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 X⎯⎯⎯1X¯1 = $ 1,188 X⎯⎯⎯2X¯2 = $ 1,792 Sample Std. Dev. s1 = $ 712 s2 = $ 800 Repair Incidents n1 = 16 n2 = 14 Source: Unpublished study by Thomas W. Lauer and Floyd G. Willoughby. (a) Construct a 95 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 95% confidence interval is from to (b) Repeat part (a), using the assumption of unequal variances with Welch's formula for d.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 95% confidence interval is from to (c) Did the assumption about variances change the conclusion? multiple choice Yes No (d) Construct separate 95% confidence intervals for each mean. (Round your intermediate tcrit value to 3 decimal places. Round your final answers to 2 decimal places.) Mean Damage Confidence Interval x⎯⎯1=$1,188x¯1=$1,188 ($ , $ ) x⎯⎯2=$1,792x¯2=$1,792 ($ , $ )
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 | X⎯⎯⎯1X¯1 | = | $ | 1,188 | X⎯⎯⎯2X¯2 | = | $ | 1,792 | ||
| Sample Std. Dev. | s1 | = | $ | 712 | s2 | = | $ | 800 | ||
| Repair Incidents | n1 | = | 16 | n2 | = | 14 | ||||
Source: Unpublished study by Thomas W. Lauer and Floyd G. Willoughby.
(a) Construct a 95 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 95% confidence interval is from to
(b) Repeat part (a), using the assumption of unequal variances with Welch's formula for d.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 95% confidence interval is from to
(c) Did the assumption about variances change the conclusion?
multiple choice
-
Yes
-
No
(d) Construct separate 95% confidence intervals for each mean. (Round your intermediate tcrit value to 3 decimal places. Round your final answers to 2 decimal places.)
| Mean Damage | Confidence Interval |
| x⎯⎯1=$1,188x¯1=$1,188 | ($ , $ ) |
| x⎯⎯2=$1,792x¯2=$1,792 | ($ , $ ) |
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