Describe type I and type II errors for a hypothesis test of the indicated claim.
ID: 3226312 • Letter: D
Question
Describe type I and type II errors for a hypothesis test of the indicated claim. A police station publicizes that at most 60% of applicants become police officers. Describe the type I error. Choose the correct answer below. A. A type I error will occur when the actual proportion of applicants who become police officers is at least 0.60, but you fail to reject H_0: p greaterthanorequalto 0.60. B. A type I error will occur when the actual proportion of applicants who become police officers is at most 0.60, but you fail to reject H_0: p lessthanorequalto 0.60. C. A type I error will occur when the actual proportion of applicants who become police officers is at most 0.60, but you reject H_0: p lessthanorequalto 0.60. D. A type I error will occur when the actual proportion of applicants who become police officers is at least 0.60, but you fail to reject H_0: p greaterthanorequalto 0.60. Describe the type II error Choose the correct answer below. A A type II error will occur when the actual proportion of applicants who become police officers is less than 0.60, but you fail to reject H_0: p lessthanorequalto 0.60. B. A type II error will occur when the actual proportion of applicants who become police officers is more than 0.60, but you fail to reject H_0: p lessthanorequalto 0.60. C. A type II error will occur when the actual proportion of applicants who become police officers is less than 0.60, but you fail to reject H_0: p greaterthanorequalto 0.60. D. A type II error will occur when the actual proportion of applicants who become police officers is more than 0.60, but you fail to reject H_0: p lessthanorequalto 0.60.Explanation / Answer
Type I error:
This kind of error occurs when a true null hypothesis is incorrectly rejected. Here the null hypothesis is that at most 60% of the applicants become police officers. Assuming this to be true now, type I error occurs when this null hypothesis is rejected. Therefore c) is the correct answer here.
Type II error:
This kind of error occurs when the false null hypothesis is incorrectly not rejected. Therefore here the type II error would occur when the proportion of the applicants who become police officers is more than 0.6 but we fail to reject H0:p < 0.6
Therefore b) is the correct answer here.