Question

test the hypothesis that Florida has been the dominant orange-producing state in the US historically (e.g. conduct an upper tailed test for Florida compared to the total US values excluding Florida (column F)). Assume a z-distribution

Year	FLORIDA	Non-Florida
1970	137.7	48.07
1971	142.3	47.13
1972	137	54.45
1973	169.7	54.96
1974	165.8	50.41
1975	173.3	64.51
1976	181.2	61.58
1977	186.8	56.15
1978	167.8	52.32
1979	164	46.6
1980	206.7	66.93
1981	172.4	72.18
1982	125.8	50.89
1983	139.6	85.58
1984	116.7	52.74
1985	103.9	54.45
1986	119.2	56.24
1987	119.7	61.475
1988	138	62.25
1989	146.6	62.45
1990	110.2	74.215
1991	151.6	27.35
1992	139.8	69.81
1993	186.6	69.16
1994	174.4	66.05
1995	205.5	58.105
1996	203.3	60.59
1997	226.2	66.82
1998	244	71.525
1999	186	38.58
2000	233	66.76
2001	223.3	57.635
2002	230	53.76
2003	203	64.04
2004	242	52.62
2005	149.8	66.7
2006	147.7	63.05
2007	129	48.28
2008	170.2	64.176
2009	162.5	48.209
2010	133.7	59.135
2011	140.5	64.449
2012	146.7	59.419
2013	133.6	56.293
2014	104.7	51.277
2015	96.95	49.652
Grand Total	7488.45	2689.025

Answer 1

Data:     

n1 = 46    

n2 = 46    

x1-bar = 162.79    

x2-bar = 58.46    

s1 = 39    

s2 = 10    

Hypotheses:    

Ho: μ1 ≤ μ2    

Ha: μ1 > μ2    

Decision Rule:    

α = 0.05    

Critical z- score = 1.64485363   

Reject Ho if z > 1.64485363   

Test Statistic:    

SE = √{(s1^2 /n1) + (s2^2 /n2)} = √((39)^2/46) + ((10)^2/46)) = 5.9363

z = (x1-bar - x2-bar)/SE = (162.79 - 58.46)/5.93625559041915 = 17.575

p- value = 0    

Decision (in terms of the hypotheses):

Since 17.57505 > 1.644853627 we reject Ho and accept Ha

Conclusion (in terms of the problem):

There is sufficient evidence that Florida has been the dominant orange-producing state in the US.