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  1. A College Algebra teacher would like to find out whether the possession of a textbook enhances achievement score $X$. From an engineering freshmen class of 50 students, she took the scores in a 20 – item quiz of 5 randomly chosen students with textbook (1) and 5 without textbook (0). Compute the correlation between X and Y. My question, is $Y$ nominal and $X$ interval scale in this data set?What correlation should I use? Spearman Rho ; Pearson R ; Chi-Square? Thanks.
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Your $X$ consists of achievement scores, so they are probably ratio scale, as I imagine they are numeric scores with a clear definition of $0$. Your $Y$ is a binary indicator variable; this one is tricky because although you may be tempted to label is as nominal, $1$ indicates the presence of a textbook and, in contrast, $0$ indicates the absence of one. In this situation, you should consider $Y$ to be ordinal.

For comparing quantitative data to a binary variable, I would start by trying a logit model:

$$ \log\left(\frac{\Pr(Y)}{1-\Pr(Y)}\right)=\beta_0+\beta_1X $$

You can then perform a t-test to test the hypothesis that $\beta_1 = 0$. If it the hypothesis is rejected, then $\beta_1$ tells us something about the direction and strength of the relationship between $X$ and $Y$.

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