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Name: In building an arena , steel bars with a mean ultimate tensile strengt
Uploaded: 2024-03-20T07:07:12.000Z
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Description: In building an arena , steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa ) with a variance of 81 MPa were delivered by the manufacturer . The project engineer tested 50 steel bars and found out that the mean ultimate tensile str

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 building an arena , steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa ) with a variance of 81 MPa were delivered by the manufacturer . The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa The decision for the extension of the contract with the manufacture depends on the engineer . Test the hypothesis whether or not there is no significant difference between the two means using a two-tailed test with a = 0.01

1. What are the appropriate hypotheses for the two tailed test ?

2. What is the test statistic to be used and the reasons for its selection ?

3. What is the critical value c?

4. What is the value of the test statistic or the computed value?

5. Formulate a conclusion about the given situation

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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