Question

1. Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the treatments (cars types). Using the data provided below, test whether the mean pressure applied to the driver’s head during a crash test is equal for each types of car. Use α = 5%.

Compact cars	Midsize cars	Full-size cars
64	46	47
65	43	45
69	52	40
Average: 66	Average: 47	Average: 44

                The average for all can be found as 52.3.

             a). Find SSG.

             b). Find SSE.

             c). Find SST

             d). Find F-value

            e). Find F-critical value from the Table.

            f). Make your decision.

Answer 1

(a)

From the given data, the following Table is calculated:

	Compact cars	Midsize cars	Full - size cars
Sum =	198	141	132
n =	3	3	3
Mean =	66	47	44
	13082	6669	5834
Std. Dev.	2.646	4.583	3.606
SS	14	42	26

Total Sample Size =N = 3 +3 + 3 = 9

Total Sum of values is given by:

Total Sum of Squated values is given by:

Total Sum of Squares = SST is given by:

Error Sum of Squated values= SSE is given by:

SSE = 14 + 42 + 26 = 82

Group Sum of Squares = SSG is given by:

SSG = SST-SSE = 936 - 82 = 854

So,

SSG = 854

(b)

Error Sum of Squated values= SSE is given by:

SSE = 14 + 42 + 26 = 82

So,

SSE = 82

(c)

Total Sum of Squares = SST is given by:

So,

SST = 936

(d)

MSG = SSG/dfG = 854/2 = 427

MSE = SSE/dfE = 82/6 = 13.667

So,

F Value = 427/13.667 = 31.244

So,

F Value = 31.244

(e)

F-critical value from the Table. = 5.143

(f)

Since calculated value of F = 31.244 is greater than critical value of F = 5.143, the difference is significant. Reject null hypothesis.

Conclusion:
The data do not upport the claim that the mean pressure applied to the driver’s head during a crash test is equal for each types of car.