A researcher wants to prove that there is a difference in the average life spans between men and women in Japan. Let mu1 = average life span of Japanese women and mu2 = average life span of Japanese men. A random sample of 10 women showed an average lifespan of 83 years, with a sample standard deviation of 7 years. A random sample of 10 men showed an average lifespan of 77 years, with a sample standard deviation of 6.4 years. Assume that life spans are normally distributed and that the population variances are equal. If alpha = .05 and the null hypothesis is mu1 – mu2 = 0, what is (are) the critical value(s) for the hypothesis test?

We are running a hypothesis for the difference of 2 sample means, assuming normality, and assuming that population variances are equal. This determines which test we run.

We have:

Sample 1: (women)

n = 10

x = 83

s = 7

Sample 2: (men)

n = 10

x = 77

s = 6.4

The hypothesis for the test are:

H0: µ1 - µ2 = 0

Ha: µ1 - µ2 ≠ 0

The significance level is 5%. The degrees of freedom is 2 less than the sum of the sample size, in this case, 18. Our t-value is: 2.101

Our critical values for the test statistic are: t < -2.101, and t > 2.101