You wish to test the following claim (Ha) at a significance level of α=0.005. Ho:μ1=μ2 Ha:μ1≠μ2 You believe both populations are normally distributed, but you do not know the standard deviations for either, and you have no reason to believe the variances of the two populations are equal. You obtain a sample of size n1=18 with a mean of M1=81.6 and a standard deviation of SD1=8.2 from the first population. You obtain a sample of size n2=23 with a mean of M2=88.9 and a standard deviation of SD2=5.8 from the second population. What is the test statistic for this sample? (Report answer accurate to two decimal places.) test statistic = 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 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 reject the claim that the first population mean is not equal to the second population mean. There is not sufficient evidence to reject the claim that the first population mean is not equal to the second population mean. There is sufficient evidence to support the claim that the first population mean is not equal to the second population mean. There is not sufficient evidence to support the claim that the first population mean is not equal to the second population mean.

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=0.005.

Ho:μ1=μ2
Ha:μ1≠μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either, and you have no reason to believe the variances of the two populations are equal. You obtain a sample of size n1=18 with a mean of M1=81.6 and a standard deviation of SD1=8.2 from the first population. You obtain a sample of size n2=23 with a mean of M2=88.9 and a standard deviation of SD2=5.8 from the second population.

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

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 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 reject the claim that the first population mean is not equal to the second population mean.
There is not sufficient evidence to reject the claim that the first population mean is not equal to the second population mean.
There is sufficient evidence to support the claim that the first population mean is not equal to the second population mean.
There is not sufficient evidence to support the claim that the first population mean is not equal to the second population mean.

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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Step 1

Given:

significance level of α=0.005.

Ho:μ1=μ2
Ha:μ1≠μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either, and you have no reason to believe the variances of the two populations are equal.

sample of size n1=18 with a mean of M1=81.6 and a standard deviation of SD1=8.2 from the first population.

sample of size n2=23 with a mean of M2=88.9 and a standard deviation of SD2=5.8 from the second population.

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