Question

High School 1 High School 2 High School 3 High School 4 High School 5 2003 67 82 94 65 88 2004 68 87 78 65 87 2005 65 83 81 45 86 2006 68 73 76 57 88 2007 67 77 75 68 89 2008 71 74 81 76 87 2009 78 76 79 77 81 2010 76 78 89 72 78 2011 72 76 76 69 89 2012 77 86 77 58 87 1 What is your Null Hypothesis there is no difference between the means between the 5 groups 2 What is your Alternate Hypothesis There is a difference between the means between the 5 groups 3 Use the Data Analysis ToolPak to run an ANOVA Single Factor. Show your work on this spreadsheet. 4 Compare your F statistics to your F Critical Value. F stastic > F critical ; Null hypothesis may be reject 5 Discuss your p value P- value > A ; fail to reject the null hypothesis 6 Are your results significant? no 7 What does this information indicate to you? Fail to reject the null hypothesis

Answer 1

The null hypothesis is

H₀ :

Because the null hypthesis is saying that there is no difference between the means between the 5 groups that is all the means are equal.

The alternate hypothesis is

H₁ :

Because the alternate hypthesis is saying that there is a difference between the means between the 5 groups that is all the means are not equal.

	HS1	HS2	HS3	HS4	HS5					Anova: Single Factor
2003	67	82	94	65	88
2004	68	87	78	65	87					SUMMARY
2005	65	83	81	45	86					Groups	Count	Sum	Average	Variance
2006	68	73	76	57	88					HS1	10	709	70.9	21.87778
2007	67	77	75	68	89					HS2	10	792	79.2	24.62222
2008	71	74	81	76	87					HS3	10	806	80.6	38.48889
2009	78	76	79	77	81					HS4	10	652	65.2	94.62222
2010	76	78	89	72	78					HS5	10	860	86	13.11111
2011	72	76	76	69	89
2012	77	86	77	58	87
										ANOVA
										Source of Variation	SS	df	MS	F	P-value	F crit
										Between Groups	2733.28	4	683.32	17.72811	8.38666E-09	2.578739
										Within Groups	1734.5	45	38.54444
										Total	4467.78	49

From the table we can see that the F-statistic > F-critical i.e. 17.72811 > 2.578739 which means that the null hypothesis should be rejected.

Also, the p-value i.e. 8.3866591064466E-09 > 0.05(alpha) which implies that we fail to reject the null hypothesis and the result is statistically nonsignificant.