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).

StatisticTest GroupControl GroupMean DamageX

1

X1=$1,200X

2

X2=$1,791Sample Std. Dev.s₁=$705s₂=$822Repair Incidentsn₁=12n₂=8

Source: Unpublished study by Thomas W. Lauer and Floyd G. Willoughby.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 final answers to 3 decimal places.Negative values should be indicated by a minus sign.)

The 99% confidence interval is fromto

(b)Repeat part (a), using the assumption of unequal variances with Welch's formula ford.f.(Round the calculation for Welch's df to the nearest integer. Round your final answers to 3 decimal places. Negative values should be indicated by a minus sign.)

The 99% confidence interval is fromto

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

multiple choice

• Yes
• No

(d)Construct separate 99% confidence intervals for each mean.(Round your intermediatet_critvalue to 3 decimal places. Round your final answers to 2 decimal places.)

Mean DamageConfidence Intervalx

1

=$1,200

x1=$1,200($, $)x

2

=$1,791

x2=$1,791($, $)