Question 65

When the null hypothesis is accepted, it indicates that there appears to be no difference between the two samples and the test statistic is less than the critical value.

Accepting the null hypothesis using a t-test suggests that there appears to be no difference between the two samples, and that the test statistic is less than the critical value.

A) The test statistic is greater than the critical value.

This option is incorrect because if the test statistic is greater than the critical value, it would lead to the rejection of the null hypothesis. Accepting the null hypothesis means that the test statistic does not exceed this threshold.

B) There appears to be a difference between the two samples.

This option is incorrect. Accepting the null hypothesis means that there is no statistically significant evidence to suggest a difference between the two samples. Therefore, this statement contradicts the conclusion drawn from accepting the null hypothesis.

C) There appears to be no difference between the two samples.

This option is correct because accepting the null hypothesis indicates that the evidence does not support a significant difference between the two samples. It reflects the conclusion drawn from the statistical test.

D) The test statistic is less than the critical value.

This option is also correct. When the null hypothesis is accepted, the test statistic must be less than the critical value, which means the observed data is consistent with the null hypothesis.

Conclusion

The correct answers, C and D, clearly indicate the implications of accepting the null hypothesis. Both options reflect the statistical reasoning that underlies hypothesis testing, wherein the absence of significant evidence leads to the conclusion that there is no difference between the samples and that the test statistic remains within acceptable limits under the critical value. All other options either misinterpret this statistical principle or contradict the accepted conclusion.