Question

The following summary statistics represent the hours of battery life for 4 brands of laptops. At the 0.05 significance level, do the data provide sufficient evidence to conclude that a difference exists between the the battery life of the fourdifferent brands?
Column n Mean Std. Dev. Brand_A 8 7.69 1.62 Brand_B 8 10.44 2.45 Brand_C 10 8.55 2.52 Brand_D 8 5.91 1.30

Answer 1

here null hypothesis: Ho :there is no difference exist among mean of battery life of the four different brands

alternate hypothesis:Ha: at least 2 batteries have different mean life,

Applying ANOVA on above data:

Group	ni	x̅i	S2i	ni*(Xi-Xgrand)2	(ni-1)*S2i
A	8	7.69	2.624	1.852	18.37
B	8	10.44	6.003	41.180	42.02
C	10	8.55	6.350	1.435	57.15
D	8	5.91	1.690	40.903	11.83
	grand mean=	8.1712		85.371	129.37
				SSTr	SSE
Source	SS	df	MS	F
between	85.37	3.000	28.4571	6.60
within	129.37	30.000	4.3124
total	214.74	33.0000

here test statistic F=6.60

at 0.05 level and (3,30) degree of freedom ; critical value F =2.92

as test statisitic is higher than critical value  ; therefore we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that at least 2 batteries have different mean life,