Question: a special bumper was installed on selected vehicles in a...
Question details
A special bumper was installed on selected vehicles in a large fleet. The dollar cost of body repairs was recorded for all vehicles that were involved in accidents over a 1year period. Those with the special bumper are the test group and the other vehicles are the control group, shown below. Each "repair incident" is defined as an invoice (which might include more than one separate type of damage). 
Statistic  Test Group  Control Group  
Mean Damage  X⎯⎯⎯1X1  = $  1,172  X⎯⎯⎯2X2  = $  1,740 
Sample Std. Dev.  s_{1}  = $  668  s_{2}  = $  808 
Repair Incidents  n_{1}  =  15  n_{2}  =  12 
Source: Unpublished study by Thomas W. Lauer and Floyd G. Willoughby. 
(a) 
Construct a 90 percent confidence interval for the true difference of the means assuming equal variances. (Round your intermediate t_{crit} value to 3 decimal places. Round your final answers to 3 decimal places. Negative values should be indicated by a minus sign.) 
The 90% confidence interval is from to 
(b) 
Repeat part (a), using the assumption of unequal variances with Welch's formula for d.f. (Round your intermediate t_{crit} value to 3 decimal places. Round your final answers to 3 decimal places. Negative values should be indicated by a minus sign.) 
The 90% confidence interval is from to 
(c)  Did the assumption about variances change the conclusion?  

(d)  Construct separate 90% confidence intervals for each mean. (Round your intermediate t_{crit} value to 3 decimal places. Round your final answers to 2 decimal places.) 
Mean Damage  Confidence Interval 
x⎯⎯1=$1,172x1$1,172  ($ , $ ) 
x⎯⎯2=$1,740x2$1,740  ($ , $ 