The following data are from a hypothetical experiment in which one group of students took a quiz in awell-lit room and another group of students took the quiz in dimly lit room. What test should you perform?Do these data indicate a significant difference between the treatments (room lighting) at the .05 level ofsignificance?

Answered: The following data are from a…

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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The following data are from a hypothetical experiment in which one group of students took a quiz in a
well-lit room and another group of students took the quiz in dimly lit room. What test should you perform?
Do these data indicate a significant difference between the treatments (room lighting) at the .05 level of
significance?

Expert Solution

Step 1

In this study, one group of students took quiz in well-lit room and another group of students took quiz in dimly lit room. Since there are two independent samples and the population standard deviation is not known two independent samples t test must be used.

Thus, the test that should be performed is two independent samples t test.

The claim is to test whether the is significant difference between the treatment or not. Let $μ_{1}$ be the population mean score of treatment 1 and $μ_{2}$ be the population mean score of treatment 2.

Null hypothesis:

$H_{0} : μ_{1} = μ_{2}$

Alternative hypothesis:

$H_{a} : μ_{1} \neq μ_{2}$

The mean for treatment 1 is,

$\begin{array}{rcl} {\bar{x}}_{1} & = & \frac{\sum_{} X_{1}}{n_{1}} \\ = & \frac{4 + 5 + 12 + 10 + 10 + 7}{6} \\ = & \frac{48}{6} \\ = & 8 \end{array}$

The mean for treatment 1 is 8.

The mean for treatment 2 is,

$\begin{array}{rcl} {\bar{x}}_{2} & = & \frac{\sum_{} X_{2}}{n_{2}} \\ = & \frac{19 + 11 + 18 + 10 + 12 + 14}{6} \\ = & \frac{84}{6} \\ = & 14 \end{array}$

The mean for treatment 2 is 14.

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