Question

In: Statistics and Probability

Farmers would like to know the amount of sunshine in given locations they may buy land.  They...

Farmers would like to know the amount of sunshine in given locations they may buy land.  They hypothesize that a place near the coast may have different cloud cover than a place further from the coast at the same latitude so that the sun angles are the same.   In the data sheet you have daily noontime reports of the fraction of cloud cover near the coast and inland.  Justify your acceptance or rejection of the hypothesis using these numbers, and state the confidence level you would use.

Cld cover coast: ,71,26,100,16,100,83,61,32,84,15

Cld cover inland: ,60,9,6,29,12,19,21,62,82,0,4,84,51,4,19

Solutions

Expert Solution

confidence level used = 0.05

coast inland
71 60
26 9
100 6
16 29
100 12
83 19
61 21
32 62
84 82
15 0
4
84
51
4
19

Sample #1   ---->   1                  
mean of sample 1,    x̅1=   58.80                  
standard deviation of sample 1,   s1 =    33.85                  
size of sample 1,    n1=   10                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   30.80                  
standard deviation of sample 2,   s2 =    29.15                  
size of sample 2,    n2=   15                  
                          
difference in sample means =    x̅1-x̅2 =    58.8000   -   30.8   =   28.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    31.0721                  
std error , SE =    Sp*√(1/n1+1/n2) =    12.6852                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   28.0000   -   0   ) /    12.69   =   2.2073
                          
Degree of freedom, DF=   n1+n2-2 =    23                  
  
p-value =        0.037542   (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value <α , Reject null hypothesis                      
                          

There is enough evidence of significant difference

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