A special bumper was Installed on selected vehicles In a large fleet The dollar cost of body repalrs was recorded for all vehicles that were Involved In accidents over a 1-year perlod. 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 X1 = $ 1,172 Control Group X2 = $ 1,740 2 =$ s88 n2 = Mean Danage Sample Std. Dev. 668 Repair Incidents n1 = 15 12 Source: Unpublished study by Thomas W. Lauer and Floyd G. Willoughby.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 varlances. (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 varlances 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 90% confidence Interval is from [ to (c) Did the assumptlon about varlances change the conclusion? O Yes O No places. Round (d) Construct separate 90% confidence Intervals for each mean. (Round your intermedlate terit value to 3 de your final answers to 2 decimal places.) Mean Damage 2 = $1,172 Confidence Interval ($
A special bumper was Installed on selected vehicles In a large fleet The dollar cost of body repalrs was recorded for all vehicles that were Involved In accidents over a 1-year perlod. 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 X1 = $ 1,172 Control Group X2 = $ 1,740 2 =$ s88 n2 = Mean Danage Sample Std. Dev. 668 Repair Incidents n1 = 15 12 Source: Unpublished study by Thomas W. Lauer and Floyd G. Willoughby.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 varlances. (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 varlances 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 90% confidence Interval is from [ to (c) Did the assumptlon about varlances change the conclusion? O Yes O No places. Round (d) Construct separate 90% confidence Intervals for each mean. (Round your intermedlate terit value to 3 de your final answers to 2 decimal places.) Mean Damage 2 = $1,172 Confidence Interval ($
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Transcription and Explanation:**
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 | \( \bar{X_1} = \$1,172 \) | \( \bar{X_2} = \$1,740 \) |
| Sample Std. Dev. | \( s_1 = 668 \) | \( s_2 = 888 \) |
| 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 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 the calculation for Welch's d.f. to the nearest integer. 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?
- [ ] Yes
- [ ] No
**(d)** Construct separate 90% confidence intervals for each mean. *(Round your intermediate \( t_{\text{crit}} \) value to 3 decimal places. Round your final answers to 2 decimal places.)*
| Mean Damage | Confidence Interval |
|------------------------|-----------------------|
| \( = \$1,172 \) | [ _______, _______ ] |
| \( = \$1,740 \) | [ _______, _______ ] |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62c5d8d4-bf52-40ff-9a64-70401b9ed938%2F4fc7d395-9132-4df5-88f5-02c5df719fc7%2F3tfo0tb_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription and Explanation:**
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 | \( \bar{X_1} = \$1,172 \) | \( \bar{X_2} = \$1,740 \) |
| Sample Std. Dev. | \( s_1 = 668 \) | \( s_2 = 888 \) |
| 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 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 the calculation for Welch's d.f. to the nearest integer. 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?
- [ ] Yes
- [ ] No
**(d)** Construct separate 90% confidence intervals for each mean. *(Round your intermediate \( t_{\text{crit}} \) value to 3 decimal places. Round your final answers to 2 decimal places.)*
| Mean Damage | Confidence Interval |
|------------------------|-----------------------|
| \( = \$1,172 \) | [ _______, _______ ] |
| \( = \$1,740 \) | [ _______, _______ ] |
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