Mike is planning to go on a cross country drive with his friends. His German min
ID: 3306708 • Letter: M
Question
Mike is planning to go on a cross country drive with his friends. His German minivan has been reliable but has 90,000 miles on it. he wants to determine if the vehicle is sound for the trip. He did a visual inspection of the vehicle and checked the oil and antifreeze levels and everything appears to look okay. The null and alternative hypotheses are . H0: minivan is mechanically sound Ha: minivan is not mechanically sound (a) What would a Type-I error be (b) What would a type-II error be (c) Which error is more significant in this situation and why? (d) What impact would going to the mechanic have on the Type-I and Type-II errors and whyMike is planning to go on a cross country drive with his friends. His German minivan has been reliable but has 90,000 miles on it. he wants to determine if the vehicle is sound for the trip. He did a visual inspection of the vehicle and checked the oil and antifreeze levels and everything appears to look okay. The null and alternative hypotheses are . H0: minivan is mechanically sound Ha: minivan is not mechanically sound (a) What would a Type-I error be (b) What would a type-II error be (c) Which error is more significant in this situation and why? (d) What impact would going to the mechanic have on the Type-I and Type-II errors and why
Mike is planning to go on a cross country drive with his friends. His German minivan has been reliable but has 90,000 miles on it. he wants to determine if the vehicle is sound for the trip. He did a visual inspection of the vehicle and checked the oil and antifreeze levels and everything appears to look okay. The null and alternative hypotheses are . H0: minivan is mechanically sound Ha: minivan is not mechanically sound (a) What would a Type-I error be (b) What would a type-II error be (c) Which error is more significant in this situation and why? (d) What impact would going to the mechanic have on the Type-I and Type-II errors and why
Explanation / Answer
Given the hypothesis:
H0: Minivan is mechanicallly sound and
Ha: Minivan is not mechanically sound
1) Type I error: The Incorrect Rejection of the true Null Hypothesis, i.e in this case, Although the minivan is mechanically sound, we think it is not mechanically sound.
2) Type II error: The incorrect retention of a false null Hypothesis, i.e The minivan is not mechanically sound, but we think it is mechanically sound.
3) In this situation, Type II error is more significant. It means, that there is trouble with the running of the minivan, but since we think that there is no trouble and therefore, somewhere, the minivan will break down.
4) Based on Type I error, If I go to the mechanic, we would find out that the minivan is fine, and we will end up having wasted some time and maybe some money.
Based on Type II error, when we go to the mechanic, we would be thinking that it would be a waste of time since we think that the minivan is fine. We would definitely find out that it was not a waste of time, and we would have to shell some money out of our pockets on repairs on the minivan.