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#### According to the historical data, the life expectancy in the United States is less than or equal to the life expectancy in Ireland

###### Statistics

According to the historical data, the life expectancy in the United States is less than or equal to the life expectancy in Ireland. A new study has been made to see whether this has changed. Records of 270 individuals from the United States who died recently are selected at random. The 270 individuals lived an average of 77.5 years with a standard deviation of 6.5 years. Records of 210 individuals from Ireland who died recently are selected at random and independently. The 210 individuals lived an average of 76.4 years with a standard deviation of 5.2 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 0.10 level of significance, is there enough evidence to support the claim that the life expectancy, , in the United States is greater than the life expectancy, , in Ireland? Perform a one-tailed test. Provide answers as specified below.

1. The null hypothesis formula Ho

2 The alternative hypothesis formula H1

3. The type of test statistic(choose one) Z , t provide degrees of freedom , chi
square provide degrees of freedom , F provide dfn and dfd

4. The value of the test statistic(round to at least 3 decimal points)

5. The critical value at the 0.10 level of significance(round to at least 3 decimal points)

6. Can we support the claim that the life expectancy in the US is greater than the life expectancy in Ireland? Specify yes or no