Question

question 6
you are analyzing data for a research project. you have a two - sided two - sample t - test with the following hypotheses being tested:
$h_0:mu_1-mu_2 = 0$
$h_a:mu_1-mu_2
eq0$
which of the following results for the confidence interval provides enough evidence to reject the null hypothesis?
a. 95% confidence interval: (-3.853, -0.943)
b. 95% confidence interval: (-0.285, 1.345)

Explanation:

Step1: Recall null - hypothesis rejection rule

In a two - sample t - test with $H_0:\mu_1-\mu_2 = 0$ and $H_a:\mu_1-\mu_2
eq0$, if the confidence interval for $\mu_1-\mu_2$ does not contain 0, we reject the null hypothesis.

Step2: Analyze Option A

The 95% confidence interval in Option A is $(-3.853,-0.943)$. Since 0 is not in this interval, we have enough evidence to reject the null hypothesis.

Step3: Analyze Option B

The 95% confidence interval in Option B is $(-0.285,1.345)$. Since 0 is in this interval, we do not have enough evidence to reject the null hypothesis.

Answer:

A. 95% confidence interval: $(-3.853,-0.943)$