You wish to test the following claim (Ha) at a significance level of α=0.001. Ho:μ=58.1 Ha:μ≠58.1You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=7 with mean M=82.6 and a standard deviation of SD=16.2.What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is...less than (or equal to) α greater than α This p-value leads to a decision to...reject the nullaccept the nullfail to reject the nullAs such, the final conclusion is that...There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 58.1.There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 58.1.The sample data support the claim that the population mean is not equal to 58.1.There is not sufficient sample evidence to support the claim that the population mean is not equal to 58.1.

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

Ho:μ=58.1
Ha:μ≠58.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=7 with mean M=82.6 and a standard deviation of SD=16.2.

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

less than (or equal to) α

greater than α

This p-value leads to a decision to...

reject the null
accept the null
fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 58.1.
There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 58.1.
The sample data support the claim that the population mean is not equal to 58.1.
There is not sufficient sample evidence to support the claim that the population mean is not equal to 58.1.

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

Step 1

$Given significance level (α) = 0.001 The null and alternative hypothesis is H_{0} : μ = 58.1 H_{a} : μ \neq 58.1 sample size (n) = 7 Mean (M) = 82.6 standard deviation (SD) = 16.2$