SOLUTION: According to the historical data, the life expectancy in the United Kingdom is less than the life expectancy in the United States. A new study has been made to see whether this has

Question 1164814: According to the historical data, the life expectancy in the United Kingdom is less than the life expectancy in the United States. A new study has been made to see whether this has changed. Records of 225 individuals from the United Kingdom who died recently are selected at random. The 225 individuals lived a mean of 78.2 years with a standard deviation of 6.5 years. Records of 265 individuals from the United States who died recently are selected at random and independently. The 265 individuals lived a mean of 76.6 years with a standard deviation of 8.1 years. Assume that the population standard deviations of lifetimes in these two countries can be estimated by the sample standard deviations, as the samples used were quite large. Construct a 95% confidence interval for m1-m2 , the difference between the life expectancy m1 in the United Kingdom and the life expectancy m2 in the United States. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal place
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
n1=225
x bar1=78.2
s1=6.5
n2=265
x bar2=76.6
s2=8.1
t=(x1 bar-x2bar)-(u1-u2) divided by sqrt ((s1^2/n1)+(s2^2/n2)); t=1.965 for df=488; bar 1-x bar2=1.6
the half-interval is t (0.975) df n1+n2-2 or 488*SE
SE is 0.6598
half-interval is 1.965*0..6598=1.297
the CI is 1.6+/- 1.30
(0.30, 2.90)

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