Final answer:
If d falls between dL and dU, the correct answer is that the null hypothesis is not rejected. This indicates that there is insufficient evidence to reject the null hypothesis based on the sample data. Therefore, the correct answer is B
Step-by-step explanation:
If d falls between dL and dU, it implies that the observed statistic is within the range of values that would not lead us to reject the null hypothesis. Therefore, the correct answer is B) The null hypothesis is accepted, or more appropriately, not rejected. It is important to understand that failing to reject the null hypothesis does not necessarily mean that we have proven it to be true, only that there is insufficient evidence against it based on our sample.
In hypothesis testing, we use a significance level (denoted as α), which is a threshold for deciding whether to reject the null hypothesis. If the p-value is less than the chosen α, we reject the null hypothesis. If the p-value is greater than α, we do not reject the null hypothesis. The choices given in the question do not reflect issues related to the width of the confidence interval (C) or the adequacy of the sample size (D).
It is also important to note that the acceptance region, defined by dL and dU, depends on the significance level. A narrower confidence interval could indicate more precise sample estimates, but this aspect is not the focus of the question.
Therefore, the correct answer is B