Question

Independent random samples from four different brands of recently produced batteries were placed on a life test. The following lifetimes (in minutes) were recorded. Brand A Brand B Brand C Brand D 110 118 108 117 113 116 107 112 108 112 112 115 115 117 108 119 112 119 109 118

a) Provide an outline for the design of this experiment.

b) Identify the response variable.

c) Create a graph for this data. Can you see a difference in the average lifetime of these four brands?

d) Is there any evidence that the sample data contradicts the claim that there are no differences in the average lifetime of these four brands?

Answer 1

a)

Here we need to compare more than 2 population means so we need to use one way ANOVA.

b)

Lifetime of batteries..

)

Following table shows the descriptive statistics:

Descriptive statistics
	Brand A	Brand B	Brand C	Brand D
count	5	5	5	5
mean	111.60	116.40	108.80	116.20
sample standard deviation	2.70	2.70	1.92	2.77
sample variance	7.30	7.30	3.70	7.70
minimum	108	112	107	112
maximum	115	119	112	119
range	7	7	5	7

Following is the graph of four means:

Here 1 on x-axis shows brand A and 2 shows brand B and soon. It seems that there is difference on average lifetime of batteries.

d)

Hypotheses are:

H0: There are no differences in the average lifetime of these four brands.

Ha: There are differences in the average lifetime of these four brands.

Following is the output of one way ANOVA:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Brand A	5	558	111.6	7.3
Brand B	5	582	116.4	7.3
Brand C	5	544	108.8	3.7
Brand D	5	581	116.2	7.7
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	205.75	3	68.58333333	10.55128	0.000451	3.238872
Within Groups	104	16	6.5
Total	309.75	19

The p-value is: 0.0005

Since p-value is less than 0.05 so we reject the null hypothesis.