Question

All cars can be classified into one of four​ groups: the​ subcompact, the​ compact, the​midsize, and the​ full-size. There are five cars in each group. Head injury data​ (in hic) for the dummies in the​ driver's seat are listed below. Use a 0.05 significance level. Find the​ P-value to test the null hypothesis that the different weight categories have the same mean. Do the sample data suggest that larger cars are​ safer?

Subcompact:

681

428

917

898

520

​Compact:

643

655

442

514

525

​Midsize:

469

627

525

454

259

​Full-size:

384

656

502

687

360

Find the​ P-value.

​(Round to three decimal places as​ needed.)

Answer 1

For given problem we use ANOVA for single factor in MS-Excel.We get output as follow

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Subcompact:	5	3444	688.8	48102.7
​Compact:	5	2779	555.8	8272.7
​Midsize:	5	2334	466.8	18100.2
​Full-size:	5	2589	517.8	22695.2
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	135225	3	45075	1.855496	0.177853	3.238872
Within Groups	388683.2	16	24292.7
Total	523908.2	19

So from the above output

p value = 0.177853

= 0.178