Question

You are asked to analyze the below speed data collected on a highway on different days of the week for similarity. Use ANOVA (analysis of variance) to support your conclusion by performing the following tasks:

Sample 1 (mph)	Sample 2 (mph)	Sample 3 (mph)
50	45	55
55	50	60
50	55	50
50	60	45
60	40	40

State your null hypothesis (H0) and alternative hypothesis (H1)

State your assumed level of significance (αα)

Calculate mean for sample 1

Calculate mean for sample 2

Calculate grand mean for sample 1 & 2

Calculate SSB (between sample sum of square errors) and the associated degree of freedom

Calculate SSW (within sample sum of square errors) and the associated degree of freedom

Calculate SST (total sample sum of square errors) and the associated degree of freedom (Hint: this validates the accuracy of your calculated SSB and SSW values)

Calculate the F value

State the critical F value (table value based on your assumed level of significance)

Make your conclusion whether or not the speed reduction strategy was effective and state why?

Answer 1

using excel>data>data analysis>ANOVA single factor

we have

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Sample 1 (mph)	5	265	53	20
Sample 2 (mph)	5	250	50	62.5
Sample 3 (mph)	5	250	50	62.5
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	30	2	15	0.310345	0.738906	3.885294
Within Groups	580	12	48.33333
Total	610	14

null hypothesis (H0) :

the alternative hypothesis (H1) :at least two means are different .

assumed level of significance (α) = 0.05

mean for sample 1 =53

mean for sample 2 =50

grand mean for sample 1 & 2 = (50+53)/2 = 51.5

SSB (between sample sum of square errors) =30 and the associated degree of freedom =2

SSW (within sample sum of square errors) = 580 and the associated degree of freedom =12

SST (total sample sum of square errors) = 610 and the associated degree of freedom =14

the F value =0.3104

the critical F value = 3.885

Do not reject H0 the speed reduction strategy was not effective because their average are same