Question
Identify the populations and the response variable. Then give k. ni, and N. Finally give the degrees of freedom of the ANOVA F test to the following question 24.26
Exercises 24 25 m e the mean restonses in seurraí jstrulatims. For each ma idennify the popr alations and the response ankable. Then wd N. Fially, give the degrees of freedcon of the serting , the 24.25 Biological rhythms. Are you a morming person, an evening person, oe neither! Does this personality trait affect how well you perform? A sample of 100 studerits took a psy chological test that found 16 morning people, 30 evening peo- ple, and 54 who were neither. All the students then took a test of their ability to memorize at 8 A.M. and again at 9 P.M. You analyze the score at 8 A.M. minus the score at 9 P.M 24.26 Caffeine and sugar. A double-blind randomized exper iment assigned healthy undergraduate students to drink one of four beverages after fasting overnight: water, water with of four beverages atter fasting ove 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 Califomia Comput- erized Assessment Package, a computerized reaction time pro gram measuring sustained attention, reaction time, and visual scanning speed. Here are the resulting reaction times (SEM is the standard erroe of the mean): Beverage 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 24.27 A medical study. The Québec (Canada) Cardiovascu- lar Study recruited men aged 34 to 64 years at random from towns in the Québec City metropolitan area. Of these, 1824 met the criteria (no diabetes, free of heart disease, and so on) for a study of the relationship between being overweight and medical risks. The 719 normal-weight men had a mean triglyc eride level of 1.5 millimoles per liter (mmol/l); the 885 over weight men had a mean of 1.7 mmol/l; and the 220 obese men had a mean of 1.9 mmol/l. 1i
Explanation / Answer
Here the population is the healthy undergraduate students and response variable is the reaction time.
here each students has been giver either one of the 4 beverages, so total number of groups=4
so k =number of different beverages = 4
ni = number of students subjected in ith group of beverages = 18 for i=1,2,3,4
N = total number of subjects = ni * k = 4*18 = 72
The degress of freedom of the F-test will be ( (k-1), (N-k)) = (3,68)