Question

Supermarkets often place similar types of cereal on the same supermarket shelf. The shelf

placement for 77 cereals was recorded as well their sugar content. A nutritionist wonders if

the average sugar content varies by shelf. In the dataset SugarData.xlsx, the sugar content (in grams per serving) for each cereal is organized by the

shelf that cereal is placed.

Using the appropriate ANOVA from StatCrunch, answer the following:

(20 points --- 5 points per problem)

a)   Based on the information provided, what are the null and alternative hypotheses for this

research scenario?

b)   Are there any concerns regarding the assumptions going into an ANOVA analysis?

(Hint: A side-by-side boxplot might be very useful.)

c)   Regardless of what you’ve found in part (b), we’ll pretend that everything is fine for an

ANOVA. What conclusion do we make regarding the hypotheses in part (a)?

d)   Using the Tukey HSD option, examine the average sugar differences between pairs of

shelves. Are there any that are statistically significantly different?

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Answer 1

a)   Based on the information provided, what are the null and alternative hypotheses for this research scenario?

Answer:

Null hypothesis: H₀: There is no any significant difference in the average sugar content for given three shelf.

Alternative hypothesis: H_a: There is a significant difference in the average sugar content for given three shelf.

b)   Are there any concerns regarding the assumptions going into an ANOVA analysis?

Answer:

Here, we have to check whether data for given three shelf is from a same population or not. The side by side box plot is given as below:

From above boxplots it is observed that three sample means are vary in given box plots.

This indicates that there is a concern or problem regarding the assumption going into an ANOVA analysis.

c)   Regardless of what you’ve found in part (b), we’ll pretend that everything is fine for an ANOVA. What conclusion do we make regarding the hypotheses in part (a)?

Answer:

Required ANOVA table is given as below:

ANOVA
Sugar content
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	244.835	2	122.417	7.293	.001
Within Groups	1242.152	74	16.786
Total	1486.987	76

The p-value for this ANOVA table is given as 0.001 which is less than alpha value 0.05, so we reject the null hypothesis that there is no any significant difference in the average sugar content for given three shelf. There is sufficient evidence to conclude that there is a significant difference in the average sugar content for given three shelf.

d)   Using the Tukey HSD option, examine the average sugar differences between pairs of shelves. Are there any that are statistically significantly different?

Answer:

The Tukey HSD matrix for multiple comparisons is given as below:

Multiple Comparisons
Sugar content Tukey HSD
(I) Shelf	(J) Shelf	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
					Lower Bound	Upper Bound
Shelf1	Shelf 2	-4.81905*	1.28009	.001	-7.8807	-1.7574
	Shelf 3	-1.86667	1.14261	.238	-4.5995	.8662
Shelf 2	Shelf1	4.81905*	1.28009	.001	1.7574	7.8807
	Shelf 3	2.95238*	1.12499	.028	.2617	5.6431
Shelf 3	Shelf1	1.86667	1.14261	.238	-.8662	4.5995
	Shelf 2	-2.95238*	1.12499	.028	-5.6431	-.2617
*. The mean difference is significant at the 0.05 level.

For pairs, shelf 1 and shelf 3, the p-value is given as 0.238 which is greater than alpha value 0.05, so we conclude that there is no any significant difference between shelf 1 and shelf 3.

For remaining all other pairs, differences are statistically significant as the p-values are less than alpha value.