Difficulty: Easy

Average Score: 100%

Which two results occur when the null hypothesis is accepted using a t-test?

Rationale

There appears to be no difference between the two samples and the test statistic is less than the critical value.

Accepting the null hypothesis in a t-test indicates that there is insufficient evidence to suggest a significant difference between the two samples being compared. This is reflected in both the test statistic being less than the critical value and the conclusion that the samples do not show a statistically significant difference.

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

If the test statistic were greater than the critical value, it would lead to the rejection of the null hypothesis, indicating a statistically significant difference between the two samples. Therefore, this choice contradicts the accepted null hypothesis scenario.

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

This option suggests that a significant difference exists between the samples, which is inconsistent with accepting the null hypothesis. Accepting the null hypothesis implies that no statistically significant difference has been found.

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

Accepting the null hypothesis directly implies that there is no statistically significant difference between the two samples. Therefore, this option accurately reflects the conclusion drawn when the null hypothesis is accepted.

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

This statement is true when the null hypothesis is accepted. A test statistic less than the critical value indicates that the observed data does not provide enough evidence to reject the null hypothesis, confirming that the samples do not differ significantly.

Conclusion

Accepting the null hypothesis during a t-test signifies that there is no significant difference between the two samples, which is represented by the conclusion that the test statistic is less than the critical value. Thus, both statements C and D accurately describe the outcomes associated with this statistical decision.

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