A certain polymer is used for evacuation systems for aircraft. It is important that the polymer be resistant tothe aging process. Fifty specimens of the polymer were used in an experiment. Twenty‐five were assignedrandomly to be exposed to an accelerated batch aging process that involved exposure to high temperatures for10 days. Question Which Treatment results in the higher mean tensile strength? (Circle One) Aging or No AgingWhich Treatment has the higher variability? (Circle One) Aging or No Aging Distributions Treatement-AgingTensile Strength, PSI209210222211223Distributions Treatement-No AgingTensile Strength, PSI122421:225 226Quantiles100.0% maximum99.5%97.5%90.0%75.0%quartile50.0% median25.0% quartile10.0%2.5%0.5%0.0%minimumQuantiles100.0% maximum99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%quartilemedianquartileminimum212212210209212212211211 N209209209225225225Summary StatisticsMeanStd DevStd Err Mean225224224223222222222222210.60.91287090.1825742Upper 95% Mean210.97681Lower 95% Mean 210.2231925Summary StatisticsMeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN223.680.90.18224.0515223.308525

Given: Treatment: Aging n1 = 25 X1 = 210.6 s1 = 0.9128709 Treatment: No Aging n2 = 25 X2 = 223.68 s2…

Answered: A certain polymer is used for…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 4GP

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Question

A certain polymer is used for evacuation systems for aircraft. It is important that the polymer be resistant to
the aging process. Fifty specimens of the polymer were used in an experiment. Twenty‐five were assigned
randomly to be exposed to an accelerated batch aging process that involved exposure to high temperatures for
10 days.

Question Which Treatment results in the higher mean tensile strength? (Circle One) Aging or No Aging
Which Treatment has the higher variability? (Circle One) Aging or No Aging

Distributions Treatement-Aging
Tensile Strength, PSI
209
210
222
211
223
Distributions Treatement-No Aging
Tensile Strength, PSI
1
224
21:
225 226
Quantiles
100.0% maximum
99.5%
97.5%
90.0%
75.0%
quartile
50.0% median
25.0% quartile
10.0%
2.5%
0.5%
0.0%
minimum
Quantiles
100.0% maximum
99.5%
97.5%
90.0%
75.0%
50.0%
25.0%
10.0%
2.5%
0.5%
0.0%
quartile
median
quartile
minimum
212
212
210
209
212
212
211
211 N
209
209
209
225
225
225
Summary Statistics
Mean
Std Dev
Std Err Mean
225
224
224
223
222
222
222
222
210.6
0.9128709
0.1825742
Upper 95% Mean
210.97681
Lower 95% Mean 210.22319
25
Summary Statistics
Mean
Std Dev
Std Err Mean
Upper 95% Mean
Lower 95% Mean
N
223.68
0.9
0.18
224.0515
223.3085
25

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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