Question

Year   Years.since.1985   Fires   Acres   Acres/Fire
2015   32   68151   10125149   148.56934
2014   31   63312   3595613   56.791967
2013   30   47579   4319546   90.786818
2012   29   67774   9326238   137.6079
2011   28   74126   8711367   117.52107
2010   27   71971   3422724   47.556988
2009   26   78792   5921786   75.157199
2008   25   78979   5292468   67.011079
2007   24   85705   9328045   108.83898
2006   23   96385   9873745   102.44068
2005   22   66753   8689389   130.17226
2004   21   65461   8097880   123.70541
2003   20   63629   3960842   62.249006
2002   19   73457   7184712   97.808405
2001   18   84079   3570911   42.470902
2000   17   92250   7393493   80.146266
1999   16   92487   5626093   60.831176
1998   15   81043   1329704   16.407389
1997   14   66196   2856959   43.159088
1996   13   96363   6065998   62.949452
1995   12   82234   1840546   22.381813
1994   11   79107   4073579   51.494545
1993   10   58810   1797574   30.565788
1992   9   87394   2069929   23.685024
1991   8   75754   2953578   38.98907
1990   7   66481   4621621   69.517922
1989   6   48949   1827310   37.330895
1988   5   72750   5009290   68.85622
1987   4   71300   2447296   34.323927
1986   3   85907   2719162   31.652392
1985   2   82591   2896147   35.066133

A. Check the assumptions for Inference. Use any output you feel is appropriate to substantiate your conclusions.

B. Construct a hypothesis test at the 95% level of confidence to answer this question: Is there a correlation between Acres/Fire and Years Since 1985?

                        C.        Construct a 95% Confidence Interval for the slope and interpret it.

Answer 1

here only part B is complete and answerable question, please find

(B) correlation between Acres/Fire and Years Since 1985=r=0.6742 ( using ms-excel function=correl())

we use t-test with

null hypothesis H0:=0 and

alternate hypothesis Ha:0 (this is two tailed test)

the statistic t =r/sqrt[(1—r²)/(n—2)]=0.6742/sqrt((1-0.6742*0.6742)/(31-2))=4.916 with n-2=31-2=29 df

the two-tailed critical t(0.05/2,29)=2.045 is less than calculated/observed t=4.916, so we reject H0 and conclude that there is linear relationship between  Acres/Fire and Years Since 1985