Question

# test the hypothesis that Florida has been the dominant orange-producing state in the US historically (e.g....

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

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.

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