According to the historical data, the life expectancy in the United States is equal to the life expectancy in Japan. A new study has been made to see whether this has changed. Records of individuals from the United States who died recently are selected at random 250. The individuals lived an average of 76.7 years with a standard deviation of 5.5 years. Records of 255 individuals from Japan who died recently are selected at random and independently. The 255 individuals lived an average of 77.5 years with a standard deviation of 5.1 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 0.5 level of significance, is there enough evidence to support the claim that the life expectancy, (mu)mean of population 1 , in the United States is not equal to the life expectancy,(mu)mean of population 2 , in Japan anymore? Perform a two-tailed test.
State the null hypothesis?
State the alternative hypothesis?
The type of test statistic?
The value of the test statistic?
The p value?
Can we support the claim?