Describe type I and type Il errors for a hypothesis test of the indicated claim.
ID: 2906794 • Letter: D
Question
Describe type I and type Il errors for a hypothesis test of the indicated claim. A police station publicizes that at most 25% of applicants become police officers Describe the type l error. Choose the correct answer below O A. A type l error will occur when the actual proportion of applicants who become police officers is at most 0.25, but you fail to reject Ho: p 0.25. 0 B. A type l error will occur when the actual proportion of applicants who become police officers is at least 0.25, but you reject Ho: p20.25. ? C. A type l error will occur when the actual proportion of applicants who become police officers is at most O25, but you reject Ho: p s 0.25. 0 D. A type l error will occur when the actual proportion of applicants who become police officers is at least 0.25, but you fail to reject Ho: p2 0.25. Describe the type Il error. Choose the correct answer below ?A. A type ll error will occur when the actual proportion of applicants who become police officers is more than 0.25, but you fail to reject Ho' ps 0.25. O B. A type ll error will occur when the actual proportion of applicants who becomepolice officers is less than 0.25, but you reject Ho: p 20.25. C. A type Il error will occur when the actual proportion of applicants who becomepolice officers is less than 0.25, but you fail to reject Ho: ps0.25 OD. A type Il error will occur when the actual proportion of applicants who becomepolice officers is more than 0.25, but you reject Ho: p20.25.Explanation / Answer
Type I error:
option (c) is correct.
Reason:
Type I error occurs when the true null hypothesis is rejected. Here the null hypothesis is that at most 25% of the applicants become police officers. Assuming this to be true now, type I error occurs when this null hypothesis is rejected.
Thus, Option (C) is correct.
Type II Error:
Type II error occurs when the false null hypothesis is not rejected. Here the type II error would occur when the proportion of the applicants who become police officers is more than 0.25 but we fail to reject H0:p < 0.25
Thus, Option (A) is correct.