# notation - summation

• Sep 7th 2009, 02:18 PM
comet2000
notation - summation
Not sure if you need Exercises 2.15 and 2.16, i have included it anyways.
Exercises 2.15
In a study of the moon illusion that we will discuss in Chapter 5, Kaufman and Rock (1962) tested an earlier hypothesis by Holway and Boring (1940) about reasons for the moon illusion. Kaufman and Rock compared how subjects performed when they were able to first look at the moon with their eyes level, and then look again with their eyes elevated. The data for the Eyes Level condition follow: 1.65, 1.00, 2.03, 1.25, 1.05, 1.02, 1.67, 1.86, 1.56, 1.73

Exercise 2.16
With reference to Exercise 2.15, the data for the Eyes Elevated condition are 1.73 1.06 2.03 1.40 0.95 1.13 1.41 1.73 1.63 1.56

Exercise 2.19
The data from Exercises 2.15 and 2.16 come from the same 10 (N) subjects. In other words, the same person had a score of 1.65 in the Eyes Level condition and a score of 1.73 in the Eyes Elevated condition. Therefore the data form pairs of scores.

(a) Multiply the scores in each pair together to get a variable called XY.
1.65 x 1.73 = 2.854
1.00 x 1.06 = 2.06
2.03 x 2.03 = 4.120
1.25 x 1.40 = 1.75
1.05 x 0.95 = 0.997
1.02 x 1.13 = 1.152
1.67 x 1.41 = 2.354
1.86 x 1.73 = 3.217
1.56 x 1.63 = 2.542
1.73 x 1.56 = 2.698

(b) Calculate ΣXY
ΣXY = (1.65 x 1.73 + 1.00 x 1.06 + 2.03 x 2.03 + 1.25 x 1.40 + 1.05 x 0.95 + 1.02 x 1.13 + 1.67 x 1.41 + 1.86 x 1.73 + 1.56 x 1.63 + 1.73 x 1.56) = 22.7496

(c) Calculate ΣXΣY
ΣXΣY = (14.82)(14.63) = 216.82

(d) Do ΣXY and ΣXΣY differ, and would you normally expect them to?
22.7496 does not equal 216.82
would you normally expect them to? yes

(e) Calculate
ΣXY - ΣXΣY/N divide by N - 1
22.7496 - (14.82)(14.63)/10 divide by 10 - 1
1.0679 divide by 9 = .11866

for Exercise 2.19, i am pretty sure i did the problems correctly. for (e), i see in the book, the answer is .1187, am i suppose to round it off or live it as it is or did i do the problem wrong?

Exercise 2.20
Use the previous data to show that
(a) Σ(X + Y) = ΣX + ΣY
(b) ΣXY does not equal ΣXΣY
(c) ΣCX = CΣX
(d) ΣX^2 does not equal (ΣX)^2
for Exercise 2.20, how do i do it?