Do grocery stores shelf breakfast cereals (Frosted Flakes, etc.) aimed at childr

Question

Do grocery stores shelf breakfast cereals (Frosted Flakes, etc.) aimed at children on the third (bottom) shelf and healthier cereals on higher shelves? We have a data set that tells us the sugar content of breakfast cereals and the shelf on which they are located. Shelf 3 is the lowest shelf, 2 is in the middle, and 1 is on the top. We ran an ANOVA with sugar in grams as the response variable and shelf as the factor. This is what we got (higher numbers mean higher sugar content):

S= 4.084

1. Obtain the test statistic to evaluate the null hypothesis (three decimal places)

2. What is the p-value associated with the test statistic - note this is a right tail test (two decimal places) -- this should be done in minitab

3. Should we reject H0? Yes or no

4. Based on this analysis, which of the following statements is the best conclusion?

a) Shelf 2 cereals are the most sugary. Shelf 3 cereals are the second most sugary and Shelf 1 cereals are the least sugary.

b) Shelf 2 cereals are the msot sugary. Shelf 1 cerals are less sugary than Shelf 2, but are equivalent to each other.

c) Shelf 3 has the most sugary cerals, while Shelf 1 and Shelf 2 have about the same sugar content.

d) All three shelves have ceral with the same mean sugar content.

If you could explan how you worked through these problems I would appreciate it!

One-way ANOVA: Sugars versus Shelf SS Source DE MS 2 220.2 110.1 6.60 0.002 Shelf Error 73 1217.7 16.7 Total 75 1437.9 4.084 R-sq 15.32s R-sq (adj) 13.009 Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev 19 5.105 4.483 21 9.619 4.129 36 6.528 3.836 10.0 12.5 5.0 7.5 Pooled StDev 4.084

Explanation / Answer

Answer:

1. Test Statistics

t = (X-bar -

- µ)/ (s/n)

t = (6.528 – 0)/ (3.836/36)

t = 10.211

Answer 2:

Degrees of freedom, df = n – 2 = 36 - 2 = 34

Using t-tables, the critical value at a = 0.05 with 34 d.f. is

t (0.05, 34) = 1.691

Answer 3:

Since test statistics is greater than the critical value, we reject Ho.

Answer 4:

Shelf 2 cereals are the most sugary. Shelf 3 cereals are the second most sugary and Shelf 1 cereals are the least sugary.

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