Question

Are all cereals created equal?

Brand	Type	Calories	Total fat (g)	Sodium (mg)
Kellogg’s Rice Krispies	Rice	120	1g	170mg
Earth’s Best Whole Rice Cereal	Rice	50	0.5g	0mg
Organic Brown Rice Crisps	Rice	110	1g	85mg
Cereal Rice Puffs	Rice	50	0g	0mg
Nature’s Path Organic Crispy Rice	Rice	30	15g	100mg
Kellogg’s Rice 24ozs	Rice	130	0g	190mg
Arrowhead Mills Rice	Rice	60	0g	0mg
Cream of Rice	Rice	150	0g	0mg
Rice Chex	Rice	110	0.5g	240mg
Organic Cream of Rice	Rice	150	0.2g	3mg
Quaker Oats Squares Cinnamon	Oat	210	2.5g	190mg
Arrowhead Oat Bran	Oat	140	2g	75mg
Honey Bunches of Oats	Oat	120	1.5g	135mg
Honey Nut Whole Grain Oat	Oat	110	1.5g	160mg
Bob’s Red Hill Oat Bran	Oat	150	2.0g	0mg
Hodgson Mill Oat Bran	Oat	150	3.0g	0mg
Nature Valley Oat Bites	Oat	210	6.0g	160mg
Quaker Simply Granola Oats, honey and Almonds	Oat	200	6.0g	25mg
Arrowhead Organic Oats	Oat	140	2.0g	75mg
Nature Valley Oat Clusters Cereal Honey	Oat	230	3.0	140mg

In the data that you have collected, assume that the data is normally distributed for all cereals.

2. Perform a hypothesis test for the difference of the two means for each of the following questions at alpha = .05. List the Ho, Ha, give the observed value of the test statistic, p-value, and write a word conclusion.

a) Is there a difference in the calorie count for the two types of cereals?

b) Do the rice cereals have less fat grams per serving than the oat cereals?

c) Do the rice cereals have more sodium (mg) per serving than the oat cereals?

3. Based on your research, which type of cereal would you prefer? Why?

Answer 1

a) Is there a difference in the calorie count for the two types of cereals?

Conclusion: The estimated p-value is 0.002. Hence, reject the null hypothesis and conclude that  there is a difference in the calorie count for the two types of cereals at 0.05 level of significance.

b) Do the rice cereals have less fat grams per serving than the oat cereals?

Conclusion: The estimated p-value is 0.760. Hence, retain the null hypothesis and conclude that the rice cereals do not have more sodium (mg) per serving than the oat cereals at 0.05 level of significance.

c) Do the rice cereals have more sodium (mg) per serving than the oat cereals?

Conclusion: The estimated p-value is 0.369. Hence, retain the null hypothesis and conclude that the rice cereals do not have more sodium (mg) per serving than the oat cereals.

3) Ans: From b) and c) the fat and the sodium are not different between the two cereal that is rice and Oat. Hence, we will prefer the cereal which has a large number of Calories.