A recent study compared the life expectancy of individuals in the UK with indivi
ID: 3428154 • Letter: A
Question
A recent study compared the life expectancy of individuals in the UK with individuals in the US. They found that the average life expectancy in the UK was 76 and the US had an average life expectancy of 72.5. But now they want to know if the social medicine helps the variance. For a sample of 15 US individuals the sample standard deviation of life expectancy is 5. The Sample standard deviation of a sample of 13 UK citizens was 3.5. At the significance level of 0.05 can we conclude that there is a difference in the variance of the life expectancy of the two countries?
What is the null hypothesis?
what is the alternative hypothesis
what is the appropriate test statistic
what is the critical value of the test staistic?
what is your decsison based on the results
interpret your results
Explanation / Answer
alpha,a = 0.05
n1 = 15 , s1 = 5
n2 = 13 , s2 = 3.5
null hypothesis
H0: Sigma1^2 = Sigma2^2
alternative hypothesis
H1: Sigma^2 is not equal to Sigma2^2
test statistic
F = s1^2 / s2^2
F = 5^2 / 3.5^2
F = 2.041
critical values are
F(a/2, n1-1, n2-1) = F(0.025, 14, 12) = 3.206
F(1 - a/2, n1-1, n2-1) = 1 / F(a/2, n2-1, n1-1) = 1/F(0.025, 12, 14) = 0.328
decsison based on the results
non-critical region is interval: (0.328 , 3.206)
since F lies inside the interval, hence H0 can not be rejected
interpretation
So, we can not conclude that there is a difference in the variance of the life expectancy of the two countries.