Family transportation costs are usually higher than most people believe because costs include car payments, insurance, fuel costs, repairs, parking, and Situation: those public transportation. We asked twenty randomly selected families in four major cities to use their records to estimate a monthly figure for transportation costs. Action: Use the following data and ANOVA to test whether there is a significant difference in monthly transportation costs for families living in these cities. Use significance level of 5%. Discuss the business implications of the findings. Use significance level of 5%. Discuss the business implications of the findings. Our P-Value is less than our significance level of 5%. Therefore we will reject the null hypothesis and conclude that at the very least one of the means of transportation cost is different. This has business implications for car dealerships, parking lots, gas stations, and insurance companies. Many people might chose to forgo these costs and take public transportation or ride sharing. Data: Atlanta New York Los Angeles Chicago $850 $680 $450 $725 $1,050 $900 $740 $650 $750 $500 $1,150 $875 $800 $875 $375 $700 $980 $800 $750 $800 Count Sum 3955 2750 4880 3815 Anova: Single Factor SUMMARY Groups Atlanta New York Los Angeles Chicago 5 5 5 5 ANOVA Source of Variation Between Groups Within Groups SS 456630 220770 Total 677400 df 3 16 19 Average Variance 791 6155 550 24062.5 976 18130 763 6845 MS F P-value F crit 152210 11.03121 0.000358 3.238872 13798.125 Situation: The general manager of a major league baseball team believes that the distribution of the tickets sold varies based on the age of the ticket purchaser. Using the chi-square goodness of fit test and either Excel or Minitab, determine age varies among ticket purchasers. Use a .01 level of significance and Action: whether the following observed frequencies of ticket purchasers. Use the hypothesis testing procedure appropriate for this problem to help you make a decision. Data: Age of Purchaser Frequency Under 20 20 to under 30 30 to under 40 40 to under 50 50 to under 60 Over 60 16 44 61 56 35 19 Groups of 30-year-olds were interviewed to determine whether the Situation: type of music most listened to by people in their age category is independent of the geographic location of their residence. Use the chi-square test of independence, a = .01, and the following contingency table to determine whether music preference is Action: independent of geographic location. Show the steps of hypothesis testing relevant to this problem and its type of test statistic and make a decision. Explain what that decision means. Data: Northeast South West Totals: Rock 140 134 154 R&B 32 41 27 428 Country 5 52 8 100 Classical 18 8 13 65 Totals: 195 235 202 39 632 Expected: Rock R&B Country Classical Totals: Northeast 132.0569620253 30.85443038 20.0553797468 12.0332278481 South 159.1455696203 37.183544304 24.1693037975 14.5015822785 West 136.7974683544 31.962025316 20.7753164557 12.4651898734 Totals: 428 100 65 39 195 235 202 632 Answer: P Chi Squared 4.479776E-012 0.4777624087 0.0425329438 3.973090002 0.3917145166 2.1632497924 0.7703421481 6.6141022032 1.2045896086 64.9197768446 11.30192807 2.958671635 32.046750606 2.91489379 7.8558952828 0.022945649 51.204573959 5.896511074 Situation: The conference Board produces a Consumer Confidence Index (CCI) that reflects people's feelings about general business conditions, employment opportunities, and their own income prospects. Some researchers may feel that consumer confidence is a function of the median household income. Perform a correlation and regression analysis to predict CCI using median household income. Discuss the following: Action: Data: CCI 116.8 91.5 68.5 61.6 65.9 90.6 100 104.6 125.4 Median House Hold Income ($1,000) 37415 36770 35501 35047 34700 34942 35887 36306 37005 SUMMARY OUTPUT Regression Statistics Multiple R 0.8294375468 R Square 0.6879666441 Adjusted R Square 0.6433904504 Standard Error 13.5389348436 Observations 9 ANOVA df Regression Residual Total Intercept X Variable 1 SS MS 1 2829.00292532 2829.003 7 1283.1192969 183.3028 8 4112.12222222 F Significance F 15.4335 0.00568626 Coefficients Standard Error t Stat P-value Lower 95% -599.3673817577 175.955626322 -3.406355 0.011344 -1015.43632 0.0192204122 0.0048924962 3.928549 0.005686 0.007651497 a. Scatter Diagram Median House Hold Income ($1,000) 38000 37500 37000 36500 36000 35500 35000 34500 34000 33500 33000 50 60 70 b. R, R2 and 1-R2 Multiple R R Square Adjusted R Square 80 90 100 110 120 0.8294375468 0.6879666441 0.6433904504 c. The regression equation d. Standard error of estimate 13.5389348436 e. The test of hypothesis with the 5-step process. Use a .05 level of significance. Does median household income appear to be good predictor of the CCI? Why or why not? 130 Upper 95%Lower 95.0% Upper 95.0% -183.2984 -1015.436 -183.2984 0.030789 0.007651 0.030789 Situation: Action: The U.S. Bureau of Mines produces data on the price of Minerals. The data below displays the average prices per year for several minerals over a decade. Use the data and multiple regression to produce a model to predict the average price of gold from other v Gold ($per oz.) 161.1 308.0 613.0 460.0 376.0 424.0 361.0 318.0 368.0 448.0 438.0 382.6 Copper (cents per lb.) 64.2 93.3 101.3 84.2 72.8 76.5 66.8 67.0 66.1 82.5 120.5 130.9 Silver Aluminum ($ per oz.) (cents per lb.) 4.4 39.8 11.1 61.0 20.6 71.6 10.5 76.0 8.0 76.0 11.4 77.8 8.1 81.0 6.1 81.0 5.5 81.0 7.0 72.3 6.5 110.1 5.5 87.8 SUMMARY OUTPUT Regression Statistics Multiple R 0.9058283595 R Square 0.8205250169 Adjusted R Squa 0.7532218983 Standard Error 53.4385927564 Observations 12 ANOVA df Regression Residual Total Intercept X Variable 1 X Variable 2 X Variable 3 SS MS F Significance F 3 104445.1 34815.0212 12.19149 0.002363 8 22845.47 2855.683196 11 127290.5 Coefficients Standard Error t Stat -51.5748865879 87.82444 -0.58724983 0.0696331122 0.87526 0.079557069 18.7834899228 3.803837 4.938037403 3.5378159359 1.167806 3.029456393 P-value Lower 95%Upper 95%Lower 95.0% 0.573232 -254.0984 150.9486 -254.0984 0.938544 -1.94872 2.087986 -1.94872 0.001138 10.01183 27.55515 10.01183 0.016323 0.844852 6.23078 0.844852 b. R, R2 and 1-R2, adjusted R2 R 0.9058283595 R2 0.8205250169 R2 Adjusted 0.7532218983 c. Standard error of estimate 53.4385927564 d. Report the t's for each value and the corresponding p-values Gold -0.5872498253 Copper 0.079557069 Silver 4.9380374026 Aluminum 3.0294563934 e. Overall test of hypothesis and decision f. Use a .05 level of significance. Cite which variables are significant and which are not significant, based on the t values a Upper 95.0% 150.9486 2.087986 27.55515 6.23078 , based on the t values and p values for each independent variable