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

[At 2:13 and 3:00, the Prof mistakenly mentions that you accept a null hypothesis. It should be failing to reject the null hypothesis]

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:

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

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

- 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 can download the z-table from the attachment below. It will be useful in the subsequent questions.

**Let’s solve the following problem stepwise** to consolidate your learning on how to make a decision about any hypothesis using the p-value method.

You are working as a data analyst at an auditing firm. A manufacturer claims that the average life of its product is 36 months. An auditor selects a sample of 49 units of the product and calculates the average life to be 34.5 months. The population standard deviation is 4 months. Test the manufacturer’s claim at a 3% significance level using the p-value method.

First, **formulate the hypotheses** for this two-tailed test, which would be:

` H₀: μ = 36 months and H₁: μ ≠ 36 months`

Now, you need to follow the three steps to **find the p-value and make a decision**.

Try out the three-step process by answering the following questions.

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.

FREQUENTLY ASKED QUESTIONS (FAQ)