Researchers at the University of Boston's Children's Hospital and Harvard Medical School analyzed records of breast cancer screening and diagnostic evaluations. † Discussing the downsides of the screening process, the article states that the rate of false-positives is higher than previously thought, and that false-positives lead to unnecessary medical follow-up that can be costly. Suppose that screening is used to decide between a null hypothesis of Ho: no cancer is present and an alternative hypothesis of H: cancer is present. (Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.) (a) Would a false-positive (thinking that cancer is present when in fact i is not) be a Type I error or a Type II error? O Type I error O Type II error (b) Describe a Type I error in the context of this problem, and discuss the possible consequences of making a Type I error. O Coming to the conclusion that cancer is present when, in fact, it is not. Treatment may be started when, in fact, it is not necessary. O Coming to the conclusion that cancer is present when, in fact, it is not. No treatment will be prescribed when, in fact, treatment is necessary. O Coming to the conclusion that no cancer is present when, in fact, it is present. No treatment will be prescribed when, in fact, treatment is necessary. O Coming to the conclusion that no cancer is present when, in fact, it is present. Treatment may be started when, in fact, it is not necessary. (c) Describe a Type II error in the context of this problem, and discuss the possible consequences of making a Type II error. O Coming to the conclusion that cancer is present when, in fact, it is not. Treatment may be started when, in fact, it is not necessary. O Coming to the conclusion that cancer is present when, in fact, it is not. No treatment will be prescribed when, in fact, treatment is necessary. O Coming to the conclusion that no cancer is present when, in fact, it is present. No treatment will be prescribed when, in fact, treatment is necessary. O Coming to the conclusion that no cancer is present when, in fact, it is present. Treatment may be started when, in fact, it is not necessary. (d) Which type of error are the researchers concerned about when they say that false-positives lead to unnecessary medical follow-up? Explain why it would be reasonable to use a small significance level. O Researchers are concerned about a Type I error. Using a small significance level reduces the probability of incorrectly diagonosing a patient with cancer, making unncessary medical follow-ups less common. O Researchers are concerned about a Type II error. Using a small significance level reduces the probability of incorrectly diagonosing a patient with cancer, making unncessary medical follow-ups less common. O Researchers are concerned about a Type I error. Using a small significance level reduces the probability of failing to detect cancer in a patient who actually has cancer, making unncessary medical follow-ups less common.