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?
Acceptance or rejection of the null hypothesis depends on what level of significance you are using (e.g., P≤.05, P≤.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.
We test the hypothesis to determine the probability that the differences found are due only to chance.
If you understand the concept, examples abound. I'll let you find them.
Random sample of n=25 scores is obtained from a population of a µ=70 .A treatment is administered to individuals in the sample and after treatment the sample mean M=78 with a standard deviation of s=20
The rejection region in hypothesis testing is a range of values or a region in the distribution of a test statistic that leads to the rejection of the null hypothesis. It is defined based on the significance level (α) chosen for the test.
The z-score is a standardized value obtained by subtracting the population mean from a test statistic and dividing it by the standard deviation. It represents how many standard deviations a given value is away from the mean. The z-score is used for calculating the p-value.
The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. It is used to determine the statistical significance of the results.
When conducting a hypothesis test, if the p-value is smaller than the chosen significance level (typically 0.05 or 0.01), we reject the null hypothesis. This suggests that the observed data provides significant evidence against the null hypothesis in favor of the alternative hypothesis. On the other hand, if the p-value is larger than the significance level, we fail to reject the null hypothesis. This means that there is insufficient evidence to reject the null hypothesis.
Statisticians are asked to complete hypothesis testing because it provides a structured approach to draw conclusions based on data. By formulating a null hypothesis and an alternative hypothesis, statisticians can make informed decisions about the validity of claims and evaluate the strength of evidence.
Hypothesis testing is commonly used in courts to establish guilt or innocence. For example, we may have a null hypothesis stating that a defendant is innocent, and an alternative hypothesis suggesting guilt. The evidence presented in court is then analyzed using hypothesis testing to determine whether the evidence provides significant proof of guilt beyond a reasonable doubt.
In medicine, hypothesis testing is used to evaluate treatments and interventions. Researchers may formulate a null hypothesis stating that a particular treatment has no effect and an alternative hypothesis stating it does. By collecting and analyzing data, they can determine whether the treatment has a statistically significant impact on patients' health outcomes.
In the field of AI, hypothesis testing can be used to assess the performance of different models or algorithms. For example, researchers may have a null hypothesis that Model A is no better than Model B, and an alternative hypothesis that Model A outperforms Model B. By conducting hypothesis tests, they can determine if there is enough evidence to support the alternative hypothesis and choose the better model.