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 (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 ? Please show the caluclations if possible.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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

(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	?

Please show the caluclations if possible.

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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