Do grocery stores shelve breakfast cereals (Frosted Flakes, etc.) aimed at child
ID: 3174040 • Letter: D
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: To test our initial hypothesis that cereal shelved on the bottom shelf is the most sugary, we could test the contrast:
H0: = 3 - ½(1 + 2) = 0
Against the alternative:
HA: = 3 - ½(1 + 2) > 0
That is, our alternative is that Shelf 3 cereals have a higher sugar content than the average of shelves 1 and 2.
Obtain the test statistic to evaluate the null hypothesis (three decimal places) ________________
What is the p-value associated with the test statistic? [Note that it is a right tail test] (two decimal places) ___________
Explanation / Answer
Result:
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: To test our initial hypothesis that cereal shelved on the bottom shelf is the most sugary, we could test the contrast:
H0: = 3 - ½(1 + 2) = 0
Against the alternative:
HA: = 3 - ½(1 + 2) > 0
That is, our alternative is that Shelf 3 cereals have a higher sugar content than the average of shelves 1 and 2.
Obtain the test statistic to evaluate the null hypothesis (three decimal places) -0.888
What is the p-value associated with the test statistic? [Note that it is a right tail test] (two decimal places) 0.8113
There is not enough evidence to conclude that Shelf 3 cereals have a higher sugar content than the average of shelves 1 and 2.
Standard error = sqrt(16.7*(1/36 +1/(4*19)+1/(4*21))) = 0.93938
test statistic = ( 6.528-(5.105+9.619)/2) /0.93938
=-0.88782
DF for t test =73
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