Pvalue Formula
The Pvalue is short for probability value. It defines the probability of getting a result that is either the same or more extreme than the other actual observations. The Pvalue represents the probability of occurrence of the given event. The Pvalue is used as an alternative to the rejection point to provide the least significance for which the null hypothesis would be rejected. The smaller the Pvalue, the stronger is the evidence in favor of the alternative hypothesis given observed frequency and expected frequency.
Pvalue  Description  Hypothesis Interpretation  
Pvalue ≤ 0.05 

Rejected  
Pvalue > 0.05 

Accepted or it “fails to reject”.  
Pvalue > 0.05  The Pvalue is near the cutoff. It is considered as marginal  The hypothesis needs more attention. 
What Is the Pvalue Formula?
Pvalue is an important statistical measure, that helps to determine whether the hypothesis is correct or not. Pvalue always only lies between 0 and 1. The level of significance(α) is a predefined threshold that should be set by the researcher. It is generally fixed as 0.05. The formula for the calculation for Pvalue is:
Step 1: Find out the test static Z is
\(Z = \frac{\hat{p}p 0}{\sqrt{\frac{p 0(1p 0)}{n}}}\)
Where,
\(\hat{p}=\) Sample Proportion
\(\mathrm{P0}=\) assumed population proportion in the null hypothesis
N = sample size
Step 2: Look at the Ztable to find the corresponding level of P from the z value obtained.
Solved Example Using Pvalue Formula
Example 1:
A statistician is testing the hypothesis H0: μ = 120 using the approach of alternative hypothesis Hα: μ > 120 and assuming that α = 0.05. The sample values that he took are as
n =40, σ = 32.17 and x̄ = 105.37. What is the conclusion for this hypothesis?
Solution:
We know that,
\(\sigma_{\bar{x}}=\dfrac{\sigma}{\sqrt{n}}\)
Now substitute the given values
\(\sigma_{\bar{x}}=\dfrac{32.17}{\sqrt{40}}=5.0865\)
As per the test static formula, we get
t = (105.37 – 120) / 5.0865
Therefore, t = 2.8762
Using the ZScore table, finding the value of P(t > 2.8762)
we get,
P (t < 2.8762) = P(t > 2.8762) = 0.003
Therefore,
If P(t > 2.8762) =1  0.003 =0.997
P value =0.997 > 0.05
As the value of p > 0.05, the null hypothesis is accepted.
Answer: Null hypothesis is accepted.
Example 1:
What conclusion should be made with respect to an experiment when the significance level is 0.05 (α = 0.05)?
Solution:
Since the pvalue of 0.068 is greater than α = 0.05, it would fail to reject the null hypothesis.
Answer: As the value of p < 0.05, the null hypothesis is rejected.
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