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 220 215 200 230 225 228 240 245 202 250 235 190 220 210 180 Test for significant differences among the calorie content of these three candies. State the null and alternative hypotheses. O Ho: Median mm = Median k = MedianMW Ho: Median Mm * MedianKK + Median Mw O Ho: Median mm = MedianKk = Medianmw He: Medianmm > MedianKK > MedianMW O Ho: Medianmm * MedianKK * Median mw H: Median mm = MedianKK = Medianmw O Ho: All populations of calories are identical. H: Not all populations of calories are identical. O H.: Not all populations of calories are identical. Ha: All populations of calories are identical. 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? O Do not reject Ho. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies. O Do not reject H. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies. Reject Ho. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies. Reject Ho. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

Answer 1

O Ho: All populations of calories are identical. H,: Not all populations of calories are identical.

count, ni =	5	5	5
mean , x̅ i =	232.000	226.00	200.00
std. dev., si =	13.0	14.3	17.9
sample variances, si^2 =	170.000	205.000	322.000
total sum	1160	1130	1000				3290	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	219.33
( x̅ - x̅̅ )²	160.444	44.444	373.778
							TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	802.222	222.222	1868.889				2893.333333
SS(within ) = SSW = Σ(n-1)s² =	680.000	820.000	1288.000				2788.0000

no. of treatment , k =   3  
df between = k-1 =    2  
N = Σn =   15  
df within = N-k =   12  
      
mean square between groups , MSB = SSB/k-1 =    2893.3333/2=   1446.6667
mean square within groups , MSW = SSW/N-k =    2788/12=   232.3333
      
test stats = F-stat = MSB/MSW =    1446.6667/232.3333=   6.23
      
P value =   0.014

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

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