What is The p-Value Method in Hypothesis Testing

Let’s get started with the p-value method of making a decision.

Prof. Tricha has defined p-value as the probability that the null hypothesis will not be rejected. This statement is not the technical (or formal) definition of p-value; it is used for better understanding of the p-value.

The higher the p-value, the higher is the probability of failing to reject a null hypothesis. And the lower the p-value, the higher is the probability of the null hypothesis being rejected.

After formulating the null and alternate hypotheses, the steps to follow in order to make a decision using the p-value method are as follows:

1. Calculate the value of the z-score for the sample mean point on the distribution.

2. Calculate the p-value from the cumulative probability for the given z-score using the z-table.

3. Make a decision on the basis of the p-value (multiply it by 2 for a two-tailed test) with respect to the given value of α (significance value).

To find the correct p-value from the z-score, find the cumulative probability first, by simply looking at the z-table, which gives you the area under the curve till that point.

Situation 1: The sample mean is on the right side of the distribution mean (the z-score is positive).

Example: z-score for sample point = + 3.02

Cumulative probability of the sample point = 0.9987

For a one-tailed test: p = 1 - 0.9987 = 0.0013

For a two-tailed test: p = 2 (1 - 0.9987) = 2 * 0.0013 = 0.0026

Situation 2: The sample mean is on the left side of the distribution mean (the z-score is negative).

Example: The z-score for the sample point = -3.02                

Cumulative probability of the sample point = 0.0013

For a one-tailed test: p = 0.0013

For a two-tailed test: p = 2 * 0.0013 = 0.0026

You learnt how to perform the three steps of the p-value method through the AC sales problem as well as the product life cycle comprehension problem given above.