We wish to conduct a test of hypothesis on two independent population means.The objective of the test is to determine if the means are the same or if they differ.Both populations are assumed to be normal with equal variance.We draw 10 observations for the first sample and 20 observations for the second sample.What would be the appropriate critical value for the test if α = 0.01?
A) 1.3125
B) 2.7633
C) 2.4573
D) 2.4620

Question

Quizplus · Accepted Answer

For a two-sample t-test with equal variances and unequal sample sizes, we use the t-distribution with degrees of freedom given by:
df = (n1 + n2 - 2) 
where n1 and n2 are the sample sizes.
For α = 0.01 and df = 28 (10+20-2), the appropriate critical value is 2.7633, which is closest to option B.

We Wish to Conduct a Test of Hypothesis on Two