Question

Suppose the National Transportation Safety Board wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the treatments (cars types). Test the claim that the mean pressure applied to the driver's head during a crash is equal for all three types of cars. Use α = 0.05

Compact Cars	643	655	702
Midsize Cars	469	427	525
Full-size Cars	484	456	402

Show your 6 steps labeled in order in the box below.

Answer 1

count, ni =	3	3	3
mean , x̅ i =	666.667	473.67	447.33
std. dev., si =	31.182	49.166	41.681
sample variances, si^2 =	972.333	2417.333	1737.333
total sum	2000	1421	1342		4763	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	529.22

square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	18890.975	3086.420	6705.790
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	56672.926	9259.259	20117.370		86049.55556
SS(within ) = SSW = Σ(n-1)s² =	1944.667	4834.667	3474.667		10254.0000

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   9
df within = N-k =   6
  
mean square between groups , MSB = SSB/k-1 =    43024.7778
  
mean square within groups , MSW = SSW/N-k =    1709.0000
  
F-stat = MSB/MSW =    25.1754
P value =   0.0012

	SS	df	MS	F	p-value	F-critical
Between:	86049.56	2	43024.78	25.18	0.0012	5.14
Within:	10254.00	6	1709.00
Total:	96303.56	8
					α =	0.05
			conclusion :	p-value<α , reject null hypothesis

Not all means are equal.

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