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In: Statistics and Probability

The table to the right contains observed values and expected values in parentheses for two categorical​...

The table to the right contains observed values and expected values in parentheses for two categorical​ variables, X and​ Y, where variable X has three categories and variable Y has two categories. Use the table to answer the question below. Complete parts ​(a) and ​(b) below.

X1 X2 X3
Y1 69 (69.845) 61 (50.725 69 (78.429
Y2 110 (109.155) 69 (79.275) 132 (122.571)

(a) Compute the value of the chi-square test statistic

(b)Test the hypothesis that X and Y are independent at the alpha=0.05 level of significance.

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