How is the rejection region defined and how is that related to the z-score and the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?
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I hope this helps. Acceptance or rejection of the null hypothesis depends on what level of significance you are using (e.g., P¡Ü.05, P¡Ü.01) and whether you are using a one-tailed or two-tailed test. If the Z score has that probability or less, reject the null hypothesis. If not, accept the null hypothesis.
The rejection region is a critical region in hypothesis testing that helps determine whether to reject or fail to reject the null hypothesis. It is a range of values in which, if the test statistic falls within that range, you reject the null hypothesis. The rejection region is defined based on the significance level, denoted as alpha (α), which represents the maximum probability of making a Type I error (rejecting a true null hypothesis).
The z-score is used to determine the distance between a raw score and the mean of a distribution in terms of standard deviations. It allows us to standardize and compare values across different normal distributions. In hypothesis testing, the z-score is used to calculate the p-value.
The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value under the assumption that the null hypothesis is true. It measures the strength of evidence against the null hypothesis. If the p-value is less than or equal to the significance level (α), typically 0.05, then we reject the null hypothesis. Otherwise, if the p-value is greater than α, we fail to reject the null hypothesis.
Statisticians are asked to complete hypothesis testing because it provides a systematic and evidence-based approach to decision-making. By formulating null and alternative hypotheses, collecting data, calculating test statistics, and comparing them to predetermined critical values or p-values, statisticians can draw conclusions about population parameters and make informed judgments about the associations and differences they are investigating.
Hypothesis testing is widely used in various fields. For example, in courts, a hypothesis test can be conducted to determine whether a defendant is guilty or not guilty. In medicine, researchers may conduct hypothesis tests to evaluate the effectiveness of a new drug by comparing it to a placebo. In my area as an AI bot, hypothesis testing could be used to measure user satisfaction before and after implementing an update to the bot and assess whether the update had a statistically significant impact on satisfaction.