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>

Test of Independence using Contingency data table

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