Question

Question 22 2 pts A study was performed to examine the reasons for attending a college. A random sample of college students was selected from five universities in Washington. The students received a questionnaire regarding their personal goals. They were asked to choose two most reasons out of ten goals listed in the questionnaire. They were also allowed to write in their goals. The results are presented in a two-way table where the rows represent the personal goals and the columns represents the college standing. For more details, see the Excel file provided in the next step. Step 1: The null hypothesis being tested by the chi-square test of the above data is that the personal goals and the class standing are associated. the distribution of personal goals changes over time. o the distribution of personal goals is the same across the class standing.

Answer 1

Observed Frequencies
	C1	C2	C3	C4	Total
R1	44	37	55	57	193
R2	41	42	34	31	148
R3	10	19	15	7	51
R4	12	15	7	8	42
R5	8	7	12	16	43
R6	13	12	8	7	40
Total	128	132	131	126	517
Expected Frequencies
	C1	C2	C3	C4	Total
R1	128 * 193 / 517 = 47.7834	132 * 193 / 517 = 49.2766	131 * 193 / 517 = 48.9033	126 * 193 / 517 = 47.0368	193
R2	128 * 148 / 517 = 36.6422	132 * 148 / 517 = 37.7872	131 * 148 / 517 = 37.501	126 * 148 / 517 = 36.0696	148
R3	128 * 51 / 517 = 12.6267	132 * 51 / 517 = 13.0213	131 * 51 / 517 = 12.9226	126 * 51 / 517 = 12.4294	51
R4	128 * 42 / 517 = 10.3985	132 * 42 / 517 = 10.7234	131 * 42 / 517 = 10.6422	126 * 42 / 517 = 10.236	42
R5	128 * 43 / 517 = 10.646	132 * 43 / 517 = 10.9787	131 * 43 / 517 = 10.8956	126 * 43 / 517 = 10.4797	43
R6	128 * 40 / 517 = 9.9033	132 * 40 / 517 = 10.2128	131 * 40 / 517 = 10.1354	126 * 40 / 517 = 9.7485	40
Total	128	132	131	126	517
	(fo-fe)²/fe
R1	(44 - 47.7834)²/47.7834 = 0.2996	(37 - 49.2766)²/49.2766 = 3.0585	(55 - 48.9033)²/48.9033 = 0.7601	(57 - 47.0368)²/47.0368 = 2.1104
R2	(41 - 36.6422)²/36.6422 = 0.5183	(42 - 37.7872)²/37.7872 = 0.4697	(34 - 37.501)²/37.501 = 0.3268	(31 - 36.0696)²/36.0696 = 0.7125
R3	(10 - 12.6267)²/12.6267 = 0.5464	(19 - 13.0213)²/13.0213 = 2.7451	(15 - 12.9226)²/12.9226 = 0.3339	(7 - 12.4294)²/12.4294 = 2.3717
R4	(12 - 10.3985)²/10.3985 = 0.2467	(15 - 10.7234)²/10.7234 = 1.7055	(7 - 10.6422)²/10.6422 = 1.2465	(8 - 10.236)²/10.236 = 0.4884
R5	(8 - 10.646)²/10.646 = 0.6577	(7 - 10.9787)²/10.9787 = 1.4419	(12 - 10.8956)²/10.8956 = 0.112	(16 - 10.4797)²/10.4797 = 2.9079
R6	(13 - 9.9033)²/9.9033 = 0.9683	(12 - 10.2128)²/10.2128 = 0.3128	(8 - 10.1354)²/10.1354 = 0.4499	(7 - 9.7485)²/9.7485 = 0.7749

Q22:

Null Hypothesis:

Ho: the distribution of personal goals is the same across the class standing.

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Q23:

1. The expected value of cell corresponding to "Increase your earning potential" and "Freshman" =

= 128 * 193 / 517 = 47.7834

2. Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 25.566

3. df = (r-1)(c-1) = 15

p-value = CHISQ.DIST.RT(25.5655, 15) = 0.0428

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Q24:

At the significance level of 5% = Reject the null hypothesis. the difference is significant.

At the significance level of 1% = Reject the null hypothesis. the difference is significant.