Hypothesis Testing for Standard DeviationA teacher claims that the ACT test score standard deviations was less than 5.5 for her students. The results areshown below. At the level of significance, is there enough evidence to support her claim?2928212823232729282820292123291624292821Use the Standard Deviation tab to complete the test.Begin by entering the data starting with J2 to get the sample standard deviation s and sample size n.Use those values to complete the C6 to C8.For C4, change the direction of the arrow to reflect the claim.Finish by entering the claim value in D4Results:Is there enough evidence to support her claim? Give your answer in complete sentences. Justify your answereither by using a rejection region or a p-value argument.

Answered: -Hypothesis Testing for Standard…

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

Hypothesis Testing for Standard Deviation
A teacher claims that the ACT test score standard deviations was less than 5.5 for her students. The results are
shown below. At the level of significance, is there enough evidence to support her claim?
29
28
21
28
23
23
27
29
28
28
20
29
21
23
29
16
24
29
28
21
Use the Standard Deviation tab to complete the test.
Begin by entering the data starting with J2 to get the sample standard deviation s and sample size n.
Use those values to complete the C6 to C8.
For C4, change the direction of the arrow to reflect the claim.
Finish by entering the claim value in D4
Results:
Is there enough evidence to support her claim? Give your answer in complete sentences. Justify your answer
either by using a rejection region or a p-value argument.

Expert Solution

Step 1

Given Data :

First we will calculate the sample standard deviation :

$X$	$X^2$
29	841
28	784
21	441
28	784
23	529
23	529
27	729
29	841
28	784
28	784
20	400
29	841
21	441
23	529
29	841
16	256
24	576
29	841
28	784
21	441
$504$	$12996$

Sample variance :

$\begin{array}{ccl} s^2 & = & \displaystyle \frac{1}{n-1} \left( \sum_{i=1}^n X_i^2 - \frac{1}{n}\left(\sum_{i=1}^n X_i\right)^2 \right) \\\\ \\\\ & = & \displaystyle \frac{1}{20 - 1} \left( 12996 - \frac{504^2}{20} \right) \\\\ \\\\ & = & 15.5368 \end{array}$