Question

1. Two researcher want to find out whether there is a difference among graduation rates (these are in percentages) of five colleges over a 10-year period. Using the Data set below, determine if there a difference between colleges? Do this manually and show all eight steps in computing. (HINT: There is one variable being examined (i.e. graduation rates) for more than two groups (i.e. college 1, 2, 3, 4, 5) that are tested only once).

	College 1	College 2	College 3	College 4	College 5
2005	67	82	94	65	88
2006	68	87	78	65	87
2007	65	83	81	45	86
2008	68	73	76	57	88
2009	67	77	75	68	89
2010	71	74	81	76	87
2011	78	76	79	77	81
2012	76	78	89	72	78
2013	72	76	76	69	89
2014	77	86	77	58	87

2. How do you interpret = 18.9, p < .05?

3. If the correlation between variable X and variable Y is perfect, what do you know about the prediction?

Answer 1

1. The hypothesis being tested is:

H₀: There is no difference among graduation rates

H_a: There is a difference among graduation rates

	Mean	n	Std. Dev
	70.900	10	4.677	College 1
	79.200	10	4.962	College 2
	80.600	10	6.204	College 3
	65.200	10	9.727	College 4
	86.000	10	3.621	College 5
	79.200	5	12.795	Block 1
	77.000	5	10.320	Block 2
	72.000	5	17.146	Block 3
	72.400	5	11.327	Block 4
	75.200	5	8.843	Block 5
	77.800	5	6.301	Block 6
	78.200	5	1.924	Block 7
	78.600	5	6.309	Block 8
	76.400	5	7.635	Block 9
	77.000	5	11.640	Block 10
	76.380	50	9.549	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatments	2,733.28	4	683.320	16.88	7.06E-08
Blocks	276.98	9	30.776	0.76	.6528
Error	1,457.52	36	40.487
Total	4,467.78	49

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference among graduation rates.

2. Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference among graduation rates.

3. The prediction will be significant and trustworthy.