1 We have 2 flavors of cough syrup PLAIN and SWEET Taste te

1) We have 2 flavors of cough syrup - PLAIN and SWEET. Taste tests are conducted with tasters rating the syrup on a 10 point scale with 1 as bad and 10 as excellent. Data are: PLAIN:7,7,6,5,6,8,5,4,6,8,9,10,5,6,4,8,8,8,9,7,8,9,6,7,8,6,7,8,5,6,5,6,7,8,9,9 SWEET: 1,6,7,7,8,5,4,4,6,9,9,9,8,7,8,7,8,5,10,6,6,7,8,8,8,5,6,4,5,6,7,8,3,4,5 I am interested in assessing preference between PLIAN and SWEET. Decide what stat approach would fit here, conduct your analysis, and draw conclusions.

Solution

Ho: there is no correlation between the tastes of two flavours of cough syrups i.e., plain and sweet.   H1: there is no correlation between the tastes of two flavours of cough syrups i.e., plain and sweet. Here we use spearman\'s rank correlation of non parametric test i.e.,r=1-[(6di²)/(n(n²-1))], wheren=35 , di²=square of difference (rank of plain - rank of sweet)=6067.5, then r=1-[(6*6067.5)/42840]=1-0.8498=0.1502. Standard error of r=1/((n-1))=1/((35-1))=0.1715. The table value of Z at 0.01 is 2.32. We now find the upper side is _r+[(2.32)*(0.1715)]=0+0.3978=0.3978. Here the calculated value of r is 0.1502 < 0.3978, so we accept null hypothesis. Therefore, there is no correlation between the tastes of two flavours of cough syrups i.e., plain and sweet.