Describe a Type I & Type II Error for each scenario.
$\left(C\right)$ A new cancer screening test reports whether a patient has cancer.

• A. Type I: The test is positive but the patient doesn't have cancer.Type II: The test is negative but the patient has cancer.
• B. Type I: The test is negative but the patient has cancer.Type II: The test is positive but the patient doesn't have cancer.
• C. Type I: The test is positive and the patient has cancer.Type II: The test is negative and the patient doesn't have cancer.
• D. Type I: The test is negative and the patient doesn't have cancer.Type II: The test is positive and the patient has cancer.

Answer: (A)

Verified step by step guidance

1. Step 1: Define the null hypothesis (H0) and the alternative hypothesis (H1) for the cancer screening test scenario. Typically, H0: The patient does not have cancer, and H1: The patient has cancer.
2. Step 2: Understand that a Type I error occurs when the test incorrectly rejects the null hypothesis when it is actually true. In this context, it means the test indicates the patient has cancer when they actually do not (a false positive).
3. Step 3: Understand that a Type II error occurs when the test fails to reject the null hypothesis when the alternative hypothesis is true. Here, it means the test indicates the patient does not have cancer when they actually do (a false negative).
4. Step 4: Summarize the errors clearly: Type I error = false positive (healthy patient diagnosed with cancer), Type II error = false negative (cancer patient diagnosed as healthy).
5. Step 5: Reflect on the implications of these errors in a medical context, such as the consequences of false positives causing unnecessary stress and treatment, and false negatives leading to missed early treatment opportunities.