Question

The data in the table to the right represent the calories and sugar​ (in grams) in one serving of seven different types of breakfast cereals. a. Compute and interpret the coefficient of​ correlation, r. b. At the 0.05 level of​ significance, is there a significant linear relationship between calories and​sugar? Product   Calories   Sugar Cereal 1   77   7 Cereal 2   102   2 Cereal 3   103   4 Cereal 4   110   4 Cereal 5   125   4 Cereal 6   186   10 Cereal 7   198   11

Answer 1

X: Calories

Y: Sugar

a) We have to find the coefficient of correlation r.

Formula is

	x	y	xy	x^2	y^2
	77	7	539	5929	49
	102	2	204	10404	4
	103	4	412	10609	16
	110	4	440	12100	16
	125	4	500	15625	16
	186	10	1860	34596	100
	198	11	2178	39204	121
Total	901	42	6133	128467	322

n = 7

b)

Claim: There is a linear relationship between calories and sugar.

The null and alternative hypothesis is

Level of significance = 0.05

r = 0.7773

n = 7

Degrees of freedom = n - 2 = 7 - 2 = 5

Critical value = 0.754

( From pearson table)

r > critical value we reject null hypothesis.

Conclusion:

There is a linear relationship between calories and sugar.