The document defines p-value as a statistical measurement used to validate a hypothesis against observed data, with lower p-values indicating greater statistical significance. It provides an example of using a p-value to test the hypothesis that the proportion of people speaking Hindi in a village is higher than 27% based on survey data. The p-value is calculated to be 0.0183, which is less than the 5% significance level, so the null hypothesis that the proportion is 27% is rejected.

1. P-VALUE:

2. DEFINITION:
 A statistical measurement used to validate a
hypothesis against observed data.
 The lower the P-Value, the greater the statistical
significance of the observed difference.

3. P-VALUE FORMULA:

4. P-VALUE
 Meaning of P-Value of 0.001
 Use of P-Value in comparison of two different
results of a hypothesis

5. EXAMPLE:
 27% of people in India speak Hindi as per a research study. A researcher is
curious if the figure is higher in his village. Hence, the frames the null and
alternate hypotheses. He tests H0: p = 0.27. Ha: p > 0.27. Here, p is the
proportion of people in the village who speak Hindi. He commissions a survey
in his village to find out the number of people who can speak Hindi. He finds
that 80 out of 240 people sampled can speak Hindi. Find out the approximate
p-value for the researcher’s test if we were to assume that the necessary
conditions are met, and the significance level is 5%.
Here, the sample size n = 240,
p0 is the population proportion. We will
have to find the sample proportion
Sample Proportion= 80 / 240
Sample Proportion= 0.33

6. Z Statistic
Calculation of Z Statistic
=0.33 – 0.27 / √ 0.27 * (1 – 0.27 ) / 240
Z Statistic will be –

7. Z Statistic will be –
Z = 2.093696
P-Value will be –
P Value = 0.0183
Since the p-value is less than the significant level of 0.05 (5%), we reject
the null hypothesis.

8. THANK YOU.