15.30 Brains at work. When our brains store information, complicated chemical changes take place. In trying to under stand these changes, researchers blocked some processes in brain cells taken from rats and compared these cells with a con trol group of normal cells. They say that "no differences were seen" between the two groups in four response variables. They give P-values 0.45, 0.83, 0.26, and 0.84 for these four compar isons.'^

(a) Say clearly what P -value P = 0.45 says about the response that was observed.

(b) It isn't literally true that "no differences were seen." Tliat is, the mean responses were not exactly alike in the two groups.
Explain what the researchers mean when they give P = 0.45 and say "no differences were seen."