Question at position 71 A test to screen for a serious but treatable and curable disease is similar to hypothesis testing, with a null hypothesis of no disease, and an alternative hypothesis of disease. If the null hypothesis is rejected treatment will be given. Otherwise, it will not. Assuming the treatment does not have serious side effects, in this scenario it is better to increase the probability of:A test to screen for a serious but treatable and curable disease is similar to hypothesis testing, with a null hypothesis of no disease, and an alternative hypothesis of disease. If the null hypothesis is rejected treatment will be given. Otherwise, it will not. Assuming the treatment does not have serious side effects, in this scenario it is better to increase the probability of:Making a Type 2 error, providing treatment when it is not needed.making a Type 2 error, not providing treatment when it is needed.Making a Type 1 error, not providing treatment when it is needed.making a Type 1 error, providing treatment when it is not needed.Clear my selection

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The question describes a screening test for a serious but treatable and curable disease, with a null hypothesis of no disease and an alternative hypothesis of disease. If the null is rejected, treatment is given; otherwise, it is not. Since the treatment in this scenario does not have serious side effects, the goal is to maximize the chance of giving treatment correctly when disease is present, while balancing the risk of giving treatment when it is not needed.

Option 1: 'Making a Type 2 error, providing treatment when it is not needed.' A Type 2 error means failing to reject the null hypothesis when the disease is present. That would result in missing treatment for individuals who actually have the disease, which is undesirable. Moreover, in this scenario the treatment has no serious side effects, but this option focuses on over-treating, which isn’t the error described.

Option 2: 'making a Type 2 error, not providing treatment when it is needed.' This describes a false negative: not treating someone who has the disease. This is precisely the outcome Type 2 errors cause and is not advantageous.

Option 3: 'Making a Type 1 error, not providing treatment when it is needed.' A Type 1 error is a false positive (treating when there is no disease). This option mixes the definitions (not providing treatment) with Type 1 error, which is inconsistent. Additionally, not providing treatment when it is needed would be more aligned with a Type 2 error, not a Type 1 error.

Option 4: 'making a Type 1 error, providing treatment when it is not needed.' This is the classic false positive: you reject the null (believe disease is present) when it is not, leading to providing treatment to some individuals who don’t actually need it. Given the assumption that treatment has no serious side effects, increasing the probability of this error is acceptable because it minimizes the more harmful Type 2 errors (missing true disease) and avoids withholding beneficial treatment.

In summary, to maximize beneficial treatment administration in this setup (where treatment is safe), one would favor increasing the chance of false positives (Type 1 errors) over missing true disease (Type 2 errors). The preferable misclassification here is the one that results in treating some disease-free individuals rather than missing individuals who truly have disease.

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