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A researcher wants to prove that there is a difference in the average life spans

ID: 3066223 • Letter: A

Question

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. The test statistics for this problem is 2.00. If alpha = .05 and the null hypothesis is mul-mu2 = 0, what is your conclusion after the difference of means hypothesis test? There is a statistically significant difference in average life spans for men and women The average life span of women is 6 years longer than the average life span of men. The difference is not statistically significant: there is not enough evidence to conclude that the average life spans are different None of the above.

Explanation / Answer

The test-statistic T ~ t-distribution with (n1 + n2 - 2) d.f.

= (10 + 10 - 2) = 18 d.f.

Hence, the p-value = 2 P(T > 2) = 2 * 0.0304 = 0.0608.

Since, p-value = 0.0608 > level of significance = 0.05,

we fail to reject H0.

The difference is not statistically significant, there is not

enough evidence that the average life spans are different.

(Ans).