Question

for which confidence interval for the difference in the means \\(\mu_1 - \mu_2\\), would you reject th
a. \\((-1.968,1.561)\\)
b. \\((-2.209,0.209)\\)
c. \\((-1.673,1.892)\\)
d. \\((-2.001,-1.873)\\)

Explanation:

Step1: Recall the rule for rejecting \( H_0 \)

When testing \( H_0: \mu_1 - \mu_2 = 0 \), we reject \( H_0 \) if the confidence interval for \( \mu_1 - \mu_2 \) does not contain \( 0 \).

Step2: Check each interval

• Option A: \( (-1.968, 1.561) \) contains \( 0 \) (since \( -1.968 < 0 < 1.561 \)).
• Option B: \( (-2.209, 0.209) \) contains \( 0 \) (since \( -2.209 < 0 < 0.209 \)).
• Option C: \( (-1.673, 1.892) \) contains \( 0 \) (since \( -1.673 < 0 < 1.892 \)).
• Option D: \( (-2.001, -1.873) \) does not contain \( 0 \) (both endpoints are negative, so \( 0 \) is not in the interval).

Answer:

D. \((-2.001, -1.873)\)