Question

Asked Nov 4, 2019

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An article in the Archives of Internal Medicine reported that in a sample of 224 men, 73 had elevated total cholesterol levels (more than 200 milligrams per deciliter). In a sample of 232 women, 44 had elevated cholesterol levels. Can you conclude that the proportion of people with elevated cholesterol levels differs betwen men and women? Use the a= 0.05 level.

Step 1

Here 224 men and 232 women are selected randomly. 73 of the men had elevated cholesterol levels, whereas 44 of the women had elevated cholesterol levels.

Denote *p*_{1} and *p*_{2} as the proportions of men with the elevated cholesterol levels, and proportions of women with the elevated cholesterol levels.

Therefore *n*_{1 }*= *224*, p*_{1 }*= *73/224 ≈ 0.3259 and* n*_{2} *= *232*, p*_{2 }*= *44/232 ≈ 0.1897.

Step 2

**Hypotheses:**

The aim is to check whether the proportion of people with elevated cholesterol levels differs between men and women.

The null hypothesis is:

*H*_{0} : *p*_{1} = *p*_{2}, that is, the elevated cholesterol levels in men and women are equal in Qatar.

The alternative hypothesis is:

*H*_{1} : *p*_{1} ≠ *p*_{2}, that is, the elevated cholesterol levels in men is different from the elevated cholesterol levels in women.

Step 3

**Test statistic:**

...

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