Example: Ice Cream Sales						
						
The local ice cream shop keeps track of how much ice cream they sell versus the temperature of that day for the last 12 days:						
Formulate a null hypothesis and verify it by Pearsons and Spearman coefficients						
H0: there is no correlation between the number of sales and temperature						
H1: there is  positive correlation  between the number of sales and temperature 						
						
						
	Temperature (°C)	Ice Cream Sales ($)		rank temperature	rank sales	d
	14.2	215		11	11	0
	16.4	325		9	10	-1
	11.9	185		12	12	0
	15.2	332		10	9	1
	18.5	406		6	8	-2
	22.1	522		4	3	1
	19.4	412		5	6	-1
	25.1	614		1	1	0
	23.4	544		2	2	0
	18.1	421		7	5	2
	22.6	445		3	4	-1
	17.2	408		8	7	1
					sumsq=	14
	average	average			n	12
	18.7	402.42		rs>crit value 	n^3-n	1716
				 H0  rejected	rs=	0.951048951
					"crit value (0,05)"	0.587
	x1-xaverage	y1-yaverage	dx*dy	dx^2		
	-4.5	-187.42	838.6895833			
	-2.3	-77.42	176.1229167			
	-6.8	-217.42	1472.997917			
	-3.5	-70.42	244.6979167			
	-0.2	3.58	-0.627083333			
	3.4	119.58	409.5729167			
	0.7	9.58	6.947916667			
	6.4	211.58	1359.422917			
	4.7	141.58	668.98125			
	-0.6	18.58	-10.68541667			
	3.9	42.58	167.1395833			
	-1.5	5.58	-8.235416667			
						
	177.0	174754.9	5325.025	sum of dx*dy		
						
						
	r>crit value 					
	H0 rejected					
	0.957506623	"critical value= 0,576"				
	d.f.	10				
	alpha	0.05