Question

A human factors psychologist studied three computer keyboard designs. Three samples of individuals were given material to type on a particular keyboard, and the number of errors committed by each participant was recorded.

What is the correct way to write the hypotheses?

The data are as follows:

Keyboard A	Keyboard B	Keyboard C
M = 1	M = 5	M =6	N = 15
T = 5	T = 25	T = 30	G = 60
SS = 12	SS = 20	SS = 14	?X2 = 356

Answer Options:

	A.	Null: H0: ?1 = ?2 = ?3 Alternative: H1: ?1 = ?2 ? ?3
	B.	Null: H0: ?1 = ?2 = ?3 Alternative: H1: all three means are different from the others
	C.	Null: H0: ?1 = ?2 = ?3 Alternative: H1: ?1 ? ?2 = ?3

PART 2:

Using the same data, what are the df_total?

	A.	2
	B.	12
	C.	14
	D.	11

PART 3

Using the same data, what is the SSwithin value?

	A.	116
	B.	46
	C.	14
	D.	70 PART 4

Using the same data, what is the critical value given an ? = .05?

	A.	4.63
	B.	3.88
	C.	3.63
	D.	D. 4.36 What is the final F-ratio? A. 9.14 B. 7.20 C. 11.28 D. 16.50 Using the same data, what is the ?2? A. .52 B. .38 C. .60 D. .69 What is your decision about the null hypothesis, including the verbal interpretation? A. Reject H0 The type of keyboard has a significant effect on number of errors committed. B. Fail to reject H0 The type of keyboard does not have a significant effect on number of errors committed. C. Reject the Ho The type of keyboard does not have a significant effect on number of errors committed. D. Fail to reject H0. The type of keyboard has a significant effect on the number of errors committed.

Answer 1

c	ni	x?i		ni*(Xi-Xgrand)2	(ni-1)*S2i
keyboard A	5	1.000		45.000	12.00
keyboard B	5	5.000		5.000	20.00
keyboard C	5	6.000		20.000	14.00
	grand mean=	4.000		70.000	46.00
				SSTr	SSE
Source of variation		SS	df	MS	F	P value	F crit
treatment		70.000	2	35.00	9.14	0.0039	3.89
error		46.000	12	3.83
total		116.000	14

1)

Null: H0: ?1 = ?2 = ?3

H1: not all means are equal

2)

dftotal =14

3)

SSwithin =46

4)

critical value given an ? = .05 =3.88

5)

final F-ratio =9.14

6)

?2 =SSbg/SST =70/116=0.60

7)

Reject H0

The type of keyboard has a significant effect on number of errors committed