and it is also prudent to use a conservative estimate. The margin of error in this case is 1 percentage point (half of 0.02). The foregoing is commonly simplified will form a 95% confidence interval for the true proportion. If this interval needs to be no more than W units wide, the equation can be solved for n, yielding n = 4/W2 = 1/B2 where B is the error bound on the estimate, i.e., the estimate is usually given as within ± B. For B = 10% one requires n = 100, for B = 5% one needs n = 400, for B = 3% the requirement approximates to n = 1000, while for B = 1% a sample size of n = 10000 is required. These numbers are quoted often in news reports of opinion polls and other sample surveys. However, the results reported may not be the exact value as numbers are preferably rounded up. Knowing that the value of the n is the minimum number of sample points needed to acquire the desired result, the number of respondents then must lie on or above the minimum. Estimation of a mean When estimating the population mean using an independent and identically distributed (iid) sample of size n, where each data value has variance σ2, the standard error of the sample mean is: This expression describes quantitatively how the estimate becomes more precise as the sample size increases. Using the central limit theorem to justify approximating the sample mean with a normal distribution yields a confidence interval of the form , where Z is a standard Z-score for the desired level of confidence (1.96 for a 95% confidence interval). If we wish to have a confidence interval that is W units total in width (W/2 being the margin of error on each side of the sample mean), we would solve for n, yielding the sample size . For example, if we are interested in estimating the amount by which a drug lowers a subject's blood pressure with a 95% confidence interval that is six units wide, and we know that the standard deviation of blood pressure in the population is 15, then the required sample size is , which would be rounded up to 97, because the obtained value is the minimum sample size, and sample sizes must be integers and must lie on or above the calculated minimum.