## What null and alternative hypotheses are appropriate?

### For example, using Z-test of hypothesis in the following Figure.

For the goodness-of-fit sample test, we formulate the null and alternative hypothesis as H : f_{Y}(y) = f_{o}(y)

H : f_{Y}(y) f_{o}(y) At the level of significance, H will be rejected in favor of H if is greater than However, it is possible that in a goodness-of-fit test, one or more of the parameters of f_{o}(y) are unknown.

### Moreover, one may utilize CI for the test of hypothesis purposes.

Common significance levels are .10, .05, and .01. Suppose you chose a .05 level of significance, meaning there is a 5% chance that you will reject the null hypothesis when it is true.

The graphs below show the relationship between a claim and the truth when the null hypothesis is true. Of course, that means the two distributions are identical.

## What is the Significance of null hypothesis? - iSixSigma

Therefore, there is not sufficient evidence to reject the null hypothesis that the two correlation coefficients are equalClearly, this test can be modified and applied for test of hypothesis regarding population correlation based on observed r obtained from a random sample of size n:provided | r | 1, and | | 1, and n is greater than 3.

## fail to reject the null hypothesis

Under the null hypothesis and normality condition, the test statistic is: where: and n= sample size associated with r, and n =sample size associated with r.

## and p P < .05 P < .05 Fail to reject null hypothesis Fail to ..

Given that two populations have normal distributions, we wish to test for the following null hypothesis regarding the equality of correlation coefficients:**H:** = , based on two observed correlation coefficients r, and r, obtained from two random sample of size n and n, respectively, provided | r | 1, and | r | 1, and n, n both are greater than 3.

## , we fail to reject the hypothesis that the coin is fair

**Example:** Consider the following three random samples from three populations, P1, P2, P3: With an F = 4.38 and a p-value of 0.023, we reject the null at = 0.05.

## Learn About Null Hypothesis and Alternative Hypothesis

Some statistical tests, such as testing equality of the means by the t-test and ANOVA, assume that the data come from populations that have the same variance, even if the test rejects the null hypothesis of equality of population means.

## "Learn About Null Hypothesis and Alternative Hypothesis."

Among three possible scenarios, the interesting case is in testing the following null hypothesis based on a set of n random sample observations: **H**: Variation is about the claimed value.

**H**: The variation is more than what is claimed, indicating the quality is much lower than expected.