Question

How do you calculate the P-value in a hypothesis test?

Answer 1

Hint:The P-value approach is involved to determine the “likely” or the “unlikely” determining the probability by assuming that the null hypothesis were true which observes the more extreme test statistic in the direction. There are two cases for the p-value.
a.) If the P-value is small, when it is less than or equal to $\alpha $, then is unlikely
b.) If the P-value is greater, when it is more than $\alpha $, then is likely

Complete step by step solution:
When the P-value is less than or equal to $\alpha $ then in the favor of the alternative hypothesis, the null hypothesis is rejected and when the P-value is greater, then the null hypothesis is not rejected.
The following steps are followed in using the P-value approach which conducts hypothesis tests.
a.) First of all specify the null and the alternative hypothesis
b.) Then assume that the null hypothesis is true based on the sample data and then calculate the value of the test statistic.
c.) Perform the hypothesis test for the population mean $\mu $, using the t-statistic
${t^*} = \dfrac{{\overline x - \mu }}{{s/\sqrt n }}$which follows a t-distribution with $(n - 1)$ degrees of freedom.
d.) Then by finding the distribution of the test statistic and then calculate the P-value.
e.) Pre-set the significance level $\alpha $ and making the probability type I error to be such
small as \[0.01,0.05\;{\text{or 0}}{\text{.10}}\]
f.) Compare the P-value to $\alpha $ and find whether the P-value is less than, equal to or
greater than alpha and accordingly find the null hypothesis it is rejected or not.

Note: Always remember the P-value and comparison between the P-value and the alpha. When the P-value is less than or equal to $\alpha $ then in the favor of the alternative hypothesis, the null hypothesis is rejected and when the P-value is greater, then the null hypothesis is not rejected.