Question

Altobene, Inc.’s  R&D department recently conducted a test of three different brake systems to determine if there is a difference in the average stopping distance among the different systems.  In the test, 21 identical mid-sized cars were obtained from one of the major domestic carmakers.  Seven (7) cars were fitted with Brake A, seven (7) with Brake B, and seven (7) with Brake C. The number of feet required to bring the test cars to a full stop was recorded.

Which of the following is the appropriate null and alternative hypotheses about the stopping distance among the different systems?

H0: = =

HA: All of the population mean stopping distances are different from each other

H0:= =

HA: At least one population mean stopping distances is different from the others

H0:= =

HA: At least one population mean stopping distance is equal to another population mean stopping distance

Ho:= =  

Ha: Exactly one population mean stopping distance is greater than the other two population mean stopping distances

An ANOVA for the Stopping Distance Effect in Question 1 has been conducted with the partial results shown in the table below. Complete the ANOVA table.  

Source

Sum of Squares

Degrees of Freedom

Mean Square

F-Calculated

Between Groups (Brakes)

1314

Within Groups

XXXXXXXXXXXXX

Total

5299

20

What is the critical value of the test statistic for the brake stopping distance ANOVA if the hypothesis of interest is tested at the α = 0.01 level of significance?

6.013                                                  b.              5.092

4.938                                                  d.              3.127

Based on the ANOVA analysis, what conclusion would you make regarding the effect the braking system has on average stopping distance?

Reject HO, there is significant evidence to conclude there is a brake effect.

Do not reject HO, there is significant evidence to conclude there is a brake  effect.

Reject HO, there is insignificant evidence to conclude there is a brake effect.

Do not reject HO, there is insignificant evidence to conclude there is a brake effect.

Answer 1

We have to test the hypothesis that

Whether or not there is difference in Average stopping distance among three different system.

i.e. Null Hypothesis - Ho : Average stopping distance among three different system are equal .

against

Alternative Hypothesis- Ha : At least on e populations mean stopping distances is different than the other.

k = number of break systems = 3

n = total number of observation . = 7 * 3 = 21

Degrees of freedom are

Total = n- 1 = 21 -1 = 20

Between group = k-1 = 3-1 = 2

Within Group (error) = n-k = 18

Mean sum of square =Sum of square / Degrees of freedom.

F-calculated = MS ( Between group ) / MS ( Within group )

Alpha = Level of significance = 0.01

Critical value = F_{k-1,n-k, 0.01}

From F-table

F_{2,18, 0.01} = 6.013

at 1% level of significance , Critical Value of test statistic = 6.013

Correct Answer : a- 6.013

Hence Anova table is

Source	Sum of square	D.F.	Mean square	F-cal.	Critical Value
Between group   ( Brake)	1314	2	657	2.9676	6.013
Within Group (Error)	3985	18	221.3889	………	………
Total	5299	20	………	………	………

Since Critical value of test statistic is greater than calculated of test statistic ( 6.013 > 2.9676). We failed to reject Ho at 1% level of significance.

Conclusion : Do not reject Ho, there is insufficient evidence to conclude there is brake effect.