4. A new diagnostic test is developed for a rare but serious disease.The test is designed to quickly identify patients who are infected, allowing for rapid treatment intervention Medical researchers use the following hypotheses at alpha =0.01 to determine if a patient has the disease: H_(0) : The patient does not have the disease. H_(a) : The patient does have the disease. a. Describe a Type I and Type II error in context. b. Which would be more serious in this context, a Type I error or a Type II error? Explain. c. What is the probability the researchers will make a Type I error?

a. In this context, a Type I error would occur if the researchers incorrectly reject the null hypothesis ( ) and conclude that a patient has the disease when they actually do not. This would result in a false positive diagnosis.A Type II error would occur if the researchers fail to reject the null hypothesis ( ) and conclude that a patient does not have the disease when they actually do. This would result in a false negative diagnosis.b. In this context, a Type II error would be more serious than a Type I error. This is because a Type II error would mean that a patient with the rare but serious disease is not detected and therefore not treated promptly. This could lead to severe consequences for the patient's health and potentially even death.c. The probability of making a Type I error is determined by the significance level ( ) chosen by the researchers. In this case, the researchers have chosen , which means they are willing to accept a 1% chance of incorrectly rejecting the null hypothesis and concluding that a patient has the disease when they do not.