Answer:
15,313
Explanation:
To find the sample size needed to estimate the percentage of adults who can wiggle their ears, you need to use the formula for sample size calculation. This formula takes into account the margin of error, the confidence level, and the estimated proportion of the population with the characteristic being studied. In this case, the margin of error is 2 percentage points, the confidence level is 90%, and the estimated proportion of the population that can wiggle their ears is p^. Since p^ is unknown, you can use 0.5 as an estimate, as this is the midpoint of the range of possible values (0 to 1). Plugging these values into the formula, we get:
N = (1.96 / 2)^2 * 0.5 * (1 - 0.5) / 0.02^2
= 2.45 * 0.5 * 0.5 / 0.0004
= 6.125 / 0.0004
= 15,312.5
Therefore, the sample size needed to estimate the percentage of adults who can wiggle their ears is 15,312.5. Since this is not a whole number, you would need to round up to the nearest whole number to get a sample size of 15,313. This means that you would need to survey at least 15,313 adults in order to estimate the percentage of adults who can wiggle their ears with a margin of error of 2 percentage points and a confidence level of 90%.