Question

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 does not provide enough evidence to reject the null hypothesis?
a. 95% confidence interval: $(-4.223,-1.989)$
b. 95% confidence interval: $(-2.945,0.983)$

Explanation:

Step1: Recall the rule for hypothesis rejection using confidence interval

If the confidence interval contains \(0\), we fail to reject the null hypothesis \(H_0:\mu_1 - \mu_2=0\). If it does not contain \(0\), we reject \(H_0\).

Step2: Check each confidence interval

• For option A: The \(95\%\) confidence interval \((-4.223,-1.989)\) does not contain \(0\). So, we would reject \(H_0\).
• For option B: The \(95\%\) confidence interval \((-2.945,0.983)\) contains \(0\). So, we fail to reject \(H_0\).

Answer:

B. \(95\%\) confidence interval: \((-2.945, 0.983)\)