Question

Explain the procedure for testing a hypothesis using the P-value approach? What is the criterion for judging whether to reject the null hypothesis?

6. What does the level of significance represent in a test of hypothesis? Give an example.

7. Explain the difference between "accepting" and "not rejecting" a null hypothesis.

Answer 1

The P-value approach involves determining "likely" or "unlikely" by determining the probability, assuming the null hypothesis were true, of observing a more extreme test statistic in the direction of the alternative hypothesis that the one observed. If the P-value is small, say less than (or equal to) , then it is "unlikely." And, if the P-value is large, say more than , then it is "likely."

If the P-value is less than (or equal to) ?, then the null hypothesis is rejected in favour of the alternative hypothesis. And, if the P-value is greater than ?, then the null hypothesis is not rejected.

6) The level of statistical significance is often expressed as the so-called p-value. Depending on the statistical test you have chosen, you will calculate a probability (i.e., the p-value) of observing your sample results (or more extreme) given that the null hypothesis is true. Another way of phrasing this is to consider the probability that a difference in a mean score could have arisen based on the assumption that there really is no difference.

7) In stage one of the hypothesis-testing process, we formulate a hypothesis called the null hypothesis. This has some special characteristics. It is a specific statement about population parameters and it provides the basis for calculating what is called a p-value.

The null hypothesis represents your current belief. If the data is consistent with it, you do not reject the null hypothesis. But if the data provides enough evidence against it, then you do reject H?. The result of the hypothesis test is either:

Statistical hypothesis testing is not geared towards proving that the null hypothesis is true, but to disprove it instead.

We do not accept the null hypothesis because it is usually very specific

So data that is very inconsistent with the null hypothesis proves 'beyond all reasonable doubt' that the null hypothesis is false.

But, data which is consistent with the null hypothesis does not necessarily prove that the null hypothesis is true.