Question

Sally’s Toyota Corolla is an old car but it served her well. She is planning to take a trip to the Grand Canyon from the east coast. Before starting the trip she checks the car to determine if the car is in good mechanical condition. She is knowledgeable about cars but no expert. The null and alternative hypotheses are given below.

H0: the Corolla is in good mechanical condition

Ha: the Corolla is not in good mechanical condition

(a) What would a Type-I error be in this situation?

(b) What would a type-II error be in this situation?

(c) Which error is more consequential in this situation and why?

(d) If Sally took the Corolla out to a certified mechanic for a checkout, what would be the likely impact on the magnitude of the Type-I and Type-II errors and why?

Answer 1

­Given information

A car is checked for its mechanical condition.

Null hypothesis

The Corolla is in good mechanical condition.

Alternative hypothesis.

The corolla is not in good mechanical condition.

(a)

Type I error is when the null hypothesis is rejected given it is true.

In this question Type I error is

Reject the hypothesis that Corolla is in good mechanical condition given it is actually in good condition.

(B)

Type II error is when the null hypothesis is failed to be rejected given it is not true.

In this question Type II error is

Accept the hypothesis that Corolla is in good mechanical condition given it is actually not in good condition.

(C)

Type II error will be more consequential, acknowledging the hypothesis testing result, she will start the trip with the car which is actually not in good mechanical condition. Driving that car might cause death for her.

(D)

If a certified mechanic checks the car, the magnitude of type II error as well as Type one error will certainly be reduced significantly. Because the certified mechanic will have more precision level.

Since the type II error Is fatal, therefore, he will fix type two error first and then will try to reduce type I error.