7. (20 points) The Canadian center for disease control reports that the average life expectancy of people of ethnic group "X" born in 1905 is 47.6 years and for ethnic group "Y" it is 33.0 years. Suppose that you randomly survey death records for people born in 1905 in a certain county. Of the 124 people of ethnic group "X" , the average life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 people of ethnic group "Y", the average life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the average life spans in the county were the same for both the groups. Test the hypothesis at or = 0.05. Assume that the degrees of freedom is 148. (1) (4 points) What is the appropriate hypothesis for this problem? (2) (7 points) What is the test statistic? (3) (3 points) What is the critical value? (4) (6 points) What is the final conclusion