Hypothesis testing with ANOVA opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students' test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks, each with a different caffeine concentration, such that there are seven students assigned to each drink. You then give each of them a plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later.
The students receive the following arithmetic test scores:
Cola
Black Tea
Coffee
Caffeine Content (mg/oz)
2.9
5.9
13.4
85
85
92
∑X2 = 147,641
86
89
87
G = 1,755
82
82
80
N = 21
75
75
89
k = 3
66
88
96
78
76
83
87
82
92
T1 = 559
T2 = 559
T3 = 559
SS1 = 338.86
SS2 = 338.86
SS3 = 338.86
n1 = 7
n2 = 7
n3 = 7
M1 = 79.8571
M2 = 79.8571
M3 = 79.8571
1.) You plan to use an ANOVA to test the impact of drinks with different caffeine contents on students' test-taking abilities. What is the null hypothesis?
(a) The population mean test score for the cola population is different from the population mean test score for the black tea population.
(b) The population mean test scores for all three treatments are equal.
(c) The population mean test scores for all three treatments are different.
(d) The population mean test scores for all three treatments are not all equal.
2.) Calculate the degrees of freedom and the variances for the following ANOVA table:
Source
SS
df
MS
Between
-
-
-
Within
702.28
-
-
Total
973.14
-
The formula for the F-ratio is:
3.) Using words, the formula of the F-ratio can be written as:
4.) Using the data from the ANOVA table given, the F-ratio can be written as:
5.) Calculate for F-ratio:
6.) At the level of significance, what is your conclusion?
(a)You can reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.
(b)You cannot reject the null hypothesis; caffeine does appear to affect test performance.
(c)You cannot reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.
(d)You can reject the null hypothesis; caffeine does appear to affect test performance.
