Answered: You wish to test the following claim…

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

You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001.

Ho:μ=77.3Ho:μ=77.3
Ha:μ>77.3Ha:μ>77.3

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=4n=4 with a mean of M=91.9M=91.9 and a standard deviation of SD=20.8SD=20.8.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

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

Given,

Sample size = 4

Sample mean = 91.9

Sample standard deviation = 20.8

Set up the null and the alternative hypothesis.

Step 2

Critical value:

The critical value at the given level of significance with 86 degrees of freedom is, 10.215

Decision rule:

Calculate test statistic:

Under the test statistic for one sample t test is,

Step by step

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