Question

for the samples taken from two populations, the difference between the sample means does not fall within the 95% confidence interval. if the null hypothesis is, \there is no difference in the sample means,\ which statement is true?
a. the null hypothesis must be accepted.
b. the null hypothesis must be rejected.
c. both the null and the alternative hypotheses must be rejected.
d. both the null and the alternative hypotheses must be accepted.

Explanation:

In hypothesis testing, a 95% confidence interval for the difference in sample means is used to assess the null hypothesis (no difference in means). If the null hypothesis value (0 difference, in this case) is not within the confidence interval, we reject the null hypothesis because the observed difference is statistically significant. Options A, C, D are incorrect: A (we reject, not accept), C (we don't reject both), D (we don't accept both).

Answer:

B. The null hypothesis must be rejected.