Question

Americans used to be on average the tallest people in the world. That is no longer the case, according a study by Dr. Richard Steckel, professor of economics and anthropology at the Ohio State University. The Norwegians and Dutch are now the tallest, at 178 centimeters, followed by the Swedes at 177, and then the Americans, with a mean height of 175 centimeters (approximately 5 feet 9 inches). According to Dr. Steckel, “The average height of Americans has been pretty much stagnant for 25 years.” Suppose that we conduct a hypothesis test to investigate whether the population mean height of Americans this year has changed from 175 centimeters.

1. 1. Provide the null and alternative hypotheses.
2. 2. Describe the two ways a correct decision could be made in the context of the problem.
3. 3. Describe what a Type I error would mean in the context of the problem.
4. 4. Describe what a Type II error would mean in the context of the problem.

Answer 1

(a)

Hypotheses are:

(b)

There are two way to make the decision: One is critical value approach and second is p-value approach

(c)

Type I: It is probability of rejecting the true null hypothesis.

That is researcher incorrectly conclude that  the population mean height of Americans this year has changed from 175 centimeters while actually it is 175 centimeters.

(d)

Type I: It is probability of fail to reject the false null hypothesis.

That is researcher incorrectly conclude that  the population mean height of Americans this year has not changed from 175 centimeters while actually it is changed from 175 centimeters.