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 (Ha) at a significance level of α=0.01.

Ho:μ1=μ2
Ha:μ1>μ2

You obtain a sample of size n1=13 with a mean of M1=65.1 and a standard deviation of SD1=15.8 from the first population. You obtain a sample of size n2=14 with a mean of M2=49.4 and a standard deviation of SD2=8.3 from the second population. Use the Theory-based inference applet to conduct the test of significance.

(a) What is the t-score for this sample?
t-score = (Round to 2 decimal places.)

(b) What is the p-value for this sample?
p-value = (Round to 4 decimal places.)

(c) The p-value is...

less than (or equal to) α

greater than α

(d) This p-value leads to a decision to...

strong evidence in support of the alternative
accept the null
null is plausible

(e) As such, the final conclusion is that...

We conclude that μ1>μ2

.
We conclude that μ1=μ2
.
We have statistically significant evidence to support the claim that μ1>μ2
..
It is plausible that μ1=μ2

Expert Solution

Step 1

given data

$α = 0.01 H_{o} : μ_{1} = μ_{2} H_{1} : μ_{1} > μ_{2} {\bar{x}}_{1} = 65.1 s_{1} = 15.8 n_{1} = 13 {\bar{x}}_{2} = 49.4 s_{2} = 8.3 n_{2} = 14$

use unequal variance assumption

df = $\frac{{(\frac{{s_{1}}^{2}}{n_{1}} + \frac{{s_{2}}^{2}}{n_{2}})}^{2}}{(\frac{{(\frac{{s_{1}}^{2}}{n_{1}})}^{2}}{n_{1} - 1} + \frac{{(\frac{{s_{2}}^{2}}{n_{2}})}^{2}}{n_{2} - 1})} = 17.8556$