Essential Mathematics And Statistics For Science 2nd Edition Graham Currell, Dr. Antony Dowman - Solutions

15.33, carry out the analysis of variance calculations and discuss your findings.Can Color Region Red Yellow Blue East 45 50 54 South 49 51 58 Midwest 43 60 50 West 38 49 44
15.50 Refer to Exercise 15.33. Suppose that a second store for each region–can color combination is added to the study, yielding the results shown in the following table. Combining these results with those of Exercise
15.49 Refer to Exercise 15.31. Having carried out the experiment to compare mean yields per acre of four varieties of corn and three brands of fertilizer, an agricultural researcher suggested that there might be some interaction between variety and fertilizer. To check this possibility, another set
15.48 In some experiments with several observations per cell the analyst is prepared to assume that there is no interaction between groups and blocks. Any apparent interaction found is then attributed to random error.When such an assumption is made, the analysis is carried out in the usual way,
15.47 Random samples of two freshmen, two sophomores, two juniors, and two seniors each from four dormitories were asked to rate, on a scale of 1 (poor)to 10 (excellent), the quality of the dormitory environment for studying. The results are shown in the following table:Dormitory Year A B C D
15.46 A researcher randomly collected the annually income(in thousand) in a village for three different age range (less than 20 years old, 20 to 30 years old and above 30 years old) based on gender (male and female). She recorded her findings in the following table.Test Type Subject Type Male
15.45 Refer to Exercise 15.44. Twelve pairs were entered in the ice-dancing competition. Once again, there were 9 judges, and contestants were assessed in seven subevents.The sums of squares between groups (pairs of contestants) and between blocks (judges) were found to be SSG = 60.10 and SSB =
15.44 Suppose that scores given by judges to competitors in the ski-jumping events of the Winter Olympics were analyzed. For the men’s ski-jumping competition, suppose there were 22 contestants and 9 judges. Each judge in seven subevents assessed each contestant.The scores given can, thus, be
15.43 Consider an experiment with treatment factors A and B, with factor A having three levels and factor B having seven levels. The results of the experiment are summarized in the following analysis of variance table:Source of Variation Sum of Squares Degrees of Freedom Treatment A groups 21 2
15.42 The partial output for an experiment with treatment factors A and B are summarized in the following table.Source of Variation Sum of Squares Degrees of Freedom Degrees of Freedom Treatment A groups 740 370 Treatment B groups 1 30 Interaction 2 130 Error 178 24 Total 1208 Compute the F ratios
15.41 Consider an experiment with treatment factors A and B, with factor A having four levels and factor B having three levels. The results of the experiment are summarized in the following analysis of variance table.Compute the mean squares and test the null hypotheses of no effect from either
15.40 Suppose that, in the two-way analysis of variance setup with one observation per cell, there are just two groups. Show in this case that the F ratio for testing the equality of the group population means is precisely the square of the test-statistic discussed in Section 10.1 for testing
15.39 Three television pilots for potential situation-comedy series were shown to audiences in four regions of the country—the East, the South, the Midwest, and the West Coast. Based on audience reactions, a score (on a scale from 0 to 100) was obtained for each show. The sums of squares between
15.38 Four brands of fertilizer were evaluated. Each brand was applied to each six plots of land containing soils of different types. Percentage increases in corn yields were then measured for the 24 brand-soil-type combinations.The results obtained are summarized in the accompanying table.Source
15.37 Four real estate agents were asked to appraise the values of 10 houses in a particular neighborhood. The appraisals were expressed in thousands of dollars, with the results shown in the following table.Source of variation Sum of Squares Between agents 304 Between houses 1330 Error 2055
15.36 For the data of Exercise 15.34, obtain sample estimates for each term on the right-hand side of the equation used in the previous exercise for the text C–multiple choice combination.
15.35 We introduced for the two-way analysis of variance the population model Xij - m = Gi + bj + eij For the data of Exercise 15.33, obtain sample estimates for each term on the right-hand side of this equation for the east region–red can combination.
15.34 An instructor in an economics class is considering three different texts. He is also considering three types of examinations—multiple choice, essay, and a mix of multiple choice and essay questions. During the year he teaches nine sections of the course and randomly assigns a
15.33 A diet soda manufacturer wants to compare the effects on sales of three can colors—red, yellow, and blue. Four regions are selected for the test, and three stores are randomly chosen from each region, each to display one color of cans. The accompanying table shows sales (in tens of cans) at
15.32 A company has test-marketed three new types of soup in selected stores over a period of 1 year. The following table records sales achieved (in thousands of dollars) for each of the three soups in each quarter of the year.Soup Quarter A B C 1 47 57 65 2 63 63 76 3 79 67 54 4 52 50 49a. Prepare
15.31 In Greece, an agricultural experiment designed to assess differences in yields of olives for four different varieties (Athenolia, Black olives, Green olives, and Koroneiki), using six different fertilizers, produced the results (in kilos per acre) shown in the following table:Fertilizer
15.30 Four financial analysts were asked to predict earnings growth over the coming year for five oil companies.Their forecasts, as projected percentage increases in earnings, are given in the accompanying table.a. Prepare the two-way analysis of variance table.b. Test the null hypothesis that the
15.29 Consider a two-way analysis of variance with one observation per cell and randomized blocks with the following results:Source of Variation Sum of Squares Degrees of Freedom Between groups 131 3 Between blocks 287 6 Error 360 18 Total 778 27 Compute the mean squares and test the hypotheses
15.28 Consider a two-way analysis of variance with one observation per cell and randomized blocks with the following results:Source of Variation Sum of Squares Degrees of Freedom Between groups 380 6 Between blocks 232 5 Error 387 30 Total 989 41 Compute the mean squares and test the hypotheses
15.27 Consider a two-way analysis of variance with one observation per cell and randomized blocks with the following results:Source of Variation Sum of Squares Degrees of Freedom Between groups 3636 33 Between blocks 7575 66 Error 9999 1818 Total 210210 2727 Compute the mean squares and test the
15.26 A pharmacist randomly selected a group of 45 individuals with a similar level of back pain. The participants randomly distributed into three treatment groups in which using three different medicines (M1, M2 and M3)to treat their back pain for a period of one month. During the treatment, the
15.25 Based on the data of Exercise 15.11, perform the Kruskal-Wallis test of the null hypothesis of equal population mean scores on the CPA exam for students using no tutoring services and using services A and B.
15.24 Refer to Exercise 15.10. Without assuming normal population distributions, test the null hypothesis that the population mean times spent outside the classroom on teaching responsibilities are the same for assistant, associate, and full professors.
15.23 Based on the data of Exercise 15.9, use the Kruskal-Wallis method to test the null hypothesis of equality of growth predictions for population mean sales for the four regions.
15.22 Using the data of Exercise 15.8, carry out a nonparametric test of the null hypothesis of equality of population mean examination scores for freshmen, sophomores, and juniors.
15.21 For the data of Exercise 15.7, test the null hypothesis that the population mean operating costs per mile are the same for all three types of cards without assuming normal population distributions.
15.20 Using the data of Exercise 15.6, carry out a test of the null hypothesis of equality of the three population mean numbers of parts per shipment not conforming to standards without assuming normality of population distributions.
15.19 Using the data of Exercise 15.5, perform a Kruskal-Wallis test of the null hypothesis that the population mean test scores are the same for students assigned to the four teaching assistants.
15.18 For the data of Exercise 15.4, use the Kruskal-Wallis test of the null hypothesis that the population mean sales levels are identical for three box colors.
15.17 Consider a problem with four subgroups with the sum of ranks in each of the subgroups equal to 227, 151, 198, and 271 and with subgroup sizes equal to 5, 9, 15, and 12. Complete the Kruskal-Wallis test and test the null hypothesis to determine whether the subgroups have equal means at 1%
15.16 Consider a problem with three subgroups with the ranks in each subgroup shown as follows. Complete the Kruskal-Wallis test and test the null hypothesis to determine whether the subgroups have equal mean at 10% significance level.Sample 1 rankings: 7, 2.5, 9.5, 6, 4, 12, 19 Sample 2 rankings:
15.15 Consider a problem with three subgroups with different subgroup sizes of n1 = 8, n2 = 7, and n3 = 6.The sum of ranks in each of these subgroups equal to 131, 58, and 42. Complete the Kruskal-Wallis test and test the null hypothesis to determine whether the three
15.14 Use the model for the one-way analysis of variance for the data of Exercise 15.12.a. Estimate m.b. Estimate Gi for each of the three magazines.c. Estimate e13, the error term corresponding to the thrid observation (11.15) for True Confessions.
15.13 Independent random samples of 6 advertisements were taken from three different magazines: EuroScientist, Focus, and Science Reporter. The fog indices, measuring the reading difficulty of a written text, were taken and are given in the accompanying table. For the one-way analysis of variance
15.12 In the study of Example 15.1, independent random samples of six advertisements from True Confessions, People Weekly, and Newsweek were taken. The fog indices for these advertisements are given in the accompanying table. Test the null hypothesis that the population mean fog indices are the
15.5 An instructor at the University of Liège, Belgium, teaches a class of 28 students. At the beginning of the semester, each student is randomly assigned to one of four teaching assistants—Lucas, Emma, Arthur, or Sofia. The students are encouraged to meet with their assigned teaching assistant
15.4 A manufacturer of cereal is considering three alternative box colors—red, yellow, and blue. To check whether such a consideration has any effect on sales, 16 stores of approximately equal size are chosen. Red boxes are sent to 6 of these stores, yellow boxes to 5 others, and blue boxes to
15.3 Given the information in the following table, compute the F ratio and test the hypothesis that the group means are equal. The SST = 378.Group 1 Group 2 Group 3 Size, ni 18 12 13 Mean, xi 2.1 6.4 5.6 SSi 33 68 49 Application Exercises
15.2 Given the following analysis of variance table, compute mean squares for between groups and within groups. Compute the F ratio and test the hypothesis that the group means are equal.Source of Variation Sum of Squares Degrees of Freedom Between groups 879 3 Within groups 798 16 Total 1,677 19
15.1 Given the following analysis of variance table, compute mean squares for between groups and within groups. Compute the F ratio and test the hypothesis that the group means are equal.Source of Variation Sum of Squares Degrees of Freedom Between groups 1,728 4 Within groups 624 13 Total 2,352 17
15.5 Two-Way Analysis of Variance: More Than One Observation per Cell
15.4 Two-Way Analysis of Variance: One Observation per Cell, Randomized Blocks
15.3 The Kruskal-Wallis Test
15.2 One-Way Analysis of Variance Multiple Comparisons Between Subgroup Means Population Model for One-Way Analysis of Variance
15.1 Comparison of Several Population Means
14.79 Suppose that a random sample of 513 individuals were randomly sampled and information was collected about the method a subject used to make an airline reservation (last reservation for either business or pleasure) and the subject’s gender. Test the null hypothesis of no association between
14.78 Nine pairs of hypothetical profiles were constructed for corporate employees applying for admission to an executive MBA program. Within each pair, these profiles were identical, except that one candidate was male and the other female. For interviews for employment of these graduates,
14.77 A random sample of 10 corporate analysts was asked to rate, on a scale from 1 (very poor) to 10 (very high), the prospects for their own corporations and for the economy at large in the current year. The results obtained are shown in the accompanying table. Using the Wilcoxon signed rank
14.76 Of a random sample of 150 clerks, 65 estimated to spend no more than €10 per meal, 48 estimated to spend more than €10 per meal, and 37 estimated to spend exactly €10 per meal. Evaluate the strength of the sample evidence suggesting that, for all clerks, more estimated to spend less
14.75 The suggested queuing time in a fast-food restaurant is 10 minutes. Of a random sample of 50 customers, 8 expected to be in queue for more than 10 minutes, 27 expected to be in queue for less than 10 minutes, and the remaining expected to be in queue for exactly 10 minutes. Do these data
14.74 In a random sample of 15 people participating in a weight loss program, 10 believe they will experience significant weight loss, 3 think their weight will remain the same, and the remaining think their weight might increase. What conclusions can be drawn from this information?
14.73 The qualifying percentage for a midterm test at a particular school is 50%. After the test, out of 20 sampled students, 2 students believed that they would fail the test, 15 believed that they would score more than 50%, and the remaining believed that they would score the pass mark. What can
14.72 What is nonparametric test? State two reasons for using such tests.
14.71 In Example 14.2 a random sample of 200 people was asked to indicate candy bar preference. Suppose that we also gathered demographic data such as whether the participants were male or female. From the 50 who preferred Mr. Goodbar, it was found that 20% were female; from the 93 who preferred
14.70 Two years ago the manager of a local supermarket that sells three national brands (brands A, B, and C) and one store brand (brand D) of orange juice found that brands A and C were equally preferred, 33% preferred brand B, and 27% preferred the store brand, D. Now, the manager thinks that
14.69 Downsizing is one method companies may use in an attempt to reduce costs. Suppose that the following contingency table shows the number of layoffs in three manufacturing plants during the last 4 months and the length of service (in months) by those employees that were laid off. Is there any
14.68 Many easy-weight-loss products are just gimmicks that attract people with the hope of a fast way to a slimmer body. Suppose that a random sample of residents in one community was asked if they had ever tried a quickweight-loss product. They were also asked if they thought that there should be
14.67 Should large retailers offer banking services? Small community banks may be concerned about their future if more retailers enter the world of banking.Suppose that a market research company conducted a national survey for one retailer that is considering offering banking services to its
14.66 Suppose that a random sample of businesses that relocated in Florida within the last 3 years is surveyed.Do the data in the following contingency table show any relationship between the primary reason for the company’s move to Florida and the industry type?Industry Type Primary Reason
14.65 A random sample of companies was surveyed and asked to indicate if they had used an Internet career service site to search for prospective employees. The companies were also asked questions concerning the posting fee for use of such a site. Is there a relationship between use of such a site
14.64 Suppose the operations manager at a Honda service center conducts a survey on the level of satisfaction for the quality of workmanship based on the customer’s gender. A random sample of 200 customers who recently availed of Honda’s services were selected and the manager summarized the
14.63 A travel agent randomly sampled individuals in her target market and asked, Did you use a travel agent to book your last airline flight? By cross-referencing the answers to this question with the responses to the rest of the questionnaire, the agent obtained data such as that in the following
14.62 The Speedi-Flex delivery service is conducting a study of its delivery operations. As part of this study it collected data on package type by originating source for one day’s operation for one district office in the Southeast.These data are shown in the table. The major originating sources
14.61 Aurica Sabou has been working on a plan for new store locations as part of her regional expansion. In the city proposed for expansion there are three possible locations: north, east, and west. From past experience she knows that the three major profit centers in her stores are tools, lumber,
14.60 The gear-cutting department in a large manufacturing firm produces high-quality gears. The number produced per hour by a single machinist is 1, 2, or 3, as shown in the table. Company management is interested in determining the effect of worker experience on the number of units produced per
14.59 A manufacturer of household appliances wanted to determine if there was a relationship between family size and the size of washing machines purchased by customers. The manufacturer was preparing guidelines for sales personnel and wanted to know if the sales staff should make specific
14.58 Sally Smith is a long-time political campaign manager from Chicago. In the primary election there are four candidates. She wishes to determine if voter preference is different over the four major districts. A random sample survey results in the candidate preference frequencies by district and
14.57 A doctor is analyzing the infection rate of a particular kind of disease in Asia and Europe. Perform a chi-square test to determine if there is a different probability of infection between the two regions at the 5%significance level. Include in your answer the expected cell values under the
14.56 An officer of a jobseekers’ website in analyzing the employment trends of university students for three different majors of Marketing, Finance, and Economic. The officer would like to know whether the students will be employed before or after their graduation from the university. A set of
14.55 An analyst conducted a survey and found that the respondents can be categorized into three broad categories professionals, speeders, and posers by three age groups of Group 1: 21 to 30 years, Group 2: 31 to 40 years, and Group 3: 41 to 50 years. The categorizations are as follows:Group 1
14.54 A researcher is analyzing the marital status of the employees(Single, Married, Divorced, and Widowed)that are working in the three different departments(Marketing, Purchasing, and Finance). The researcher collected data from a few companies that consists of these departments and listed the
14.51 On October 18, 2018, the fuel prices in Portugal went down after having risen to a five-year high the previous week. The Fuel Prices data file contains the price per liter of gasoline and of diesel, in Portugal, recorded every Monday for two consecutive years. Test the two data sets stored in
14.50 The Tesla Stock Prices data file shows the closing price of Tesla’s stocks in the first day of each month for a period of 12 consecutive months. Test for randomness using the runs test.
14.49 The data file Brent Oil Price contains the monthly oil prices for Brent crude oil, covering the years 2012 to 2020.a. Plot the time series of the crude oil price for the year 2012. Perform a runs test to test this series for randomness using these 12 observations.b. Now plot the time series
14.48 The data file Euribor 12 Months shows an average annual interest rate of certain European banks over 18 consecutive years. Use the runs test to test this series for randomness.
14.47 Use the runs test to test for randomness the number of miles traveled per week for a car in three months.Week Distance (miles) Week Distance (miles)1 253 7 450 2 452 8 678 3 308 9 529 4 414 10 120 5 386 11 379 6 197 12 298 Application Exercises
14.46 A time series contains 50 observations. What is the probability that the number of runs isa. no more than 13?b. fewer than 15?c. greater than 34?
14.45 A time series contains 10 and 16 observations. Determine the probability of the number of runs for the following.a. n = 10, P(R 7 5)b. n = 16, P(4 6 R 6 7)
14.44 Given a sequence 0.16, 0.27, 0.58, 0.63, 0.45, 0.21, 0.72, 0.87, 0.27, 0.15, 0.92, 0.85.a. How many runs for the sequence in total?b. What is the probability the number of run is less than 6?
14.43 The accompanying table shows, for a random sample of 20 long-term-growth mutual funds, percentage return over a period of 12 months and total assets (in millions of pounds).Return Assets Return Assets Return Assets 26.4 300 17.5 421 11.5 75 23.4 70 16.7 99 14.9 610 28.7 3004 18.8 756 8.4 264
14.42 Petron has formulated a new chemical to be added in their petrol. To determine the effectiveness of the new formulated chemical, they recorded the amount of chemical had been added in the petrol (in liter) and the distances traveled (in km) by 10 automobiles in the follow table:Chemical 1.8
14.41 An investment company is going to make decision on which mobile app they are to invest from two different mobile application developments. The company accesses the ability on the two apps by monitoring the daily number of users downloading the apps for 20 days. The company ranked the daily
14.40 JW Intelligent proposed a new moisturizing cream that includes herbal essence as a key ingredient. A random sample of 15 women were selected for a pilot trial of the new product. The women used the product and evaluated its effectiveness using a skin test machine to see whether their skin was
14.39 A newsletter rates mutual funds. Independent random samples of 12 funds with the highest rating and 12 funds with the lowest rating were chosen. The following figures are percentage rates of return achieved by these 24 funds in the next year.Highest rated 8.8 10.8 8.4 9.0 5.4 5.0 6.8 11.2 8.2
14.38 Two different drugs for deliberating headaches are being analyzed for effectiveness. The analyst uses a random selection of 15 patients to test the first drug and 13 patients for the second drug. For each patient, the analyst records the number of hours of relief from headache as follows:Drug
14.37 GreenEnergy, a manufacturing company in Finland, wants to know the consumer satisfaction level for two products—A and B. A random sample of 12 consumers are invited to participate in a survey. The participants are divided into two equal groups and are asked to rate the satisfaction they
14.36 The human resources department of Alfa Laval, Sweden, is analyzing on the number of years of work experience of employees in the marketing and finance departments. For a random sample of 12 marketing staff members, the number of years of work experience were as follows:4 15 6 8 2 3 5 7 13 14
14.34 A study compared firms with and without an audit committee. For samples of firms of each type, the extent of directors’ ownership was measured using the number of shares owned by the board as a proportion of the total number of shares issued. In the sample, directors’ ownership was,
14.33 A random sample of 80 owners of videocassette recorders was taken. Each sample member was asked to assess the amounts of time in a month spent watching material he or she had recorded from television broadcasts and watching purchased or rented commercially recorded tapes. The 80 differences
14.32 A consultant is interested in the impact of the introduction of a total-quality management program on job satisfaction of employees. A random sample of 30 employees was asked to assess level of satisfaction on a scale from 1 (very dissatisfied) to 10 (very satisfied)three months before the
14.31 A random sample of 40 business majors who had just completed introductory courses in both statistics and accounting was asked to rate each class in terms of level of interest on a scale of 1 (very uninteresting)to 10 (very interesting).The 40 differences in the pairs of ratings were
14.30 Sixteen freshmen on a college campus were grouped into eight pairs in such a way that the two members of any pair were as similar as possible in academic backgrounds—as measured by high school class rank and achievement test scores—and also in social backgrounds.The major difference
14.29 A random sample of 10 students was asked to rate, in a blind taste test, the quality of two brands of ice cream, one reduced-sugar and one regular ice cream. Ratings were based on a scale of 1 (poor) to 10(excellent).The accompanying table gives the results.Use the Wilcoxon test to test, at
14.28 A random sample of 160 shoppers was asked to compare two new energy bars. From the sample, 91 shoppers preferred energy bar A, 61 preferred energy bar B, and 8 expressed no preference. Use the normal approximation to determine, at the 1% level, if there is an overall preference for either
14.27 A random sample of 60 professional economists was asked to predict whether next year’s inflation rate would be higher than, lower than, or about the same as that in the current year. The results are shown in the following table. Test the null hypothesis that the profession is evenly divided

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Essential Mathematics And Statistics For Science 2nd Edition Graham Currell, Dr. Antony Dowman - Solutions

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