11. Which two results occur when the null hypothesis is accepted using a t-test?
Answer: A,B
The test statistic is less than the critical value and there appears to be no difference between the two samples.
Accepting the null hypothesis in a t-test indicates that the test statistic falls below the critical value, which suggests that there is insufficient evidence to support a difference between the two samples being compared.
A) The test statistic is less than the critical value.
This statement is correct as it directly aligns with the definition of accepting the null hypothesis in a t-test. When the test statistic is less than the critical value, it indicates that the observed data does not provide strong enough evidence to reject the null hypothesis.
B) There appears to be no difference between the two samples.
This option is also correct because accepting the null hypothesis implies that the analysis indicates no statistically significant difference between the two samples being tested, supporting the conclusion that they are likely similar.
C) There appears to be a difference between the two samples.
This statement is incorrect. If a difference were observed between the two samples, the null hypothesis would typically be rejected, indicating that the t-test results suggest a significant effect or difference.
D) The test statistic is greater than the critical value.
This option is incorrect. A test statistic greater than the critical value would lead to the rejection of the null hypothesis, signifying that there is a significant difference between the samples.
Conclusion
The correct answers, A and B, illustrate the fundamental interpretation of accepting the null hypothesis in a t-test: the test statistic being less than the critical value indicates no significant difference between the samples. Options C and D contradict this interpretation, reinforcing why they are not valid in this context.