Question

The head injury data are shown in the following table.

Subcompact: 681 428 917 898 420

Compact: 643 655 442 514 525

Midsize: 469 727 525 454 259

Full-size: 384 656 602 687 360

Table 5: Head Injury & Car Crash

At α = 0.05 level of significance, test the claim that different weight categories have the same mean by using the data in table 5.

(a) Clearly state H0 and H1.

H0 :

H1 :

(b) Find all related critical values, draw the distribution, clearly mark and shade the critical region(s). Give the name of the program you used for this step as well as any degrees of freedom. Drawing & Shading Required.

(c) Find the computed test statistic, and the P-value.

C.T.S. :

P-Value :

(d) Use non-statistical terminology to state your final conclusion.

Answer 1

Subcompact	Compact	Midsize	Fullsize
681	643	469	384
428	655	727	656
917	442	525	602
898	514	454	687
420	525	259	360

(a)

(a) H0: There is no difference between the treatment means; that is, μ1 = μ2 = μ3 = μ4
H1: At least one among μ1, μ2, μ3 and μ4 is different from the other three

(b) Df (Treatment) = 3, Df (Error) = 16, α = 0.05, Critical F score = 3.2389

(c) ANOVA

SUMMARY
Groups	Count	Sum	Average	Variance
Subcompact	5	3344	668.8	58542.7
Compact	5	2779	555.8	8272.7
Midsize	5	2434	486.8	28110.2
Fullsize	5	2689	537.8	23905.2
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	88425	3	29475	0.992167	0.42157	3.238872
Within Groups	475323.2	16	29707.7
Total	563748.2	19

Test F- score = 0.9922, p- value = 0.4216

Since the p- value > 0.05, we fail to reject Ho

There is no sufficient evidence that the four groups have significantly different means.

[I have used Excel for the ANOVA table and STATDISK to get the plot]