Question

What does the "P-value" represent? Examples

Answer 1

The p-value in the testing of hypothesis is the marginal level of significance which is the probability of the occurrence of the given event. In simple words, the p-value is the smallest level of significance at which we reject the null hypothesis H₀. We find the p-value by using distribution related to the test. For example, if we are using one sample t test for the population mean, then we use t-table or excel for finding the p-value. Let us see one simple example. Suppose, we want to check whether the average data use of the Smartphone users is more than 1 GB. For checking this claim, we use random sample data with size 25 which gives sample mean as 1.25 GB and sample standard deviation as 0.50 GB. This is an upper tailed test. We have

t = (Xbar - µ)/[S/sqrt(n)] = (1.25 – 1)/[0.50/sqrt(25)] = 0.25/0.1 = 2.5

df = n – 1 = 25 – 1 = 24

P-value = 0.0098

(by using t-table)

So, this P-value represents the smallest level of significance at which we reject the null hypothesis.

For the significance levels greater than 0.0098, we do not reject the null hypothesis.