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:

Caffeine content mg/oz:

Water Cola Coffee
0 2.9 13.4
78 85 92
88 86 87
72 82 80
64 66 96
81 78 83
82 87 92
T1=537 T2=559 T3=619
SS1=381.43 SS2=338.86 SS3=185.71
n1=7 n2=7 n3=7
M1=76.7143 M2=79.8571 M2=88.4286
∑
X
2
=
141
,
479

G
=
1715

N
=
21

K
=
3

a. You plan to use an ANOVA to test the impact of drinks with different caffein contents on students test-taking abilities, What is the null hypothesis?

A. The population mean test scores for all three treatments are different.

B. The population mean test score for the water population is different from the population mean test for the cola population.

C. The population mean test score for all three treatments are equal.

D. The population mean test scores for all three treatments are not all equal.

b. Calculate the degree of freedom and the variance for the following ANOVA table:

source SS df MS
Between
Within 906.00
Total 1420.67
The formula for the F-ratio is:

F
=
M
S
b
e
t
w
e
e
n
M
S
w
i
t
h
i
n

- Using words the formula for the F-ration can be written as:

- Using the data from the ANOVA table given, the f-ratio can be written as:

hence F: