Answer:
Step-by-step explanation:
A test statistic is a numerical value calculated from sample data during hypothesis testing. It is used to assess whether there is enough evidence to reject or fail to reject a null hypothesis. In hypothesis testing, researchers make assumptions about a population parameter (e.g., mean, proportion) and then collect sample data to test whether the assumed parameter value is plausible or not.
The general process of hypothesis testing involves the following steps:
Formulate the null hypothesis (H0): This is a statement of no effect or no difference. It represents the status quo or the assumption to be tested. For example, "The average height of males is equal to 175 cm."
Formulate the alternative hypothesis (Ha or H1): This is the statement that contradicts the null hypothesis and represents the effect or difference that researchers want to find evidence for. Using the previous example, the alternative hypothesis might be, "The average height of males is not equal to 175 cm."
Choose a significance level (alpha): This is the probability of making a Type I error, which is the probability of rejecting the null hypothesis when it is true. Commonly used significance levels are 0.05 (5%) and 0.01 (1%).
Collect sample data: Researchers gather data from a sample to estimate population parameters.
Calculate the test statistic: The test statistic is a function of the sample data and is chosen to measure the difference between the sample result and the value expected under the null hypothesis.
Compare the test statistic with the critical value or p-value: The critical value(s) are pre-determined values used to define the rejection region(s). The p-value, on the other hand, is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.
Make a decision: If the test statistic falls in the rejection region (i.e., it is beyond the critical value(s) or has a p-value less than the significance level), the null hypothesis is rejected in favor of the alternative hypothesis. If the test statistic does not fall in the rejection region (i.e., it is within the critical value(s) or has a p-value greater than the significance level), the null hypothesis is not rejected.
The choice of test statistic depends on the type of data and the hypothesis being tested. Common test statistics include t-statistics for means, z-statistics for proportions, F-statistics for variances, and chi-square statistics for categorical data.