Question

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 complete parts​ (a) and​ (b) below. Upper X 1 Upper X 2 Upper X 3 Upper Y 1 33 left parenthesis 34.59 right parenthesis 42 left parenthesis 43.96 right parenthesis 54 left parenthesis 50.45 right parenthesis Upper Y 2 15 left parenthesis 13.41 right parenthesis 19 left parenthesis 17.04 right parenthesis 16 left parenthesis 19.55 right parenthesis LOADING... Click the icon to view the​ Chi-Square table of critical values. ​(a) Compute the value of the​ chi-square test statistic. chi Subscript 0 Superscript 2equals nothing ​(Round to three decimal places as​ needed.) ​(b) Test the hypothesis that X and Y are independent at the alpha equals 0.1 level of significance. A. Upper H 0​: The Upper Y category and Upper X category are independent. Upper H 1​: The Upper Y category and Upper X category are dependent. B. Upper H 0​: The Upper Y category and Upper X category are dependent. Upper H 1​: The Upper Y category and Upper X category are independent. C. Upper H 0​: mu Subscript xequals Upper E Subscript x and mu Subscript yequals Upper E Subscript y Upper H 1​: mu Subscript xnot equals Upper E Subscript x or mu Subscript ynot equals Upper E Subscript y D. Upper H 0​: The Upper Y category and Upper X category have equal proportions. Upper H 1​: The proportions are not equal. What range of​ P-values does the test statistic correspond​ to? The​ P-value is ▼ greater than .10. between .01 and .025. between .05 and .10. between .025 and .05. less than .01. Should the null hypothesis be​ rejected? A. No​, do not reject Upper H 0. There is sufficient evidence at the alphaequals0.1 level of significance to conclude that X and Y are dependent because the ​P-valueless thanalpha. B. Yes​, reject Upper H 0. There is not sufficient evidence at the alphaequals0.1 level of significance to conclude that X and Y are dependent because the ​P-valueless thanalpha. C. Yes​, reject Upper H 0. There is not sufficient evidence at the alphaequals0.1 level of significance to conclude that X and Y are dependent because the ​P-valuegreater thanalpha. D. No​, do not reject Upper H 0. There is not sufficient evidence at the alphaequals0.1 level of significance to conclude that X and Y are dependent because the ​P-valuegreater thanalpha. Click to select your answer(s).

Upper X 1X1

Upper X 2X2

Upper X 3X3

Upper Y 1Y1

3333

left parenthesis 34.59 right parenthesis(34.59)

4242

left parenthesis 43.96 right parenthesis(43.96)

5454

left parenthesis 50.45 right parenthesis(50.45)

Upper Y 2Y2

1515

left parenthesis 13.41 right parenthesis(13.41)

1919

left parenthesis 17.04 right parenthesis(17.04)

1616

left parenthesis 19.55 right parenthesis(19.55)

Answer 1