Question

A double-blind randomized experiment assigned healthy undergraduate students to drink one of four beverages after fasting overnight: water, water with 75 mg of caffeine, water with 75 g of glucose, and water with 75 mg of caffeine and 75 g of glucose. Subjects performed a number of cognitive tasks, including the California Computerized Assessment Package, a computerized reaction time program measuring sustained attention, reaction time, and visual scanning speed. Here are the resulting reaction times (SEM is the standard error of the mean):

Beverage	n	ˉx	SEM
Water	18	389.35	18.50
Water and caffeine	18	320.16	17.98
Water and glucose	18	318.16	17.04
Water, caffeine, and glucose	18	336.44	14.02

What is the null and alternative hypothesis?

Answer 1

The given problem is related ANOVA one way classification. So we have to use Analysis of variance (F-test) technique for testing the equality of four group means.

Under the ANOVA technique

Null Hypothesis (Ho) : All the four group population means are equal (mu1 = mu2 = mu3 = mu4)

Against

Alternative hypothesis (Ha): Not all the four population means are equal.( Not all mu's are equal).