For each of the following situations give the degrees of freedom and an appropriate bound on the Pvalue (give the exact value if you have software available) for the x2 statistic for testing the null hypothesis of no association between the row and column variables. (a) A 2 by 2 table with x2 = 1.08. df: P-value = (b) A 4 by 4 table with 2? df: Pvalue : (c) A 2 by 8 table with x2 df: Pvalue = (d) A 5 by 3 table withxz 212.15, df: Pavalue = How are returns on common stocks in overseas markets related to returns in U.S. markets? Measure U.S. returns by the annual rate of return on the Standard & Poor's SODStock Index and overseas returns by the annual rate of return on the Morgan Stanley EAFE (Europe, Australasia, Far East) index. Both are recorded in percents. Regress the EAFE returns on the SELF 500 returns for the 30 years 1971 to 2000. Here is part of the Minitab output for this regression. The regression equation is EAFE : 4.76 + 0.663 5&P. "Analysis of Variance" Source DF 55 MS F P Regression 1 3445.9 3445.9 9.5 0.005 Residual Error Total 29 13598.3 What are the values of the regression standard error 3 and the squared correlation r 2 ? (Enter your answers to four decimal places.) A recent study of undergraduates looked at gender differences in dieting trends. There were 189 women and 101 men who participated in the survey. The table below summarizes whether a student tried a low-fat diet or not by gender: Gender Tried lowfat diet Women Men Yes 40 8 No (a) Fill in the missing cells of the table. Gender Tried lowfat diet Women Yes 40 No (b) Summarize the data numerically. What percent of each gender has tried lowfat diets? (Round your answers to two decimal places.) women % men % (c) Test that there is no association between gender and the likelihood of trying a low7fat diet. (Round yourx2 to three decimal places, and round your Pivalue to four decimal places.) X2: df Here are the row and column totals for a twoway table with two rows and two columns. a (3200 c dZOO 200 200 400 Find two different sets of counts a, b, C, and o'for the body of the table. This demonstrates that the relationship between two variables cannot be obtained solely from the two marginal distributions of the variables. (Stalt with the given value of a.) a b C o' 30 A research project based on a study of older adults examined the relationship between physical activity and pet ownership. The data collected included information concerning pet owner characteristics and the type of pet owned. Here are data giving the relationship between pet ownership status and gender. Pet ownership status Gender Nonpet owners Dog owners Cat owners Female 1027 158 86 Male 9 14 170 8 1 Analyze the data. (Round youny2 to three decimal places and your Pivalue to four decimal places.) 12 of Pivalue Summarize your results and conclusions. '1'.) The relationship between gender and pet ownership is signicant. 0 The relationship between gender and pet ownership is not significant. The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both. The data data5.dat gives the scores of 60 students who did this. How can we relate the two tests? (a) Plot the data with SAT on the X axis and ACT on the y axis. Describe the overall pattern and any unusual observations. (b) Find the leastsquares regression line and draw it on your plot. Give the results of the significance test for the slope. (Round your regression slope and intercept to three decimal places, your test statistic to two decimal places, and your Pvalue to four decimal places.) ACT = (SAT) t: p: (c) What is the correlation between the two tests? (Round your answer to three decimal places.) The Leaning Tower of Pisa is an architectural wonder. Engineers concerned about the tower's stability have done extensive studies of its increasing tilt. Measurements of the lean of the tower over time provide much useful information. The following table gives measurements for the years 1975 to 1987. The variable "lean" represents the difference between where a point on the tower would be if the tower were straight and where it actually is. The data are coded as tenths of a millimeter in excess of 2.9 meters, so that the 1975 lean, which was 2.9642 meters, appears in the table as 642. Only the last two digits of the year were entered into the computer. (data103.dat) (a) Plot the data. Consider whether or not the trend in lean over time appears to be linear. (Do this on paper. Your instructor may ask you to turn in this graph.) (b) What is the equation of the leastrsquares line? (Round your answers to two decimal places.) y : + x What percent of the variation in lean is explained by this line? (Round your answer to one decimal place.) 0/0 (c) Give a 99% confidence interval for the average rate of change (tenths of a millimeter per year) of the lean. (Round your answers to two decimal places.) ( . How are returns on common stocks in overseas markets related to returns in U.S. markets? Measure U.S. returns by the annual rate of return on the Standard & Poor's BOO-Stock Index and overseas returns by the annual rate of return on the Morgan Stanley EAFE (Europe, Australasia, Far East) index. Both are recorded in percents. Regress the EAFE returns on the S&P 500 returns for the 27 years 1973 to 2000. Here is part of the output for this regression. The regression equation is EAFE = 5.62 + 0.684 5&P. (Round your answer for F to two decimal places and your answers for 55 and MS to one decimal place.) for Analysis of Variance Source DF 55 MS F Regression 1 1424.9 1424.9 Residual Error Total 26 13991.6 Complete the analysis of variance table by filling in the missing boxes. (Round your answer for s to two decimal places and your answer for r2 to three decimal places.) What is s? What is r2? obs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 sat 950 719 648 905 1263 995 1184 672 882 1082 875 951 1045 679 794 722 1227 746 1145 716 1208 950 890 761 969 647 857 991 798 666 761 660 631 1121 978 883 807 895 1184 869 582 1070 642 937 1086 1013 713 1144 990 878 870 1090 1095 781 1046 675 act 17 19 17 22 29 25 25 13 17 21 17 20 22 19 18 16 28 14 27 19 28 21 23 17 17 11 21 21 17 14 19 20 16 26 26 18 18 19 23 17 14 20 16 23 27 26 19 25 24 16 26 27 26 19 21 13 57 58 59 60 1257 1099 620 714 25 27 10 13 obs 1 2 3 4 5 6 7 8 9 10 11 12 13 year 75 76 77 78 79 80 81 82 83 84 85 86 87 lean 636 646 657 665 684 687 696 709 718 729 737 755 762