Question

QUESTION 12

1. Shock Absorbers Question 3
   
   A manufacturer of automobile shock absorbers was interested in comparing the durability of its shocks with that of the shocks produced by its biggest competitor. To make the comparison, one of the manufacturer's and one of the competitor's shock absorbers were randomly selected and installed on the rear wheels of each of six cars. After the cars had been driven for 20,000 miles, the strength of each test shock absorber was measured, coded, and recorded; results are shown in the table below. Note that the higher the measurement, the more durable is the shock absorber.
   
   Shock Absorber Strength
   

   Car	Manufacturer’s	Competitor’s
   1	8.8	8.4
   2	10.5	10.1
   3	12.5	12.0
   4	9.7	9.3
   5	9.6	9.0
   6	13.2	13.0

   
   
   If one wants to demonstrate that the mean strength of the manufacturer’s brand exceeds that of the competitor’s by at least 0.5 units after 20,000 miles of use, what is the p-value of the appropriate test of hypotheses?

   	a.	0.309
   	b.	0.168
   	c.	0.293
   	d.	0.503
   	e.	0.907

Answer 1

SAMPLE 1	SAMPLE 2	difference , Di =sample1-sample2	(Di - Dbar)²
8.8	8.4	0.400	0.000
10.5	10.1	0.400	0.000
12.5	12	0.500	0.007
9.7	9.3	0.400	0.000
9.6	9	0.600	0.034
13.2	13	0.200	0.047

Ho :   µd=   0.5
Ha :   µd >   0.5
      

mean of difference ,    D̅ =ΣDi / n =   0.4167       0.9167          
               0.2924          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    0.1329                  
                          
std error , SE = Sd / √n =    0.1329   / √   6   =   0.0543      
                          
t-statistic = (D̅ - µd)/SE = (   0.416666667   -   0.5   ) /    0.0543   =   -1.536
                          
Degree of freedom, DF=   n - 1 =    5                  
  
                          
p-value =        0.907    [excel function: =t.dist.rt(t-stat,df) ]