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Watch the video: What are the steps in hypothesis testing for the p-value method? Write two sentences to tell what happens for each step. (You need to follow these steps in the assignment and in the homework for Weeks 6 and 7. The more you explain here, the easier it will be for you in the homework/project). What is the goal of hypothesis testing? What are null and alternative hypotheses?

Type I and Type II errors can occur. Define each type of error. Let's say a woman visits the doctor with a very sore throat. The doctor runs a strep throat test, and the results are positive for strep. The doctor tells her that she has strep throat.

The woman tells the doctor that he has made a mistake and leaves the office. What type of error could this scenario show, and why? Tie this to what you would declare as your null hypothesis.

Paper For Above instruction

Hypothesis testing is a critical process in statistics used to make inferences about a population based on sample data. The steps in hypothesis testing for the p-value method involve first formulating the null hypothesis (H0) and alternative hypothesis (Ha), which establish a claim to be tested. Next, a test statistic is calculated from the sample data, which measures how much the data deviate from what we would expect under the null hypothesis. The third step involves calculating the p-value, which quantifies the probability of observing data as extreme or more extreme than the sample, assuming the null hypothesis is true. Finally, the decision rule is applied: if the p-value is less than the predetermined significance level (alpha), we reject the null hypothesis; if not, we fail to reject it, leading to conclusions about the population.

The goal of hypothesis testing is to determine whether there is enough statistical evidence from sample data to support or reject a specific claim about a population parameter. The null hypothesis (H0) typically states that there is no effect or no difference, serving as a default assumption, while the alternative hypothesis (Ha) represents the assertion we seek to support, such as the presence of an effect or difference.

A Type I error occurs when the null hypothesis is true but is incorrectly rejected, indicating a false positive. Conversely, a Type II error occurs when the null hypothesis is false but is wrongly failed to reject, leading to a false negative. In the scenario where a woman visits the doctor with a sore throat, and the test results are positive for strep, the doctor concludes she has strep throat. However, if this diagnosis is incorrect—say the woman actually does not have strep but is told she does—it illustrates a potential Type I error. This is because the null hypothesis, which could be that the woman does not have strep (H0: no strep), was rejected even if it was true, resulting in a false positive diagnosis.

This error highlights the importance of setting an appropriate significance level during hypothesis testing, as it influences the likelihood of making Type I errors. Medical tests aim to balance sensitivity (detecting true positives) and specificity (avoiding false positives). In practice, the doctor’s null hypothesis might be that the patient does not have strep throat (H0: no strep), and rejecting this null hypothesis based on a positive test result could lead to a Type I error if the test is false positive. Therefore, understanding and controlling these errors are crucial in clinical decision-making to avoid unnecessary treatment or missed diagnoses.

References

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• U.S. Food & Drug Administration. (2021). Understanding the Results of Diagnostic Tests. FDA.gov.
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• Wasserstein, R. L., & Lazar, N. A. (2016). The ASA's Statement on p-Values: Context, Process, and Purpose. The American Statistician, 70(2), 129-133.
• Lehmann, E. L., & Romano, J. P. (2005). Testing Statistical Hypotheses. Springer.
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