Which two results occur when the null hypothesis is accepted using a t-test?
The test statistic is less than the critical value and there appears to be no difference between the two samples.
When the null hypothesis is accepted in a t-test, it indicates that there is insufficient evidence to suggest a significant difference between the two samples being compared. This acceptance is typically due to the test statistic falling below the critical value, supporting the notion that any observed differences could be attributed to random chance rather than a true effect.
This statement is true; when the null hypothesis is accepted, the t-test statistic must be less than the critical value. This outcome means that the sample means are not significantly different, which is a fundamental aspect of hypothesis testing.
This statement contradicts the premise of accepting the null hypothesis. When the null hypothesis is accepted, it suggests that any observed differences between the two samples are not statistically significant, thus indicating no real difference.
This statement is incorrect as well; if the test statistic were greater than the critical value, the null hypothesis would be rejected. This would imply that there is significant evidence of a difference between the samples, which is the opposite of accepting the null hypothesis.
This statement is accurate and complements the acceptance of the null hypothesis. Accepting the null hypothesis indicates that the data does not provide enough evidence to conclude that a significant difference exists between the two samples.
In summary, accepting the null hypothesis during a t-test leads to the conclusion that the test statistic is less than the critical value, and consequently, there appears to be no significant difference between the two samples. This understanding is crucial for interpreting the results of hypothesis tests in statistical analysis.
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