Final answer:
The test statistic is calculated by conducting statistical tests, such as 2-SampZTest, z-Test, T-Test, or chi-square tests, to determine the significance of results against a null hypothesis.
Step-by-step explanation:
Calculating the test statistic involves using statistical tests to determine the significance of the results by comparing the gathered data to a null hypothesis. Depending on the type of data and the hypothesis tested, different statistical tests are applied, and the TI-83/84 calculators have built-in functions that can be used to perform these tests efficiently.
For example, when conducting a 2-SampZTest on the TI-83/84 calculator, you would input the standard deviations, sample means, sample sizes, and then specify the alternative hypothesis before calculating the p-value and the test statistic.
Similarly, when conducting a z-Test, one would input the hypothesized mean, standard deviation, sample mean, sample size, and select the appropriate alternative hypothesis to obtain the test statistic (z-score) and p-value.
These test statistics and p-values are crucial in decision-making about the hypotheses. A small p-value (typically less than 0.05) indicates strong evidence against the null hypothesis, leading to its rejection. Different tests such as 2-SampTTest, T-Test, and chi-square tests are used for different study designs and data types.