Test Statistic

A

A test statistic is a value calculated from a sample and used to accept or reject the null hypothesis concerning a population's parameter.

A test statistic is a value calculated from a sample and used to make inferences about a population. The purpose of using a test statistic is to assess whether the data from the sample provides evidence to support or reject a specific hypothesis, known as the null hypothesis.

In hypothesis testing, we start with a null hypothesis, denoted as H0, which represents a claim or statement that we want to test. The null hypothesis typically assumes that there is no significant difference or relationship between variables in the population. For example, H0 might state that the mean of a population is equal to a specific value.

To test the null hypothesis, we collect a sample from the population of interest. The test statistic is then calculated using the sample data and a predefined statistical formula or procedure. The test statistic is a numerical value that summarizes the information contained in the sample and helps us evaluate the likelihood of observing such data if the null hypothesis were true.

The test statistic is compared to a critical value or a p-value to determine the conclusion of the hypothesis test. The critical value is a predetermined threshold or cutoff point that helps determine whether the test statistic is extreme enough to reject the null hypothesis. The p-value, on the other hand, represents the probability of observing a test statistic as extreme as or more extreme than the one calculated from the sample, assuming the null hypothesis is true.

Now, let's go through the answer choices:

A. A test statistic is indeed a value calculated from a sample and used to accept or reject the null hypothesis. This choice correctly describes the purpose and function of a test statistic in hypothesis testing.

B. Option B states that all of the answers are correct. While the statement in option A is accurate, it doesn't cover all the aspects of a test statistic. Hence, option B is not the correct choice.

C. This option states that a test statistic is a sample value used to measure a population parameter. However, it is important to note that the test statistic is not a direct measure of a population parameter itself. Instead, it is a value derived from the sample that allows us to make inferences about the population parameter. Therefore, option C is not the correct choice.

D. A parameter characterizing the null hypothesis is not the correct definition of a test statistic. A parameter refers to a fixed characteristic or numerical measure of a population, whereas the test statistic is calculated from the sample data. Therefore, option D is not the correct choice.

In summary, the correct answer is A. A test statistic is a value calculated from a sample and used to accept or reject the null hypothesis.