Answered: Many properties of the fabric used in…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Many properties of the fabric used in different textiles, such as sheets and clothing, are influenced by whether the diameter of yarn used in the creation of the textile is consistent. Therefore, various methods can be used to measure the diameter of yarn at specified intervals, such as every 2mm, to determine the consistency of the diameter. These measurements are normally distributed. Suppose that one textile manufacturer will not use any yarn in which the variance of the diameters is greater than 0.0009mm. In order to ensure that the yarn is usable, the diameter of a length of yarn is measured at 400 random intervals. The variance of those measurements is found to be 0.000992mm. Does this evidence provide support that the batch of yarn is unusable by the manufacturer? Use a 0.005 level of significance.

Step 2 of 3 :

Compute the value of the test statistic. Round your answer to three decimal places.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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