Question

3) A researcher wants to assess if there is a difference in the average life spans between men and women in Japan. A random sample of 10 women showed an average life span of 83 years old, with a sample standard deviation of 7 years. A random sample of 10 men showed an average life span of 77 years, with a sample standard deviation of 6.4 years. Assume that life spans are normally distributed.

a. State the null and alternative hypothesis

b. Give the p-value

c. Give a conclusion for the hypothesis test

Answer 1

A researcher wants to assess if there is a difference in the average life spans between men and women in Japan.

n1 = 10,  1 = 83, s1 = 7

n2 = 10, 2 = 77, s2 = 6.4

Let μ1 = average life span of Japanese women and

μ2 = average life span of Japanese men

Hypothesis test:

The null and alternative hypothesis is:

Conclusion: Fail to reject H0. The difference is not statistically significant. There is not enough evidence to conclude that the average life spans are different.