Answered: 1 Thickness Strength 2.4066 4.9175…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.CR: Chapter Review

Problem 37E: Find the positive geometric mean between 4 and 64.

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Question

6 A valve manufacturer produces a butterfly valve composed of two semicircular plates on a
common spindle that is used to permit flow in one direction only (seen here:
http://en.wikipedia.org/wiki/Butterfly_valve). The semicircular plates are supplied by a vendor
with specifications that the plates be 2.37 millimeters thick and have a tensile strength of five
pounds per millimeter. A random sample of 20 such plates is taken. Electronic calipers are used
to measure the thickness of each plate. A universal testing machine was used to test the tensile
strength. The sample data are found in homework 5.xlsx.
a. Find point estimates of the thickness and tensile strength data. Compare with the
specifications.
b. Construct a 95% confidence interval for mean thickness. Draw conclusions regarding the
specification relative to the confidence interval.
c. Construct a 95% confidence interval for mean tensile strength. Draw conclusions
regarding the specification relative to the confidence interval.
d. Construct a 95% confidence interval for the standard deviation of tensile strength.
e. Construct a 95% confidence interval for the proportion of plates whose thickness is
greater than the specification.

B
1 Thickness Strength
2
2.4066
4.9175
3
2.1328
4.8067
4 2.5937
5.1246
5 2.1933 4.7555
6
2.4579
4.7233
7 2.0665 4.3934
8
2.1994
4.4609
9
2.4575
4.7377
10
2.6724
4.3407
11
2.2738
4.9487
12
2.5392
4.4265
13 2.7956
4.3583
14
2.1228
4.5608
15
2.2055
4.8207
16
2.4359
4.7769
17
2.3353
5.2468
18
2.3238
4.8706
19
2.5267 4.5138
20
2.2146
4.4402
21 2.2699
4.6548
22

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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