For Exercises 51–58, do the following:

  1. State the hypotheses and the rejection rule.
  2. Calculate .
  3. Find the -value.
  4. State the conclusion and the interpretation.

Question 9.164

58. Americans' Height. Americans used to be, on average, the tallest people in the world. That is no longer the case, according to 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.”5 Suppose a random sample of 100 Americans taken this year shows a mean height of 174 centimeters, and we assume . Test, using level of significance , whether the population mean height of Americans this year has changed from 175 centimeters.