Question

The table to the right contairs observed values and expected values in parentheses for two categorical variables, X and Y where variable: X has the categories and variable: Y hasta categories. Use the table to complete aarts(a) and (b) helow. 23.05 (42313 45.643 16 1916 114.15 (17.6939.16 2 (a) Compute the value of the chi-square test statistic. Round to three decimal places needed. (b) Test the hypothesis that X and Y are Independent at the a=0.1 level of algnilcance. O A. Hy: The Y category and X category are independent H: The y category ard X category are dependent OB. Hy: The category ard X category live equal proportions. Hy: The proportions are not equal. OC. Ho Ho - E, and My-E, Hyry OD. Hy: The y category and X category are dependent. H: The Y category and X category independent What is tha P-value? P valueRound ta three decimal places as needed.) Should the null hypothesis be rejected? O A. Yes, reject H. There is not sufficient evidence at the a-0.1 level of significance to conclude that X and Y are dependent because the P-value <«. O B. No, da nat reject Ho. There is sufficient evidence at the a=0.1 level of significance to conclude that X and Y are rependent because the P-value OC. Yes, reject H. There is not sufficient evidence at the a-0.1 level of eignificance to conclude that X and Y are dependent because the P-value> OD. No, to nat reject Hp. There is not sufficient evidence at the e=0.1 level of significanon to conclude that X and Y are dependent because the P-value>

Answer 1

(a). The $\chi ^{2}$ statistic:

x2 = 1.221

(b). Test the hypothesis:

A: $H_{0}:$ The Y category and the X category are independent

  The Y category and the X category are dependent

H1

(c). What is the p-value?

p-value =0.5432

(d). Should the Null hypothesis be rejected?

D. No, do not reject $H_{0}$ , There is not sufficient evidence at the $\alpha =0.1$ level of significance to conclude that X and Y are dependent.

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OBS	X1	X2	X3	Total
Y1	32	41	49	122
Y2	16	19	16	51
Total	48	60	65	173
EXP	X1	X2	X3	Total
Y1	33.84971	42.31214	45.83815	122
Y2	14.15029	17.68786	19.16185	51
Total	48	60	65	173
$\chi ^{2}$	X1	X2	X3	Total
Y1	0.101077	0.040691	0.2181	0.359868
Y2	0.241792	0.097338	0.521729	0.86086
Total	0.342869	0.138029	0.739829	1.220727