Question 1074976: According to the historical data, the life expectancy in the United States is equal to the life expectancy in Germany. A new study has been made to see whether this has changed. Records of 205 individuals from the United States who died recently are selected at random. The 205 individuals lived an average of 77.7 years with a standard deviation of 4.8 years. Records of 255 individuals from Germany who died recently are selected at random and independently. The 255 individuals lived an average of 76.5 years with a standard deviation of 4.3 years. Assume that the population standard deviation of the life expectancy can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.01 level of significance, is there enough evidence to support the claim that the life expectancy, , in the United States is not equal to the life expectancy, , in Germany anymore? Perform a two-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.)
1. The null hypothesis: Ho:
2. The Alternative Hypothesis: H1
3. Type of statistic: drop down choices are: Z, t, Chi square, F
4. The value of the test statistic. Round to at least three decimal places
5. The p-value. Round to at least three decimal places
6. Can we support the claim that the life expectancy in the United States is NOT equal to the life expectancy in Germany? YES or NO
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! let u(1) be the average age for US individual at death
let u(2) be the average age for German individual at death
:
1) Ho: u(1) - u(2) = 0
2) H1: u(1) - u(2) not = 0
3) Z since both samples' sizes are > 30
:
u = (77.7 - 76.5) = 1.2
:
std. dev = square root( (4.8^2 / 205) + (4.3^2 / 255) ) = 0.43
:
4) Z-value = 1.2 / 0.43 = 2.791
:
5) p-value = (1 - 0.9974) * 2 = 0.005
:
6) p-value is < 0.01, therefore we reject Ho and answer is YES
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