Answered: An experiment was run to determine…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 2E

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Question

An experiment was run to determine whether four specific firing temperatures
affect the density of a certain type of brick. The experiment was laid out using completely
randomized design. Analysis showed that at least one firing temperature has a different mean
density.

Pairwise mean comparison of the firing temperatures was conducted. Based on the output
below, which is the following is(are) TRUE at 5% level of significance?

I. The mean density is significantly different at higher temperatures as compared with 100 OC.
II. The mean density at 125 OC is significantly different with the mean density at 150 OC.

A. I only

B. II only

C. Both I and II

D. Neither I nor II

Post Hoc Comparisons - temperature
Comparison
temperature
temperature
Mean Difference
SE
df
Ptukex
100
125
0.2750
0.0901
12.0
3.051
0.043
150
-0.0250
0.0901
12.0
-0.277
0.992
175
0.0500
0.0901
12.0
0.555
0.943
125
150
-0.3000
0.0901
12.0
-3.328
0.027
175
-0.2250
0.0901
12.0
-2.496
0.111
150
175
0.0750
0.0901
12.0
0.832
0.838

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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