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 a random sample of 100 Americans taken this year shows a mean height of 174 centimeters, and we assume σ = 10 centimeters. If appropriate, test using level of significance α = 0.01 whether the population mean height of Americans this year has changed from 175 centimeters.

Answer 1

Null Hypothesis, 175

Alternative Hypothesis, 175

Here, sample mean, 174, Population std. dev., 10, Sample size, n = 100

Here the significance level, 0.01. This is two tailed test; hence rejection region lies to the both sides. = -2.58 and = 2.58

Test statistic,

z = (174 - 175)/(10/sqrt(100))
z = -1

p-value = 2(z < -1)
p-value = 0.3173

As p-value > 0.01, fail to reject H0
there is not sufficient evidence to conclude that the mean height of Americans is changed from 175cm.