Question

Healthy cereal? Researchers collected data on 76 brands of cereal at a local supermarket. 27 For each brand, the sugar content (grams per serving) and the shelf in the store on which the cereal was located (1 = bottom, 2 = middle, 3 = top) were recorded. A dotplot of the data is shown here.

Part (a) Is the variability in sugar content of the cereals on the three shelves similar or different? Justify your answer.

Part (b) Critics claim that supermarkets tend to put sugary cereals where kids can see them. Do the data from this study support this claim? Justify your answer. (Note that Shelf 2 is at about eye level for kids in most supermarkets.)

Short answer

Part (a) Similar

Part (b) yes

Step-by-step solution

Part (a) Step 1. Given information. 

The sugar content (grammes per serving) and the shelf location in the store (1 = bottom, 2 = middle, 3 = top) were recorded.

Part (a) Step 2. Is the sugar content variability of the cereals on the three shelves similar

We notice that the sugar content appears to range from 0 to 15 grams per serving for each shelf.

This implies that the variability in sugar content appears to be similar across all three shelves.

As a results its is Similar

Part (b) Step 1. Sugary cereals, according to critics, are often displayed in supermarkets where children can see them. yes  this study support this claim

We can see that the distribution of shelf 2 is skewed to the left because the distribution's peak is to the right in the dotplot, with a tail of fewer dots to the left.

However, the distributions of shelf 1 and shelf 3 are right-skewed, because the distribution's peak is to the left in the dotplot, with a tail of fewer dots to the right.

We then observe that the critics' claim appears to be correct, because the left-skewed distribution has significantly higher sugar contents than the right-skewed distribution, and thus the sugary cereals appear to be placed on shelf 2.

As a result yes this study support the claim.