failing to reject the null hypothesis when it is true.

This means that when the observed t-value exceeds the criticalt-value (i.e., the t-value marking that portion of the curvecontaining 5% of the area), the researcher will reject the nullhypothesis, but in doing so, he/she is taking up to a 5%chance of claiming a significant difference when none exists.

The failure to reject does not imply the null hypothesis is true.

This exercise doesn't use critical values to decide whether to rejectthe null hypothesis.

30/01/2013 · Fail to reject the null hypothesis ..

Below are copies of the objections they have lodged. As the designated authority, the Council has itself to decide whether to reject the application immediately, or allow it to proceed to a hearing. This could either be by way of a specially convened Commons and Village Green Registration Panel, or an independent Inquiry.

fail to reject the null hypothesis or that we don't have ..

There are many applications where it is of interest to compare two independent groups with respect to their mean scores on a continuous outcome. Here we compare means between groups, but rather than generating an estimate of the difference, we will test whether the observed difference (increase, decrease or difference) is statistically significant or not. Remember, that hypothesis testing gives an assessment of statistical significance, whereas estimation gives an estimate of effect and both are important.

Let's return finally to the question of whether we reject or fail to reject the null hypothesis.

If we fail to reject the null hypothesis, ..

We do not reject H0 because -0.96 > -2.145. We do not have statistically significant evidence at α=0.05 to show that the mean total cholesterol level is lower than the national mean in patients taking the new drug for 6 weeks. Again, because we failed to reject the null hypothesis we make a weaker concluding statement allowing for the possibility that we may have committed a Type II error (i.e., failed to reject H0 when in fact the drug is efficacious).

Decide whether the null hypothesis should be rejected

Now instead of testing 1000 plant extracts, imagine that you are testing just one. If you are testing it to see if it kills beetle larvae, you know (based on everything you know about plant and beetle biology) there's a pretty good chance it will work, so you can be pretty sure that a P value less than 0.05 is a true positive. But if you are testing that one plant extract to see if it grows hair, which you know is very unlikely (based on everything you know about plants and hair), a P value less than 0.05 is almost certainly a false positive. In other words, if you expect that the null hypothesis is probably true, a statistically significant result is probably a false positive. This is sad; the most exciting, amazing, unexpected results in your experiments are probably just your data trying to make you jump to ridiculous conclusions. You should require a much lower P value to reject a null hypothesis that you think is probably true.

The question we need to answer is whether the mean difference of 1.4 issufficiently different from 0 to reject the null hypothesis.

we use to decide whether the value stated in the null ..

When considering whether we reject the null hypothesis and accept the alternative hypothesis, we need to consider the direction of the alternative hypothesis statement. For example, the alternative hypothesis that was stated earlier is:

Notice how the critical t-value decreases as the researcher'swillingness to erroneously reject a true null hypothesis increases.

Solution-Decide whether to reject the null hypothesis

As mentioned in lesson 8, the logic of hypothesis testing is to reject the null hypothesis if the sample data are not consistent with the null hypothesis. Thus, one rejects the null hypothesis if the observed test statistic is more extreme in the direction of the alternative hypothesis than one can tolerate. The critical values are the boundary values obtained corresponding to the preset level.

31/08/2008 · Decide whether to accept or reject the null hypothesis

Decide to either reject the null hypothesis in favor of the ..

Once the type of test is determined, the details of the test must be specified. Specifically, the null and alternative hypotheses must be clearly stated. The null hypothesis always reflects the "no change" or "no difference" situation. The alternative or research hypothesis reflects the investigator's belief. The investigator might hypothesize that a parameter (e.g., a mean, proportion, difference in means or proportions) will increase, will decrease or will be different under specific conditions (sometimes the conditions are different experimental conditions and other times the conditions are simply different groups of participants). Once the hypotheses are specified, data are collected and summarized. The appropriate test is then conducted according to the five step approach. If the test leads to rejection of the null hypothesis, an approximate p-value is computed to summarize the significance of the findings. When tests of hypothesis are conducted using statistical computing packages, exact p-values are computed. Because the statistical tables in this textbook are limited, we can only approximate p-values. If the test fails to reject the null hypothesis, then a weaker concluding statement is made for the following reason.