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 s1 = $ 712 s2 = $ 800 Repair Incidents n1 = 16 n2 = 14 Source: Unpublished study by Thomas W. Lauer and Floyd G. Willoughby.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=$1,792 ($ , $ )

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Source: Unpublished study by Thomas W. Lauer and Floyd G. Willoughby.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

(d) Construct separate 95% 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=$1,188x¯1=$1,188	($ , $ )
x⎯⎯2=$1,792x¯2=$1,792	($ , $ )

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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