Answered: The diameter of steel rods manufactured…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

The diameter of steel rods manufactured on two different machines is being investigated. Suppose that the diameter of a rod is normally distributed, despite which machine is used to make the rod. Independent samples of n1=15 rods (from the first machine) and n2=17 rods (from the second machine) are randomly selected. The sample mean and sample variance of the first sample (of 15 rods) are xbar1=8.73, s1^2=0.34, respectively. The sample mean and sample variance of the second sample (of 17 rods) are xbar2=8.68 and s2^2=0.39, respectively. Based on these two samples, one can be 95% confident that that ratio of the two population variances, sigma1^2/sigma2^2 (i.e., the population variance of diameter of steel rods manufactured on the first machine over that on the second machine). Based on the data from these two independent random samples that we assume to arise from two normal populations, we would like to test the null hypothesis that the two population variances are the same versus the alternative hypothesis that the first population variance, sigma1^2, is lower than that of the second population, sigma2^2. What is the p-value of this lower-tailed test? Please keep three digits past the decimal point.

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.

Expert Solution