Do grocery stores shelve breakfast cereals (Frosted Flakes, etc.) aimed at child

Question

Do grocery stores shelve 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):

  
One-way ANOVA: Sugars versus Shelf

Source DF      SS     MS     F      P
Shelf    2   220.2 110.1 6.60 0.002
Error   73 1217.7   16.7
Total   75 1437.9

S = 4.084   R-Sq = 15.32%   R-Sq(adj) = 13.00%


                         Individual 95% CIs For Mean Based on
                         Pooled StDev
Level   N   Mean StDev -------+---------+---------+---------+--
1      19 5.105 4.483 (------*-------)
2      21 9.619 4.129                    (------*-------)
3      36 6.528 3.836          (----*-----)
                         -------+---------+---------+---------+--
                              5.0       7.5      10.0      12.5

Pooled StDev = 4.084

Question 2:

In testing the null hypothesis, the appropriate test statistic is equal to

______

(two decimal places) and the p-value is

______

(three decimal places).

I can find the p-value from the minitab data but what formula do I use to find the test statistic? Thanks in advance!

Explanation / Answer

Question 1.

First let's see what we can state on the basis of given data. Since the P-value is very small, we can say that there is a significant difference in the sugar content of the breakfast cereals on the three shelves, but it does not tell us which of these shelves has different sugar content or if all of them have different different sugar contents and which one has higher sugar content.

Judging by the confidence intervals it doesn't seem like the sugar content of the cereals are decreasing as we move on to the higher shelves.

Question 2:

To find the test statistic I need more information. Since with only this knowledge I can't even tell which test statistic do we need to compute. I reccomend you to post the full question seperately.

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