You wish to test the following claim at a significance level of α=0.05 H0:μ=52.6 H1:μ>52.6You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size 87 with mean 53.5 and a standard deviation of 7.2.What is the test statistic for this sample? (Report answer accurate to 3 decimal places.)What is the p-value for this sample? (Report answer accurate to 4 decimal places.)This test statistic leads to a decision toreject the nullaccept the nullfail to reject the nullAs such, the final conclusion is thatthere is sufficient evidence to conclude that the population mean is equal to 52.6.there is not sufficient evidence to conclude that the population mean is equal to 52.6.there is sufficient evidence to conclude that the population mean is greater than 52.6.there is not sufficient evidence to conclude that the population mean is greater than 52.6.

Name: You wish to test the following claim at a significance level of α=0.05
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Description: You wish to test the following claim at a significance level of α=0.05 H0:μ=52.6 H1:μ>52.6You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size 87 with mean 53.5 and a st

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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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You wish to test the following claim at a significance level of α=0.05

H0:μ=52.6
H1:μ>52.6

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size 87 with mean 53.5 and a standard deviation of 7.2.

What is the test statistic for this sample? (Report answer accurate to 3 decimal places.)

What is the p-value for this sample? (Report answer accurate to 4 decimal places.)

This test statistic 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 conclude that the population mean is equal to 52.6.
there is not sufficient evidence to conclude that the population mean is equal to 52.6.
there is sufficient evidence to conclude that the population mean is greater than 52.6.
there is not sufficient evidence to conclude that the population mean is greater than 52.6.

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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