trees.Less than 74 trees.

34 The following sample data give the number of pizzas sold by a Pizza Hut over a period of 15 days:754580908590928695959086949978Prepare a box plot for these data and comment on the shape of this data set.Find the mean, median, and standard deviation of these data.

35 The following sample data give the GRE scores (actual score—2000) of 20 students who have recently applied for admission to the graduate program in an engineering school of a top‐rated US university:268320290310300270250268330290240269295325316320299286269250Find the sample mean and the sample standard deviation .Determine the percentage of the data that falls in the interval .Determine the range of the middle 50% of the observations.

36 Assume that the data in Problem 35 come from a population having a bell‐shaped probability distribution. Then, using the empirical rule, determine how many data values one would expect to fall within the intervals and . Compare your results with the actual number of data values that fall in these intervals. Also, using technology, verify the assumption that the observations come from a population having a bell shaped probability distribution.

37 The following data give the number of defective parts received in the last 15 shipments at a manufacturing plant:8101211139151410161812141613Find the mean of these data.Find the standard deviation of these data.Find the coefficient of variation for these data.

38 The owner of the facility in Problem 37 has another plant where the shipments received are much larger than at the first plant. The quality engineer at this facility also decides to collect the data on defectives received in each shipment. The last 15 shipments provided the following data:213038475839351559604347393041Find the mean and the standard deviation of these data.Find the coefficient of variation of these data, compare it with the one obtained in Problem 37, and comment on which facility receives more stable shipments.

39 Prepare box plots for the data in Problems 37 and 38. Comment on the shape of the distribution of these two data sets.

40 The following data give the test scores of 40 students in a statistics class:68789280877974858688919771728186604076772099807989878780839592988786959676757980Find the sample mean and the sample standard deviation S for these data.Prepare a frequency distribution table for these data.Use the grouped data in part (b) to determine the grouped mean and the grouped standard deviation .Compare the values of and with the values of and the standard deviation . Notice that the grouped mean and grouped standard deviations are only the approximate values of the actual mean and standard deviations of the original (i.e., ungrouped) sample.

41 The following two data sets give the number of defective ball bearings found in 20 boxes randomly selected from two shipments:Shipment I6065797167687356596366597277796971706055Shipment II4555565059604838424137575549433945515355Find the quartiles for each of these two sets.Prepare the box plots for each of the two data sets and display them side by side on one sheet of graph paper.Use part (b) to compare the two shipments. Which shipment in your opinion is of better quality?

42 The following data give the number of flights that left late at a large airport over the past 30 days:5059633012055494743514751576258503953504543465259483651334232Prepare a complete frequency distribution table for these data.Prepare a box plot for these data to comment on the shape of the distribution of these data. Does the set contain any outliers?Find the mean and the standard deviation for these data.

43 The following data gives the inflation rate and interest rates in the United States over 10 consecutive periods. Determine the correlation coefficient between the inflation rate and the interest rates in the United States. Interpret the value of the correlation coefficient you determined.Period12345678910Inflation rate2.342.542.222.671.983.222.512.572.752.67Interest rate4.554.654.754.824.464.854.354.254.554.35

44 The following data gives the heights (in.) and weights (lb) of eight individuals. Determine the correlation coefficient between the heights and weights. Interpret the value of the correlation coefficient you have determined.Individuals12345678Heights 77 72 73 76 72 73 77 72Weights156172195181158164164191

45 It is generally believed that students' performance on a test is related to number of hours of sleep they have the night before the test. To verify this belief, 12 students were asked how many hours they slept on the night before the test. The following data shows the number of hours of sleep on the night before the test and the test scores of each of the 12 students. Determine the correlation coefficient between the hours of sleep and test scores. Interpret the value of the correlation coefficient you have determined.Student123456789101112Hours of sleep 8 8 6 5 8 8 7 6 7 5 4 6Test scores898488858797939087908672