Question

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. A consumer advocacy group claims that the mean mileage for the Carter Motor​ Company's new sedan is less than 32 miles per gallon. Identify the type I error for the test.

Answer 1

Answer:

Type I error: Concluding that mean mileage is less than 32 miles per hour when actually it is greater than or equal to 32 miles per gallon.

Step-by-step explanation:

We are given the following in the question:

Hypothesis:

Mean mileage for the Carter Motor​ Company's new sedan

We can design the null hypothesis and alternate hypothesis as:

$H_{0}: \mu \geq 32\text{ miles per gallon}\\H_A: \mu < 32\text{ miles per gallon}$

Type I error:

• It is the false positive error.
• It is the error of rejection a true hypothesis.

Type II error:

• It is the false negative error.
• It is the non rejection of a false null hypothesis.

Thus, type I error for the given hypothesis is concluding that mean mileage is less than 32 miles per hour when actually it is greater than or equal to 32 miles per gallon.

Type II error would be concluding that mean mileage is greater than or equal to 32 miles per gallon when actually it is less than 32 miles per gallon.