Question

suppose that we want to estimate what proportion of the adult population of the United States has high blood pressure, and we want to be “99% sure” that the error of our estimate will not exceed 2 percentage points. How large a sample will we need if (a) we have no idea what the true proportion might be; (b) we found research that states the true proportion lies on the interval from 5% to 20%

Answer 1

A ) Given that

Confidence level = C = 0.99

Margin of error = E = 0.02

we want to find the sample size when true proportion is not given

Therefor Assume that true proportion = p = 0.5

A ) Therefor the sample size is calculated as

Where Zc = Critical value for C = 2.58 ...........( From Z table)

..........( Round to the next number)

Therefor the required sample size is n = 4161 .............( ANSWER)

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B ) Given that, the true proportion lies on the interval from 5% to 20%

i.e.

i.e. 99% Confidence interval for true proportion is

i.e. Lower limit = ...............( Equation 1)

and Upper limit = ............( Equation 2)

Therefor Equation 2 + Equation 1 is

i.e.   

i.e.

i.e.

i.e.

The required sample size is  

  .......( Round to the next number)

Therefor the required sample size is n = 1821 .............( ANSWER)