Waht is the Mean/ variance?

Question

In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research Question: Are the mean crash damages the same or each of the three vehicles? Crash 1

GOLAITH VARMINT WEASEL

1,600 1,290 1,090

760 1,400 2,100

880 1,390 1,830

1,950 1,850 1,250

1,220 950 1,920

Answer 1

Assuming you have some knowledge on ANOVA, otherwise, it is hard to understand.

You have to use 1-way ANOVA

Set Ho: the crash damages are the same

________GOLAITH__ VARMINT__ WEASEL

__________1600______1290_______1090

__________ 760 ______1400_______2190

__________ 880 ______1390_______1830

__________1950______1850_______1250

__________1220______ 950 _______1920

______________________________________... SUM

SUM______6410______6880_______8280    ------>   21570

SUMSQ_ 9202900___9881200 ___14582000 ---> 33666100

no.of sample_5_________5__________5   -------->      15

CM = 21570^2 / 15 = 31017660

SS = 33666100 - 31017660 = 2648440

SST = 6410^2/5 + 6880^2/5 + 8280^2/5 - 31017660 = 378520

SSE = SS - SST = 3648440 - 378520 = 3269920

MST = SST / degree of freedoms of SST = 378520/2 = 189260

MSE = SSE / 15 = 3269920 / 15 = 24661.33

F = MST / MSE = 189260 / 24661.33 = 7.674

Use Excel to find a:

=FDIST(7.674,2,15)

gives a = 0.00507 < 0.05 (95% confidence interval)

Reject Ho:

There are difference between the crash damages of the types of autos.

Answer 2

So I did your dirty work for you. :)

Goliaths mean is 1282

Varmint is 1376

Weasel is 1638