Hi, I have a question on this Exhibit 30 example. I am not sure why this is a one-tailed test. Given Hypothesis set up is H0: R = 0 ; Ha: R != 0 If the null hypothesis is rejected, then the Alt Hypothesis can be positively correlated and negative correlated. Isn't this is indicating a two- tailed test? Thanks <div class="clearfix cfa-exhibit-header"> Exhibit 30-- Test of Independence of Size and Investment Type for 1,594 ETFs </div> <div id="CFA0129-R-EXH30" class="cfa-exhibit"> Step 1 State the hypotheses. H0: ETF size and investment type are not related, so these classifications are independent; Ha : ETF size and investment type are related, so these classifications are not independent. Step 2 Identify the appropriate test statistic. <span id="MathJax-Element-101-Frame" class="MathJax" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; font-family: var(--content-font); font-size: 16px; color: var(--content-dark); display: inline; font-style: normal; font-weight: normal; line-height: 1.4; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="χ2=∑i=1m(Oij−Eij)2Eij">χ2=∑i=1m(Oij−Eij)2Eijχ2=∑i=1m(Oij−Eij)2Eij Step 3 Specify the level of significance. 5% Step 4 State the decision rule. With (3 − 1) × (3 − 1) = 4 degrees of freedom and a one-sided test with a 5% level of significance, the critical value is 9.4877. </div>

A CFA Level 1 Discussion About Test Of Independence Using Contingency Data Table

Add A Reply

Topic Resolution: Not Resolved

This topic has 0 replies, 1 voice, and was last updated Sep-213:27 am by metwoboy.

Author

Posts

metwoboy

Participant

CFA Level 1

07 Sep 2021 at 3:27 am

Hi,

I have a question on this Exhibit 30 example. I am not sure why this is a one-tailed test.

Given Hypothesis set up is H0: R = 0 ; Ha: R != 0

If the null hypothesis is rejected, then the Alt Hypothesis can be positively correlated and negative correlated. Isn’t this is indicating a two- tailed test?

Thanks
<div class=”clearfix cfa-exhibit-header”>

Exhibit 30– Test of Independence of Size and Investment Type for 1,594 ETFs

</div>
<div id=”CFA0129-R-EXH30″ class=”cfa-exhibit”>

Step 1	State the hypotheses.	H₀: ETF size and investment type are not related, so these classifications are independent; H_a: ETF size and investment type are related, so these classifications are not independent.
Step 2	Identify the appropriate test statistic.	<span id=”CFA0129-R-eq101″><span id=”MathJax-Element-101-Frame” class=”MathJax” style=”margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; font-family: var(–content-font); font-size: 16px; color: var(–content-dark); display: inline; font-style: normal; font-weight: normal; line-height: 1.4; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;” tabindex=”0″ role=”presentation” data-mathml=” $χ^{2} = \sum_{i = 1}^{m}^{(O_{i j} - E_{i j})} 2 E_{i j}$ “><span id=”m101″ class=”math”><span id=”MathJax-Span-2485″ class=”mrow”><span id=”MathJax-Span-2486″ class=”mrow”><span id=”MathJax-Span-2487″ class=”msup”><span id=”MathJax-Span-2488″ class=”mi”>χ</span><span id=”MathJax-Span-2489″ class=”mn”>2</span></span><span id=”MathJax-Span-2490″ class=”mo”>=</span><span id=”MathJax-Span-2491″ class=”mstyle”><span id=”MathJax-Span-2492″ class=”mrow”><span id=”MathJax-Span-2493″ class=”munderover”><span id=”MathJax-Span-2494″ class=”mo”>∑</span><span id=”MathJax-Span-2495″ class=”mrow”><span id=”MathJax-Span-2496″ class=”mi”>i</span><span id=”MathJax-Span-2497″ class=”mo”>=</span><span id=”MathJax-Span-2498″ class=”mn”>1</span></span><span id=”MathJax-Span-2499″ class=”mi”>m</span></span><span id=”MathJax-Span-2500″ class=”mrow”><span id=”MathJax-Span-2501″ class=”mfrac”><span id=”MathJax-Span-2502″ class=”mrow”><span id=”MathJax-Span-2503″ class=”msup”><span id=”MathJax-Span-2504″ class=”mrow”><span id=”MathJax-Span-2505″ class=”mrow”><span id=”MathJax-Span-2506″ class=”mo”>(</span><span id=”MathJax-Span-2507″ class=”mrow”><span id=”MathJax-Span-2508″ class=”msub”><span id=”MathJax-Span-2509″ class=”mi”>O</span><span id=”MathJax-Span-2510″ class=”mrow”><span id=”MathJax-Span-2511″ class=”mi”>i</span><span id=”MathJax-Span-2512″ class=”mi”>j</span></span></span><span id=”MathJax-Span-2513″ class=”mo”>−</span><span id=”MathJax-Span-2514″ class=”msub”><span id=”MathJax-Span-2515″ class=”mi”>E</span><span id=”MathJax-Span-2516″ class=”mrow”><span id=”MathJax-Span-2517″ class=”mi”>i</span><span id=”MathJax-Span-2518″ class=”mi”>j</span></span></span></span><span id=”MathJax-Span-2519″ class=”mo”>)</span></span></span><span id=”MathJax-Span-2520″ class=”mn”>2</span></span></span><span id=”MathJax-Span-2521″ class=”mrow”><span id=”MathJax-Span-2522″ class=”msub”><span id=”MathJax-Span-2523″ class=”mi”>E</span><span id=”MathJax-Span-2524″ class=”mrow”><span id=”MathJax-Span-2525″ class=”mi”>i</span><span id=”MathJax-Span-2526″ class=”mi”>j</span></span></span></span></span></span></span></span></span></span></span><span class=”MJX_Assistive_MathML” role=”presentation”> $χ^{2} = \sum_{i = 1}^{m}^{(O_{i j} - E_{i j})} 2 E_{i j}$ </span></span></span>
Step 3	Specify the level of significance.	5%
Step 4	State the decision rule.	With (3 − 1) × (3 − 1) = 4 degrees of freedom and a one-sided test with a 5% level of significance, the critical value is 9.4877.

</div>

Author

Posts

Viewing 0 reply threads

You must be logged in to reply to this topic.