P-Values: Calculating The Evidence Against Null Hypothesis And For Alternative Hypothesis

-The probability that such an extreme test statistic occurs, assuming the null hypothesis is true-Found by comparing the test statistic to values from statistical tables

P-value

The probability that such an extreme test statistic occurs, assuming the null hypothesis is true, is known as the p-value. The p-value provides a measure of the evidence against the null hypothesis and in favor of the alternative hypothesis.

The calculation of the p-value involves comparing the test statistic to the values from a statistical distribution. This distribution is determined by the null hypothesis and the type of test being conducted. For example, if we are conducting a t-test, then we use the t-distribution to calculate the p-value.

Once we have calculated the test statistic and determined the appropriate distribution, we can find the p-value by looking up the probability of observing a value as extreme or more extreme than our test statistic. This is done using statistical tables or computer software.

If the p-value is very small (typically less than 0.05), we reject the null hypothesis in favor of the alternative hypothesis. This suggests that there is strong evidence that the alternative hypothesis is true. On the other hand, if the p-value is large (typically greater than 0.05), we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to suggest that the alternative hypothesis is true.

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