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

### Null and Alternative Hypotheses for a Mean

You calculate the sum of the ranks for each group, then the test statistic, H. H is given by a rather formidable formula that basically represents the variance of the ranks among groups, with an adjustment for the number of ties. H is approximately chi-square distributed, meaning that the probability of getting a particular value of H by chance, if the null hypothesis is true, is the *P* value corresponding to a chi-square equal to H; the degrees of freedom is the number of groups minus 1. For the example data, the mean rank for DNA is 10.08 and the mean rank for protein is 10.68, H=0.043, there is 1 degree of freedom, and the *P* value is 0.84. The null hypothesis that the F_{ST} of DNA and protein polymorphisms have the same mean ranks is not rejected.

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

(Hint: You should reject the null hypothesis when the percentage inthe box in the center of the distribution is less than 2.5%.)The above exercise is very similar to how a researcher uses anindependent samples t-test.

The p-value is p = 0.236. This is not below the .05 standard, so we do not reject the null hypothesis. Thus it is possible that the true value of the population mean is 72. The 95% confidence interval suggests the mean could be anywhere between 67.78 and 73.06.

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

The other factor affecting the critical t-value(s) is whether thealternative hypothesis is one- or two-tailed (see Hypothesis Testingtutorial for review of one-tailed and two-tailed hypotheses).

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

When the data indicate that one cannot reject the null hypothesis, does it mean that one can accept the null hypothesis? For example, when the p-value computed from the data is 0.12, one fails to reject the null hypothesis at = 0.05. Can we say that the data support the null hypothesis?

## Assumptions and Null hypothesis Flashcards | Quizlet

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.

## 14/10/2014 · Assumptions of null hypothesis testing ..

When testing hypotheses using a t-test, the critical t-value isdetermined by a researcher's willingness to make a Type I error andwhether the hypothesis is two-tailed or one-tailed.

## null hypothesis significance testing assumptions

Because the t-distribution is a family of sampling distributions, aresearcher must always report the sample sizeused to test the hypothesis so that other researchers knowwhat critical t-values were used.

## estimates when the null hypothesis is true and when the null ..

How do we determine whether to reject the null hypothesis? It depends on the level of significance α, which is the probability of the Type I error.