Question

The better-selling candies are often high in calories. Assume that the following data show the calorie content from samples of M&M's, Kit Kat, and Milky Way II.

M&M's	Kit Kat	Milky Way II
220	215	200
210	205	208
240	245	202
250	235	190
220	230	180

Assuming we don't know about the shape of the population distribution, use the Kruskal-Wallis Test to test for significant differences among the calorie content of these three candies.

State the null and alternative hypotheses.

H₀: Median_MM = Median_KK = Median_MW
H_a: Median_MM > Median_KK > Median_MW

H₀: Not all populations of calories are identical.
H_a: All populations of calories are identical.    

H₀: Median_MM ≠ Median_KK ≠ Median_MW
H_a: Median_MM = Median_KK = Median_MW

H₀: All populations of calories are identical.
H_a: Not all populations of calories are identical.

H₀: Median_MM = Median_KK = Median_MW
H_a: Median_MM ≠ Median_KK ≠ Median_MW

Find the value of the test statistic. (Round your answer to two decimal places.)

=?

Find the p-value. (Round your answer to three decimal places.)

p-value =

At a 0.05 level of significance, what is your conclusion?

Reject H₀. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.   

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

Answer 1

The null and alternative hypotheses.

H₀: All populations of calories are identical.
H_a: Not all populations of calories are identical.

The data in sorted order with ranks (given in brackets) are,  

180 (1), 190 (2),  200 (3), 202 (4),  205 (5), 208 (6), 210 (7),  215 (8),  220 (9.5), 220 (9.5), 230 (11), 235 (12), 240 (13), 245 (14), 250 (15)

Give tied values the average rank.

M&M's	Kit Kat	Milky Way II
220 (9.5)	215 (8)	200 (3)
210 (7)	205 (5)	208 (6)
240 (13)	245 (14)	202 (4)
250 (15)	235 (12)	190 (2)
220 (9.5)	230 (11)	180 (1)

Add up the different ranks for each group/sample.

M&M's : 9.5 + 7 + 13 + 15 + 9.5 = 54

Kit Kat : 8 + 5 + 14 + 12 + 11 = 50

Milky Way II : 3 + 6 + 4 + 2 + 1 = 16

H Statistic is given as,

= 8.72

Degree of freedom = c - 1 = 3 -1 = 2

The test statistic H will follow Chi Square distribution with 2 degree of freedom.

P-value = P( > 8.72) = 0.013

Since P-value is less than 0.05 level of significance, the conclusion is,

Reject H₀. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.