Question

A study surveys students to determine the amount of Facebook use during the time they are doing Math homework. Students are classified into three groups: Non- User, Rarely-Use, Regularly-Use, and their Math scores are recorded. The following data summarize the results.

Facebook Use While Doing Homework
Non-User	Rarely-Use	Regularly-Use
n = 6	n = 8	n = 10	N = 24
M = 6	M = 2	M = 2	G = 72
SS = 30	SS = 33	SS = 42	ΣX2tot = 393

Use an ANOVA with α = .05 to determine whether there are significant differences among the means of the three groups.

a)The alternative hypothesis is:

b)The Critical F-value is:

c)The F-statistic is:

d)Your decision is

Answer 1

from above:

Group	ni	x̅i		ni*(Xi-Xgrand)2	(ni-1)*S2i
1	6	6		54.000	30.00
2	8	2		8.000	33.00
3	10	2		10.000	42.00
	grand mean=	3.0000		72.0000	105.00
				SSTr	SSE
Source	SS	df	MS	F	Fcrit
between	72.000	2	36.0000	7.200	3.4668
within	105.000	21	5.0000
total	177.000	23

a)

The alternative hypothesis is : at least one mean difference is significant: at least two means are significantly different

b)

Critical F-value is =3.47

c)

F-statistic is =7.20

d)

reject the null hypothesis. we have sufficient evidence to conclude that at least one mean difference is significant