Answered: A sample of 100 observations has a…

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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Question

A sample of 100 observations has a sample mean of 500 and a sample standard deviation of 50. Conduct a hypothesis test to determine if the population mean is equal to 480 at a significance level of 0.05.

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 + ...

Expert Solution

Step 1

Introduction:

Hypothesis testing is a statistical method used to make decisions about a population based on a sample of data. In this problem, we are conducting a hypothesis test to determine if the population mean is equal to 480, using a sample of 100 observations with a mean of 500 and a standard deviation of 50. We will use a significance level of 0.05, meaning that we are willing to accept a 5% chance of making a type I error (rejecting a true null hypothesis). To perform the test, we will calculate a test statistic and compare it to a critical value to determine whether or not to reject the null hypothesis.