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.

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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. 

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Expert Answer

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 p1 and p2 as the proportions of men with the elevated cholesterol levels, and proportions of women with the elevated cholesterol levels.

Therefore n1 = 224, p1 = 73/224 ≈ 0.3259 and n2 = 232, p2 = 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 : p1 = p2, that is, the elevated cholesterol levels in men and women are equal in Qatar.

The alternative hypothesis is:

H : p1p2, 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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Image Transcriptionclose

Pooled sample proporti on пр. + п,р, р- п, + п, 73+44 224 232 117 456 0.2566

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Hypothesis Testing

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