65. Which two results occur when the null hypothesis is accepted using a t-test?
Answer: C,D
Accepting the null hypothesis indicates that there appears to be no difference between the two samples and that the test statistic is less than the critical value.
When the null hypothesis is accepted in a t-test, it implies that there is no statistically significant difference between the two samples being compared. This is evidenced by the test statistic being less than the critical value, affirming that the observed results could easily occur under the null hypothesis.
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, indicating a significant difference between the samples rather than acceptance.
B) There appears to be a difference between the two samples.
This option is also incorrect, as accepting the null hypothesis suggests that there is no significant difference between the two samples. The presence of a difference would contradict the acceptance of 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 data does not provide sufficient evidence to conclude that there is a difference between the samples. This reflects the fundamental purpose of the null hypothesis in statistical testing.
D) The test statistic is less than the critical value.
This option is correct as well. Accepting the null hypothesis occurs when the test statistic is less than the critical value, supporting the conclusion that the observed difference is not statistically significant.
Conclusion
The correct answers, C and D, demonstrate essential aspects of hypothesis testing in statistics. Accepting the null hypothesis means recognizing that there is no significant difference between the samples, which is confirmed by the test statistic being less than the critical value. Other options incorrectly suggest a difference or an opposite relationship, making them invalid in this context.