Question

A researcher hypothesizes that caffeine will affect the speed with which people read. To test this, the researcher randomly assigns 8 people into one of two groups: 50mg Caffeine (n1 = 4) or No Caffeine (n2 = 4). An hour after the treatment, the 8 participants in the study are asked to read from a book for 1 minute; the researcher counts the number of words each participant finished reading. The following are the data for each sample:

50mg Caffeine (group 1)- 450 400 500 450; No Caffeine (group 2) - 400 410 430 440

Using the Analysis of Variance:
What is the research hypothesis?
What is the null hypothesis?
What is dfbetween and dfwithin? What is the total df for this problem? What is SSbetween and SSwithin? What is the total SS for this problem? What is MSbetween and MSwithin?

Calculate F. (As a check, the square root of F should be the same value as t in (1).)

Use an alpha-level of .05 to answer the questions (g) – (j) below:

Draw a picture of the F Distribution for dfbetween and dfwithin above, and locate F on the x-axis.

What is the critical value of F, given dfbetween and dfwithin? Indicate the critical value of F (and its value) in your drawing in (g). Also indicate what the area is in the tail beyond the critical value of F. (As a check, the square root of the critical value of F should be the same as the critical value of t in (1).)

Can you reject the null hypothesis? Why or why not?

Can you accept the research hypothesis? Why or why not?

SHOW ALL THE WORKING

Answer 1

	Group 1	Group 2		Squares Table
	450	400		202500	160000
	400	410		160000	168100
	500	430		250000	184900
	450	440		202500	193600
Counts	4	4		Total Count (N)	8
Totals	1800	1680		Sum of squares =	1521600.00
Grand Total	3480
(1) Correction Factor, CF = Grand Total^2 /N =		1513800.00
(2) SS Total = Sum of the squares of all the scores - CF =				7800.00
(3) SS Between = Sum of the (squares of the totals for the treatments/Number of scores in treatment) - CF =							1800.00
(4) SS Within = SS Total - SS Between =		6000.00
(5) Df Total = N - 1 =		7
(6) Df Between = Number of treatments - 1 = 4 - 1 =			1
(7) Df Within = Df Total - Df Between =		6
(8) MS Between = SS Between / Df Between =		1800.00
(9) MS Within = SS Within / Df Within =		1000.00
(10) F = MS Between/MS Within =		1.8
(11) p- value =		0.2283

ANSWERS:

Ha: μ1 ≠ μ2

Ho: μ1 = μ2

df bet = 1

df within = 6

SS bet = 1800

SS within = 6000

SS Total = 7800

MS bet = 1800

MS within = 1000

F = 1.8