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 monthsNow, 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)