# For any power calculation, you will need to know:

Consider *p*, the true proportion of voters who favor a particular political candidate. A pollster is interested in testing at the *α* = 0.01 level, the null hypothesis *H*_{0}: *p *= 0.50 against the alternative hypothesis that *H*_{A}: *p* > 0.50. Find the sample size *n *that is necessary to achieve 0.80 power at the alternative *p *= 0.55.

## Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

### Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

The p-value is equal to 0.062, indicating that there is moderate evidence against the null hypothesis that the three populations are statistically identical.

### Then we test with a calculated t-value.

Using the JavaScripts, we obtain the needed information in constructing the following ANOVA table: **Conclusion:** The p-value is P= 0.006, indicating a strong evidence against the null hypothesis.

## the null hypothesis represented by H 0 and the alternative ..

For each null hypothesis anddistribution, we can define a __region of rejection__, which contains valuesof the statistic that would cause us to reject H_{0}.

## How do to calculate Likelihood Ratio Test/Power in hypothesis testing

**Solution.** Setting *α*, the probability of committing a Type I error, to 0.05, implies that we should reject the null hypothesis when the test statistic *Z* ≥ 1.645, or equivalently, when the observed sample mean is 103.29 or greater:

## power analysis sample size null hypothesis

In the olden days, when people looked up *P* values in printed tables, they would report the results of a statistical test as "*P**P**P*>0.10", etc. Nowadays, almost all computer statistics programs give the exact *P* value resulting from a statistical test, such as *P*=0.029, and that's what you should report in your publications. You will conclude that the results are either significant or they're not significant; they either reject the null hypothesis (if *P* is below your pre-determined significance level) or don't reject the null hypothesis (if *P* is above your significance level). But other people will want to know if your results are "strongly" significant (*P* much less than 0.05), which will give them more confidence in your results than if they were "barely" significant (*P*=0.043, for example). In addition, other researchers will need the exact *P* value if they want to combine your results with others into a .