Final answer:
To estimate the proportion of the adult US population with high blood pressure with a 95% confidence level and a 4% margin of error, a sample size of 601 is needed.
Step-by-step explanation:
To determine the sample size needed to estimate the proportion of the adult population of the United States with high blood pressure, we can use the formula for sample size calculation for proportions.
The formula is:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n is the sample size
- Z is the Z-score corresponding to the desired confidence level (in this case, 95%)
- p is the estimated proportion of the population (unknown in this case)
- E is the maximal allowable difference between the sample proportion and the true population proportion (in this case, 4%)
Since we don't have an estimate for the population proportion, we can use 0.5 as a conservative estimate to calculate the sample size. Therefore, the formula becomes:
n = (Z^2 * 0.5 * (1-0.5)) / E^2
Converting the confidence level of 95% to a Z-score (which represents the number of standard deviations away from the mean), we find that the corresponding Z-score is approximately 1.96.
Substituting the values into the formula, we get:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.04^2 = 600.25
Rounding up to the nearest whole number, we conclude that a sample size of 601 is necessary to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%.