The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 13 different varieties of cereal.

Sugar (gms) 4 15 12 11 8 6 7 2 7 14 20 3 13

Calories. 120 200 140 110 120 80 190 100 120 190 190 110 120

(a)Find thecorrelation coefficientandcoefficient of determination.What can youconcludefrom their values?

(b)Testat a 1% significance level whether the linear correlation coefficient between the two variables listed in the table is positive. Useboththe p-value and critical value (including reject and non-reject regions) approaches.