For Exercises 3.42 to 3.44, see pages 144–145; for 3.45, see page 146; for 3.46 and 3.47, see page 147; for 3.48 and 3.49, see page 150; for 3.50 and 3.51, see page 152; for 3.52, see page 153; for 3.53 and 3.54, see page 154; and for 3.55, see page 156.
3.51 Statistical significance.
The financial aid office of a university asks a sample of students about their employment and earnings. The report says that “for academic year earnings, a significant difference was found between the sexes, with men earning more on the average. No significant difference was found between the earnings of black and white students.” Explain the meaning of “a significant difference” and “no significant difference” in plain language.
3.51
“A significant difference” means that the difference found between the sexes is unlikely to have occurred by chance alone and that sex is likely a contributor to the difference found in earnings. “No significant difference” means that the difference between black and white students is small enough that it is likely due to just chance. Whichever group happens to have more or less earnings, the difference is not due to race.