n = sample size
z = z-score for the desired confidence level (95% confidence corresponds to a z-score of 1.96)
p = estimated proportion of the population with the characteristic of interest (in this case, the proportion of high school students with asthma)
E = margin of error (in this case, 6% expressed as a proportion, or 0.06)
We need to find the value of "n" that satisfies the conditions of the problem. We know that:
The desired confidence level is 95%, corresponding to a z-score of 1.96
The margin of error is 6%, expressed as a proportion of 0.06
We do not know the estimated proportion of high school students with asthma, so we will assume a conservative estimate of 50% (0.5) because this will give us a maximum sample size.
Plugging these values into the formula, we get:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.06^2
Simplifying the expression, we get:
n = 384.16
Rounding up to the nearest whole number, we get:
n = 385
Therefore, the researcher needs to sample at least 385 high school students to be 95% confident that her estimate is within 6% of the true percentage of all high school students with asthma.