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?

head injury data for the dummies in the​ driver's seat.

​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.

The​ P-value is ___?(Round to three decimal places as​ needed.)

Do the sample data suggest that larger cars are​ safer?

A.

There is not sufficient evidence to reject the alternative hypothesis. It can be concluded that larger cars are safer.

B.

There is sufficient evidence to reject the null hypothesis. It can not be concluded that larger cars are safer.

C.

There is not sufficient evidence to reject the null hypothesis. It cannot be concluded that larger cars are safer.

Answer 1

For the given data using Anova single facto in Excel we get output as

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
subcompact	5	3444	688.8	48102.7
compact	5	2779	555.8	8272.7
mid size	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

• The​ P-value is 0.178

p value > lo.s

i.e, 0.178 > 0.05

so fail to reject h0

• There is not sufficient evidence to reject the null hypothesis. It cannot be concluded that larger cars are safer.