Our cereal data can be examined by looking at a contingency table. The following

Question

Our cereal data can be examined by looking at a contingency table. The following contingency table shows the cereals in the study broken down by whether they had low(under 6), medium(6-10, or high (over 6) sugar grams and whether they had low (under 2), medium (2-4), or high fiber(over 4) grams.

Use the contingency table to answer the following questions.

A. What proportion of cereals are high in fiber?

B. What proportion of cereals are high in sugar?

C. What proportion of cereals are high in both fiber and sugar?

D. Of the cereals that are high in fiber, what proportion are also high in sugar?

E. What proportion of cereals that are low in sugar are high in fiber?

F. What proportion of cereals are ideal? Low in Sugar, but high in fiber?

G. Is being low in sugar independent of being high in fiber? Explain and include mathematical support.

Rows: High In Sugar? Columns: High in Fiber? 1 Low 2 Medium 3 High Total 1 Low 8 6 5 19 2 Medium 7 13 14 34 3 High 31 21 24 76 Total 46 40 43 129

Explanation / Answer

A:

Out of 129 cereals, 43 are high in fibers so proportion of cereals are high in fiber is

P(high in fiber) = 43 /129 = 0.3333

B:

Out of 129 cereals, 76 are high in sugar so proportion of cereals are high in sugar is

P(high in sugar) = 76 /129 = 0.5891

C:

Out of 129 cereals, 24 are high in sugar and fiber so proportion of cereals are high in sugar and fiber both is

P(high in fiber and high in sugar) = 24 /129 = 0.1860

D:

P(high in sugar | high in fiber) = P(high in fiber and high in sugar) / P(high in fiber) = 24 / 43 = 0.5581

E:

P(low in sugar and high in fiber) = 5/129

P(low in sugar) = 19/129

So

P(high in fiber | low in sugar) = P(low in sugar and high in fiber)/P(low in sugar) = 5/19= 0.2632

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