2. Research Question: Does the treatment result in a lower completion time (group 1 =treatment, 0 = control)?moreGroup StatisticsMeanStd. DeviationStd. Error Mean1421.615.2191.3951.1518.174.6131.191Independent Samples TestLevene's Test for Equality ofVariancest-test for Equality of MeansSig.Sig. (2-tailed)yEqual variances assumed.114.7381.88027.071Equal variances not1.87226.024.073assumed

Name: 2. Research Question: Does the treatment result in a lower completion
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Description: 2. Research Question: Does the treatment result in a lower completion time (group 1 =treatment, 0 = control)?moreGroup StatisticsMeanStd. DeviationStd. Error Mean1421.615.2191.3951.1518.174.6131.191Independent Samples TestLevene's Test for Equality

Answered: 2. Research Question: Does the…

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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$H_{0} : μ_{1} = μ_{2} v s H_{0} : μ_{2} < μ_{1} μ_{1} : p o p u l a t i o n m e a n o f t r e a t m e n t g r o u p μ_{2} : p o p u l a t i o n m e a n o f c o n t r o l g r o u p$

As the Population Standard Deviation is unknown the test statistic is given as :

$t_{0} = \frac{{\bar{x}}_{1} - {\bar{x}}_{2}}{S_{p} \sqrt{\frac{1}{n_{1}} + \frac{1}{n_{2}}}}, {\bar{x}}_{1} : s a m p l e m e a n o f t r e a t m e n t g r o u p {\bar{x}}_{2} : s a m p l e m e a n o f c o n t r o l g r o u p S_{p} = \frac{(n_{1} - 1) {s^{2}}_{1} + (n_{2} - 1) {s^{2}}_{2}}{n_{1} + n_{2} - 2}, s_{1} : s a m p l e s \tan d a r d d e v i a t i o n o f t r e a t m e n t g r o u p s_{2} : s a m p l e s \tan d a r d d e v i a t i o n o f c o n t r o l g r o u p w h e r e b o t h t h e p o p u l a t i o n s \tan d a r d d e v i a t i o n s o f t h e t r e a t m e n t g r o u p (σ_{1}) a n d t h e c o n t r o l g r o u p (σ_{2}) a r e a s s u m e d t o b e e q u a l .$

else,

$t_{0} = \frac{{\bar{x}}_{1} - {\bar{x}}_{2}}{\sqrt{\frac{{s^{2}}_{1^{}}}{n_{1}} + \frac{{s^{2}}_{2}}{n_{2}}}}, {\bar{x}}_{1} : s a m p l e m e a n o f t r e a t m e n t g r o u p {\bar{x}}_{2} : s a m p l e m e a n o f c o n t r o l g r o u p s_{1} : s a m p l e s \tan d a r d d e v i a t i o n o f t r e a t m e n t g r o u p s_{2} : s a m p l e s \tan d a r d d e v i a t i o n o f c o n t r o l g r o u p w h e r e b o t h t h e p o p u l a t i o n s \tan d a r d d e v i a t i o n s o f t h e t r e a t m e n t g r o u p (σ_{1}) a n d t h e c o n t r o l g r o u p (σ_{2}) a r e a s s u m e d t o b e u n e q u a l .$

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