A certain type of capacitor is designed to store a mean energy capacity of 180 joules when fully charged. During a routine check, the capacities (in joules) were measured from a sample of 6 charged capacitors, yielding the following values:177, 178.2, 179.3, 180.5, 180.9, 181.6Assume that the capacity is (at least approximately) normally distributed. At a 5% significance level, does the evidence suggest that the capacitors have a mean energy which is not 180 joules? Report also a p-value.

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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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A certain type of capacitor is designed to store a mean energy capacity of 180 joules when fully charged. During a routine check, the capacities (in joules) were measured from a sample of 6 charged capacitors, yielding the following values:
177, 178.2, 179.3, 180.5, 180.9, 181.6

Assume that the capacity is (at least approximately) normally distributed. At a 5% significance level, does the evidence suggest that the capacitors have a mean energy which is not 180 joules? Report also a p-value.

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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