Question

A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large must the sample be in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%?

Answer 1

56788988999

Explanation:

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Answer 2

The researcher would need a sample size of 271 individuals to be 90% confident that the sample proportion will not differ from the true proportion of adults

How to find the sample size ?

To determine the sample size needed to estimate the proportion of the adult population of the United States with high blood pressure with a 90% confidence level and a margin of error (precision) of 5%, you can use the formula for sample size for estimating proportions. The formula is:

`\[n = (Z^2 \cdot p(1-p))/(E^2)\]`

E is the margin of error as a proportion (in this case, 5% or 0.05).

Plug in the values:

`\(n = ((1.645)^2 \cdot 0.5(1-0.5))/((0.05)^2)\)`

`\(n = (2.706025 \cdot 0.25)/(0.0025)\)`

`\(n = (0.67650625)/(0.0025)\)`

n = 270.6025

= 271 people