Question

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 1-year 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	XBar1	=	$	1,245		XBar2	=	$	1,790
Sample Std. Dev.	s1	=	$	721		s2	=	$	835
Repair Incidents	n1	=		17		n2	=		14

Source: Unpublished study by Thomas W. Lauer and Floyd G. Willoughby.

(a) Construct a 99 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 99% 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_critvalue to 3 decimal places. Round your final answers to 3 decimal places. Negative values should be indicated by a minus sign.)

The 99% confidence interval is from  to  

(c) Did the assumption about variances change the conclusion?
  

• Yes

• No

(d) Construct separate 99% 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=$1,245x¯1=$1,245	($  , $  )
x¯2=$1,790x¯2=$1,790	($  , $

Answer 1

a.

μ₁: mean of Sample 1

µ₂: mean of Sample 2

Difference: μ₁ - µ₂

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Sample 1	17	1245	721	175
Sample 2	14	1790	835	223

Estimation for Difference

Difference	Pooled StDev	99% CI for Difference
-545	774	(-1315, 225)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
-1.95	29	0.061

b.Equal variances are not assumed

Estimation for Difference

Difference	99% CI for Difference
-545	(-1335, 245)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
-1.92	25	0.066

c. Yes 99%CI for both the type are different.

d.