The data that follow are coded serious head injury data that

The data that follow are coded serious head injury data that occur in car wrecks. The higher the number the more serious the head injury.Using a 0.05 level of significance do the data suggest that larger cars are safer?

subcompact

compact

mid-size

Full-size

681

643

469

384

428

655

727

656

917

442

525

602

898

514

454

687

420

525

259

360

Solution

Hypothesis

Null hypothesis : Data suggests larger cars are safer

alternate hypothesis: Data suggests large cars not safer

let

total number of observations in i th sample = n_i

the j th observation in i th sample is denoted by y_ij

mean of ith sample = y^\'_i

grand mean = y

SS treatment = sumof (ni * (yi\' - y)^2)

Sum of square error   = sum of (yij - yi\')^2

total sum of squares = sum of(yij - y)^2

p-value = 0.128

since test static is less than p-value , we reject null hypothesis