How does sample size affect the decision to reject or failure to reject of a null hypothesis?
What will be an ideal response?
The null hypothesis has the status of a maintained hypothesis–one held to be true–unless the data contain strong evidence to reject the hypothesis. By setting the significance level, α at a low level, we have a small probability of rejecting a true null hypothesis. When we reject a true null hypothesis, the probability of error is the significance level, α. But if there is only a small sample, then we will reject the null hypothesis only when it is wildly in error. As we increase the sample size, the probability of rejecting a false null hypothesis is increased. But failure to reject a null hypothesis leads to much greater uncertainty because we do not know the probability of the Type II error. Thus, if we fail to reject, then either the null hypothesis is true or our procedure for detecting a false null hypothesis does not have sufficient power–for example, the sample size is too small.
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