A recent survey by Genworth Financial Inc., a financial-services company, conclu
ID: 3175010 • Letter: A
Question
A recent survey by Genworth Financial Inc., a financial-services company, concludes that the cost of long-term care in the United States varies significantly, depending on where an individual lives (The Wall Street Journal, May 16, 2009). An economist collects data from the five states with the highest annual costs (Alaska, Massachusetts, New Jersey, Rhode Island, and Connecticut) in order to determine if his sample data are consistent with the survey's conclusions. The economist provides the following portion of an ANOVA table. Use Table 4: a. Complete the ANOVA table. Assume that long-term care costs are normally distributed. b.Specify the competing hypotheses to test whether some differences exist in the moan long-term care costs in those five states. H_0: mu_Alaska = mu _Massachusetts = mu _Now Jersey = mu _Rho do Island = mu _Connecticut, H_A: Not all population means are equal. H_0: mu __Alaska lessthanorequalto mu _Massachusetts lessthanorequalto mu _New Jersey lessthanorequalto mu _Rhode Island lessthanorequalto mu_Connecticut H_A: Not all population means are equal. H_0: mu _Alaska greaterthanorequalto mu _Massachusotts greaterthanorequalto mu _New Jersey greaterthanorequalto mu _Rho do Island greaterthanorequalto mu _Connecticut H_A: Not all population means are equal. c. At the 5% significance level, can we conclude that mean costs differ? Yes, since the p-value is less than a. Yes, since the p-value is not less than a. No, since the p-value is less than a. No. since the p-value is not less than a.Explanation / Answer
a. means sum of squares
between blocks = 635.0542/4 = 158.76 , within groups = 253.2192/20 = 12.66 , F = 158.76/12.66 = 12.54 ,
F-critical value at 5% = 2.87, p-value = 0.0002.
b. aswer is first option.
c. answer is the first option.