Question

A transportation department tests the braking abilities of various cars. For this​ experiment, the department measured the stopping distances on dry pavement at 100 kph​ (kilometers per​ hour, about 62​ mph) of four​ models: A,​ B, C, and D. Each car accelerated to 100 kilometers per hour on a test​ track; then the brakes were applied. The distance required to come to a full stop was​ measured, in meters. The test was repeated for each car 10 times under identical conditions. The data are shown in the accompanying table. Complete parts​ (a) through​ (f).

1) Y= ( )+D(A)+D(C)+D(D)

2) F statistic= F=

3) p-value=

​(Round to two decimal places as​ needed.)

Model    Distance (meters)
A   45.2
A   44.7
A   44.7
A   45.4
A   45.5
A   45.5
A   45.3
A   44.4
A   44.4
A   45.8
B   47.1
B   50.0
B   49.2
B   48.2
B   49.5
B   48.8
B   48.5
B   48.5
B   48.2
B   48.3
C   42.5
C   43.2
C   42.9
C   43.5
C   42.4
C   43.4
C   42.7
C   43.6
C   43.3
C   42.8
D   48.3
D   49.0
D   45.6
D   47.1
D   47.5
D   48.0
D   47.0
D   47.9
D   48.4
D   47.8

Answer 1

H0: The mean distance taken by the cars to come to full stop are equal

Ha: The mean distance taken by the cars to come to full stop are not equal.

As we are testing the four cars on the basis of the single factor we are using one way ANOVA.

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	10	450.9	45.09	0.249888889
Column 2	10	486.3	48.63	0.649
Column 3	10	430.3	43.03	0.182333333
Column 4	10	476.6	47.66	0.884888889
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	192.79475	3	64.26491667	130.7452388	2.06113E-19	2.866265551
Within Groups	17.695	36	0.491527778
Total	210.48975	39

(i Calculated F value= 130.75

(ii) p value=0.00000001 As, we are testing at 5% level of significance so calculated p value is less than 0.05. So null hypothesis is rejectedi.e. the mean distance taken by the cars to come to rest are not equal.