Question

In a study of life expectancy, a random sample of 15 men lived an average of 69.5 years with a sample standard deviation of 6.4 years, and a random sample of 14 women lived an average of 73.2 years with a sample standard deviation of 6.8 years. Use a one-tailed test at the 5% level to see if women live longer than men. You may assume the true variances are equal.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 > μ2

Rejection Region
This is right tailed test, for α = 0.05 and df = n1 + n2 - 2 = 27
Critical value of t is 1.703.
Hence reject H0 if t > 1.703

Pooled Variance
sp = sqrt((((n1 - 1)*s1^2 + (n2 - 1)*s2^2)/(n1 + n2 - 2))*(1/n1 + 1/n2))
sp = sqrt((((14 - 1)*6.8^2 + (15 - 1)*6.4^2)/(14 + 15 - 2))*(1/14 + 1/15))
sp = 2.451

Test statistic,
t = (x1bar - x2bar)/sp
t = (73.2 - 69.5)/2.451
t = 1.51

P-value Approach
P-value = 0.0713
As P-value > 0.05, fail to reject the null hypothesis.

answered by: anonymous