Question

A researcher working for the Ray-Ban Corporation decides to perform a hypothesis test to investigate whether there is a significant positive correlation between monthly temperature and number of sunglasses sold at one of their locations. The researcher randomly selected the following sample from this location. Monthly Temperature (°F) Number of Sunglasses Sold 80 91 61 34 56 66 99 72 71 74 95 125 43 65 (TEMP SUMS: 2x = 505; E x2 = 38,973) (NBR SUMS: 2 x = 527; E x2 = 44,303) Based on the conclusion for this hypothesis test at a= 5%, the researcher can conclude: a. none of these O b. there is a significant positive correlation between the number of sunglasses sold per month and monthly temperature at this location. c. insufficient information d. there is a no significant correlation between the number of sunglasses sold per month and monthly temperature at this location. e. there is a significant negative correlation between the number of sunglasses sold per month and monthly temperature at this location.

Answer 1

S.No х 1 2 3 4 5 6 7 Total Mean 80 61 56 99 71 95 43 505 Y 91 34 66 72 74 125 65 527 (x-7) 61.7347 124.1633 260.5918 721.3061 1.3061 522.4490 849.3061 2540.8571 (y-7) 246.94 1704.51 86.22 10.80 1.65 2471.51 105.80 4627.4286 SSY (x-x)(y-7) 123.4694 460.0408 149.8980 -88.2449 1.4694 1136.3265 299.7551 2082.7143 72.143 75.2857 SSX SXY

null hypothesis: Ho:           ρ'=		0
Alternate Hypothesis: Ha: ρ>		0

correlation r='Sxy/(√Sxx*Syy) =		0.607
test stat t=	r*(√(n-2)/(1-r2))=	1.7097
P value    =	0.0740	(from excel:tdist(1.7097,5,1)

since p value >0.05

d. there is a no significant correlation between the number of sunglasses sold per month and monthly temperature at this location.