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 2mm2⁢mm, 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 100 random intervals. The variance of those measurements is found to be 0.001119mm. Does this evidence provide support that the batch of yarn is unusable by the manufacturer? Use a 0.025 level of significance. Step 3 of 3 : Draw a conclusion and interpret the decision. 1. We reject the null hypothesis and conclude that there is sufficient evidence at a 0.025 level of significance that the batch of yarn is unusable. 2. We fail to eject the null hypothesis and conclude that there is sufficient evidence at a 0.025 level of significance that the batch of yarn is unusable. 3. We reject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance that the batch of yarn is unusable. 4. We fail to eject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance that the batch of yarn is unusable.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 2mm2⁢mm, 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 100 random intervals. The variance of those measurements is found to be 0.001119mm. Does this evidence provide support that the batch of yarn is unusable by the manufacturer? Use a 0.025 level of significance.

Step 3 of 3 : Draw a conclusion and interpret the decision.

1. We reject the null hypothesis and conclude that there is sufficient evidence at a 0.025 level of significance that the batch of yarn is unusable.

2. We fail to eject the null hypothesis and conclude that there is sufficient evidence at a 0.025 level of significance that the batch of yarn is unusable.

3. We reject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance that the batch of yarn is unusable.

4. We fail to eject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance that the batch of yarn is unusable.

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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