Family transportation costs are usually higher than most people believe because those costs include car payments, insurance, fuel costs, repairs, parking, and public transportation. Several randomly selected families in four major European cities (Amsterdam, Madrid, Frankfurt and Dublin) were asked to use their records to estimate a monthly figure for transportation cost. The data obtained and ANOVA are used to test whether there is a significant difference in monthly transportation costs for families living in these cities. Reported below is the ANOVA output and summary statistics for the four cities together with estimated pooled standard deviation (omitted output values are denoted ?).

Statistics and Probability Analysis of Variance (ANOVA ) Source of Variation df SS Ms F P-value F critical Between Groups 3 1,701 567 2.949 0.039699 2.76 Within Groups 61 11,728 192.262 Total 64 13,429 Answer Detail computation: MS Between Groups = SS Between Groups/ df Between Groups MS Between Groups = 1:701/ 3 MS Between Groups = 567 MS Within Groups = 53 Within Groups/ df Within Groups MS Within Groups = 11.728 / 61 MS Within Groups = 192.262 F = MS Between Groups / MS Within Groups F = 567 / 192.262 F = 2.949 To determine the pvalue, just input this excel function in the excel software: =F.DIST.RT(2.949,3,61) Therefore, pvalue = 0.039699 Referring to the table of critical values of F: Foes ( 3 , 61) = 2.76 Referring to the table of critical values of F: F005 ( 3 , 61 ) = 2.76 Critical value = 2.76 Conclusion: Since F = 2.949 > Critical value = 2.76 and p-value = 0.039699 Critical value = 2.76 and p-value = 0.039699