Question

The table to the right contains observed values and expected values in parentheses for two categorical variables, and where variable X has three categories and variable Yhas two Categories. Use the table to complete parts (a) and (b) below. M X. X X, 34 42 53 34702 16 22 18 15 3018972173 Y; (4) Compute the value of art statistic x-Round to the decimal places needed) MTest the hypothesis that X and Y are independent the 01 level of sigilance OM Hg The Y category and X category have equal proportions H, The proportions are not equal OBH They category and X category are dependent H, They category and X category are independent OCH E, and OD 1 The Y category and X category are independent H, The Yound X category are dependent Click to see your answers

Answer 1

Observed Frequencies
	C1	C2	C3	Total
R1	34	40	53	127
R2	16	22	18	56
Total	50	62	71	183
Expected Frequencies
	C1	C2	C3	Total
R1	50 * 127 / 183 = 34.7	62 * 127 / 183 = 43.03	71 * 127 / 183 = 49.27	127
R2	50 * 56 / 183 = 15.3	62 * 56 / 183 = 18.97	71 * 56 / 183 = 21.73	56
Total	50	62	71	183
	(fo-fe)²/fe
R1	(34 - 34.7)²/34.7 = 0.014	(40 - 43.03)²/43.03 = 0.213	(53 - 49.27)²/49.27 = 0.282
R2	(16 - 15.3)²/15.3 = 0.032	(22 - 18.97)²/18.97 = 0.483	(18 - 21.73)²/21.73 = 0.639

a)

Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 1.663

b)

Ho: The Y category and X category are independent.

H1: The Y category and X category are dependent.

c)

df = (r-1)(c-1) = 2

p-value = CHISQ.DIST.RT(1.663, 2) = 0.4353

Decision:

p-value > α, Do not reject the null hypothesis.

Answer B.