CFA CFA Level 1 Test of Independence using Contingency data table

# Test of Independence using Contingency data table

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• metwoboy
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• CFA Level 1
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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
 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. χ2=i=1m(OijEij)2Eij ${\chi }^{2}=\sum _{i=1}^{m}\frac{{}^{\left(}}{}2{E}_{ij}$ 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.