Asian residents in Boston have the highest average life expectancy of any racial or ethnic group—a decade longer than black residents (The Boston Globe, August 16, 2010). Suppose sample results indicative of the overall results are as follows. Asian Black Latino WhiteX−1= 83.7 years X−2= 73.5 years X−3= 80.6 years X−4= 79.0 yearsS21= 26.3 S22= 27.5 S23= 28.2 S24= 24.8n1 = 20 n2 = 20 n3 = 20 n4 = 20
a. Specify the competing hypotheses to test whether there are some differences in average life expectancies between the four ethnic groups. H0: μAsian = μBlack = μLatino = μwhite; HA: The population means are not all equal. H0: μAsian ≤ μBlack ≤ μLatino ≤ μwhite; HA: The population means are not all equal. H0: μAsian ≥ μBlack ≥ μLatino ≥ μwhite; HA: The population means are not all equal. b. Construct an ANOVA table. Assume life expectancies are normally distributed. (Round intermediate calculations to at least 4 decimal places. Round "SS" to 2 decimal places, "MS" to 4 decimal places, "F" to 3 decimal places.)c. At the 5% significance level, what is the conclusion to the test?Reject H0; we can conclude that some mean life expectancies differ. Reject H0; we cannot conclude that some mean life expectancies differ. Do not reject H0; we can conclude that some mean life expectancies differ. Do not reject H0; we cannot conclude that some mean life expectancies differ.