Question

1. Study examines whether low-carb nutrition labels increase the actual consumption of hedonic chocolate candies by overweight and normal-weight consumers. To achieve this, we asked adult family members participating in a university open house to serve themselves unusual colors of M&M’s (gold, teal, purple, and white), which were clearly labeled either as “New Colors of Regular M&M’s” (Nutrition label indicates 50 grams of carbohydrate per serving) or as “New ‘Low-Carb’ M&M’s” (Nutrition label indicates 20 grams of carbohydrate per serving). We then measured how many calories of M&M’s they ate.

	overweight	regular weight
High carbohydrate option	200, 220, 240, 255, 300, 145, 220, 233, 214, 80	125, 252, 125, 165, 145, 256, 352, 136, 185, 250
Low carbohydrate option	125, 300, 256, 450, 250, 365, 193, 254,123,199	211, 135, 80, 189, 152, 60, 235, 100, 124, 62

Solve the problem using ANOVA Model III. Write down the Null Hypotheses and the alpha values for the corresponding hypothesis. Make sure you use the F table to identify the F-crit value. Indicate under what conditions you have decided to use Model III (Do Not Use R). Use the results of Model III to write down the conclusion in plain English.

Answer 1

The hypothesis being tested is:

H₀: There is no main effect of weight

H_a: There is a main effect of weight

The p-value is 0.0121.

Since the p-value (0.0121) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a main effect of weight.

The hypothesis being tested is:

H₀: There is no main effect of carbohydrate option

H_a: There is a main effect of carbohydrate option

The p-value is 0.6311.

Since the p-value (0.6311) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is a main effect of carbohydrate option.

The hypothesis being tested is:

H₀: There is no interaction effect

H_a: There is an interaction effect

The p-value is 0.0370.

Since the p-value (0.0370) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is an interaction effect.

	overweight	regular weight
High carbohydrate option	200	125
	220	252
	240	125
	255	165
	300	145
	145	256
	220	352
	233	136
	214	185
	80	250
Low carbohydrate option	125	211
	300	135
	256	80
	450	189
	250	152
	365	60
	193	235
	254	100
	123	124
	199	62
		Factor 2
	Means:
		overweight	regular weight
	High carbohydrate option	210.7	199.1	205
Factor 1	Low carbohydrate option	251.5	134.8	193
		231.1	167.0	199
	10	replications per cell
ANOVA table
Source	SS	df	MS	F	p-value
Factor 1	1,380.62	1	1,380.62	0.23	.6311
Factor 2	41,152.23	1	41,152.23	6.99	.0121
Interaction	27,615.03	1	27,615.03	4.69	.0370
Error	2,11,911.10	36	5,886.42
Total	2,82,058.98	39

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