Question

Jonathan heard a news report that eating a gluten-free diet makes a person more likely to have a positive outlook on life. This sounded appealing, but he felt he should investigate the claim before drastically changing his diet. Jonathan asked 128128128 people at his school whether they eat gluten-free and then determined whether they are positive or negative people. Jonathan found that there was no association between eating gluten-free and having a positive outlook. With this knowledge, fill in the missing joint frequencies below:

Gluten-free Non- Gluten-free Row Total
Positive ________ ______________ 64
Negative ________ ______________ 64
Column Total 12 116 128

Answer 1

The answer is "6, 58, 6 and 58"

Explanation:

Using formula:

`Cell\ value = ((row \ total) * (column \ total))/(total)`

`Gluten-free \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Not\ gluten \ free \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Row \ total`

`Positive\ \ \ \ \ \ \ \ \ \ \ (12* 64)/(128)=6 \ \ \ \ \ \ \ \ \ \ \ \ (116* 64)/(128)=58 \ \ \ \ \ \ \ \ \ \ \ 64 \\\\Negative\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (12* 64)/(128)=6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ (116* 64)/(128)=58\ \ \ \ \ \ \ \ \ \ \ 64 \\\\Column\ Total \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 12\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 116\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 128`