Use the following information for questions:
A researcher wants to assess if there is a difference in the average life spans between men and women in Japan. Let $µ_1$ = average life span of Japanese women and $µ_2$ = 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.
-What is the value of the test statistic?
A) t = 1.65
B) t = 1.80
C) t = 2.00
D) None of the above

Question

Use the following information for questions:
 A researcher wants to assess if there is a difference in the average life spans between men and women in Japan. Let $µ_1$ = average life span of Japanese women and $µ_2$ = 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.
-What is the value of the test statistic?
A) t = 1.65
B) t = 1.80
C) t = 2.00
D) None of the above

Quizplus · Accepted Answer

The test statistic is calculated using the formula for the t-test for two independent samples with equal variances: $ t = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{s_p^2(\frac{1}{n_1} + \frac{1}{n_2})}} $, where $ s_p^2 $ is the pooled variance. Here, $ s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2} $. Substituting the given values, the test statistic $ t $ is approximately 2.00.

Use the Following Information for Questions: a Researcher Wants µ1µ_1µ1​

Use the Following Information for Questions:
a Researcher Wants $µ_1$