Question

# All cars can be classified into one of four​ groups: the​ subcompact, the​ compact, the​midsize, and...

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.)

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

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