## rejecting the null hypothesis when the alternative is true.

### not rejecting the null hypothesis when the alternative is true.

If (that is, ), we say the data are consistent with a population mean difference of 0 (because has the sort of value we expect to see when the population value is 0) or "we **fail to reject the hypothesis that the population mean difference is 0**". For example, if t were 0.76, we would fail reject the hypothesis that the population mean difference is 0 because we've observed a value of t that is unremarkable if the hypothesis were true.

### Null and Alternative Hypothesis | Real Statistics Using …

One of the main goals of statistical hypothesis testing is to estimate the *P* value, which is the probability of obtaining the observed results, or something more extreme, if the null hypothesis were true. If the observed results are unlikely under the null hypothesis, your reject the null hypothesis. Alternatives to this "frequentist" approach to statistics include Bayesian statistics and estimation of effect sizes and confidence intervals.

After you do a statistical test, you are either going to reject or accept the null hypothesis. Rejecting the null hypothesis means that you conclude that the null hypothesis is not true; in our chicken sex example, you would conclude that the true proportion of male chicks, if you gave chocolate to an infinite number of chicken mothers, would be less than 50%.

## Hypothesis Test at 95% Confidence Level - BrainMass

which we get by inserting the hypothesized value of the population mean difference (0) for the population_quantity. If or (that is, ), we say the data are not consistent with a population mean difference of 0 (because does not have the sort of value we expect to see when the population value is 0) or "we **reject the hypothesis that the population mean difference is 0**". If t were -3.7 or 2.6, we would reject the hypothesis that the population mean difference is 0 because we've observed a value of t that is unusual if the hypothesis were true.

## the null hypothesis and the alternative ..

In general, there are three possible alternative hypotheses and rejection regions for the one-sample -test:The rejection regions for three posssible alternative hypotheses usingour example data are shown in the following graphs.

## P Value and Confidence Interval | P Value | Null Hypothesis

If two means, for example, came from the *same* population, then we would expect them to both lie within the shaded blue area representing 90% of the possible values centred on the population mean (*i.e.* μ±45%). If, on the other hand, the means were from *different populations*, then we would expect one of them to fall in the either of the white areas each representing 5% of the possible values – one above, and one below, the population mean.

## How to Conduct a Hypothesis Test in Statistics - …

We might be faced with a scenario in which a known source of contamination could *increase* the pH over time. In this case, we could use a one-tailed test to see if the stream indeed has a higher pH than one year ago. For this, we would use the alternate hypothesis *H*_{A}: *μ*_{old} *μ*_{new}. A more likely scenario, however, is that the pH could have increased, decreased, or stayed the same. As a result, we would want to use a more rigorous two-tailed test for the hypothesis that:

## "How to Conduct a Hypothesis Test." ThoughtCo, May

The next figure illustrates two study results that are both statistically significant at P__ 0.05, because both confidence intervals lie entirely above the null value (RR or OR = 1). The upper result has a point estimate of about two, and its confidence interval ranges from about 0.5 to 3.0, and the lower result shows a point estimate of about 6 with a confidence interval that ranges from 0.5 to about 12. The narrower, more precise estimate enables us to be confident that there is about a two-fold increase in risk among those who have the exposure of interest. In contrast, the study with the wide confidence interval is "statistically significant," but it leaves us uncertain about the magnitude of the effect. Is the increase in risk relatively modest or is it huge? We just don't know.__