According to the historical data, the life expectancy in France is less than or

Question

According to the historical data, the life expectancy in France is less than or equal to the life expectancy in Germany. A new study has been made to see whether this has changed. Records of 250 individuals from France who died recently are selected at random. The250 individuals lived an average of 78.1 years with a standard deviation 7.5 of years. Records of295 individuals from Germany who died recently are selected at random and independently. The 295 individuals lived an average of 77.1 years with a standard deviation of 6.5 years. Assume that the population standard deviations of the life expectancies can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.1 level of significance, is there enough evidence to support the claim that the life expectancy,1,in France is greater than the life expectancy,2, in Germany? Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic:The value of the test statistic: (Round to at least three decimal places.) The critical value at the level of significance: (Round to at least three decimal places.) Can we support the claim that the life expectancy in France is greater than the life expectancy in Germany?

Explanation / Answer

Data:     

n1 = 250    

n2 = 295    

x1-bar = 78.1    

x2-bar = 77.1    

s1 = 7.5    

s2 = 6.5    

Hypotheses:    

Ho: 1 2    

Ha: 1 > 2    

Decision Rule:    

= 0.1    

Degrees of freedom = 250 + 295 - 2 = 543

Critical t- score = 1.28311259   

Reject Ho if t > 1.28311259   

Test Statistic:    

Pooled SD, s = [{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] = (((250 - 1) * 7.5^2 + (295 - 1) * 6.5^2)/(250 + 295 - 2)) = 6.976380831

SE = s * {(1 /n1) + (1 /n2)} = 6.97638083125932 * ((1/250) + (1/295)) = 0.599718463

t = (x1-bar -x2-bar)/SE = (78.1 - 77.1)/0.599718462523541 = 1.667449082

p- value = 0.04800086    

Decision (in terms of the hypotheses):

Since 1.66744908 > 1.283112591 we reject Ho and accept Ha

Conclusion (in terms of the problem):

There is sufficient evidence that the life expectancy of France is more than that of Germany.

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