In a bumper test, three test vehicles of each of three types of autos were crashed into a barrier at 5 mph, and the resulting damage was estimated. Crashes were from three angles: head-on, slanted, and rear-end. The results are shown below. Research questions: Is the mean repair cost affected by crash type and/or vehicle type? Are the observed effects (if any) large enough to be of practical importance (as opposed to statistical significance)? 5 mph Collision Damage ($)Crash TypeGoliathVarmintWeaselHead-On7001,7002,280 1,4001,6501,670 8501,6301,740Slant1,4301,8502,000 1,7401,7001,510 1,2401,6502,480Rear-end7008601,650 1,2501,5501,650 9701,2501,240 (b) Fill in the missing data. (Round your table of means values to 1 decimal place, SS and F values to 2 decimal places, MS values to 3 decimal places, and p-values to 4 decimal places.) Table of Means Factor 2 (Vehicle)Factor 1 (Angle)GoliathVarmintWeaselTotalHead-On Slant Rear-End Total Two-Factor ANOVA with ReplicationSourceSSdfMSFp-valueFactor 1 (Angle) Factor 2 (Vehicle) Interaction Error Total (d) Perform Tukey multiple comparison tests. (Input the mean values within the input boxes of the first row and input boxes of the first column. Round your t-values and critical values to 2 decimal places and other answers to 1 decimal place.) Post hoc analysis for Factor 1: Tukey simultaneous comparison t-values (d.f. = 18) Rear-EndHead-OnSlant Rear-End Head-On Slant Critical values for experimentwise error rate: 0.05 0.01 Post hoc analysis for Factor 2: Tukey simultaneous comparison t-values (d.f. = 18) GoliathVarmintWeasel Goliath Varmint Weasel critical values for experimentwise error rate: 0.05 0.01

*Answer: b)Applying two way ANOVA from megastat: Goliath Varmint Weasel total Head-On 983.3…

Answered: a bumper test, three test vehicles of…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.3: Modeling Data With Power Functions

Problem 6E: Urban Travel Times Population of cities and driving times are related, as shown in the accompanying...

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In a bumper test, three test vehicles of each of three types of autos were crashed into a barrier at 5 mph, and the resulting damage was estimated. Crashes were from three angles: head-on, slanted, and rear-end. The results are shown below. Research questions: Is the mean repair cost affected by crash type and/or vehicle type? Are the observed effects (if any) large enough to be of practical importance (as opposed to statistical significance)?

5 mph Collision Damage ($)
Crash Type	Goliath	Varmint	Weasel
Head-On	700	1,700	2,280
	1,400	1,650	1,670
	850	1,630	1,740
Slant	1,430	1,850	2,000
	1,740	1,700	1,510
	1,240	1,650	2,480
Rear-end	700	860	1,650
	1,250	1,550	1,650
	970	1,250	1,240

(b) Fill in the missing data. (Round your table of means values to 1 decimal place, SS and F values to 2 decimal places, MS values to 3 decimal places, and p-values to 4 decimal places.)

Table of Means
	Factor 2 (Vehicle)
Factor 1 (Angle)	Goliath	Varmint	Weasel	Total
Head-On
Slant
Rear-End
Total

Two-Factor ANOVA with Replication
Source	SS	df	MS	F	p-value
Factor 1 (Angle)
Factor 2 (Vehicle)
Interaction
Error
Total

(d) Perform Tukey multiple comparison tests. (Input the mean values within the input boxes of the first row and input boxes of the first column. Round your t-values and critical values to 2 decimal places and other answers to 1 decimal place.)

Post hoc analysis for Factor 1:

Tukey simultaneous comparison t-values (d.f. = 18)
	Rear-End	Head-On	Slant

Rear-End
Head-On
Slant
Critical values for experimentwise error rate:
	0.05
	0.01

Post hoc analysis for Factor 2:

Tukey simultaneous comparison t-values (d.f. = 18)
	Goliath	Varmint	Weasel

Goliath
Varmint
Weasel
critical values for experimentwise error rate:
	0.05
	0.01

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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