What is the test statistic and how do you find it

the test statistic and how do you find it are the following

Explanation:

A test statistic is a random variable that is calculated from sample data and used in a hypothesis test. You can use test statistics to determine whether to reject the null hypothesis. The test statistic compares your data with what is expected under the null hypothesis. The test statistic is used to calculate the p-value.

A test statistic measures the degree of agreement between a sample of data and the null hypothesis. Its observed value changes randomly from one random sample to a different sample. A test statistic contains information about the data that is relevant for deciding whether to reject the null hypothesis. The sampling distribution of the test statistic under the null hypothesis is called the null distribution. When the data show strong evidence against the assumptions in the null hypothesis, the magnitude of the test statistic becomes too large or too small depending on the alternative hypothesis. This causes the test's p-value to become small enough to reject the null hypothesis.

For example, the test statistic for a Z-test is the Z-statistic, which has the standard normal distribution under the null hypothesis. Suppose you perform a two-tailed Z-test with an α of 0.05, and obtain a Z-statistic (also called a Z-value) based on your data of 2.5. This Z-value corresponds to a p-value of 0.0124. Because this p-value is less than α, you declare statistical significance and reject the null hypothesis.