Question

Find the sample size needed to estimate the percentage of adults who can wiggle their ears. Use a margin of error of 5 percentage points and use a confidence level of 95%.

a. Assume that p^ and q^ are unknown n=

Answer 1

To estimate the percentage of adults who can wiggle their ears, we can use the error bound formula. Based on the given margin of error and confidence level, the sample size needed is 385.

Step-by-step explanation:

To calculate the sample size needed to estimate the percentage of adults who can wiggle their ears, we can use the error bound formula. The formula is:

n = (z^2 * p^ * q^) / E^2

In this case, we have a margin of error of 5 percentage points (E = 0.05) and a confidence level of 95% (z^ = 1.96). Since p^ and q^ are unknown, we can assume the most conservative estimate of 0.5 for both. Plugging these values into the formula, we get:

n = (1.96^2 * 0.5 * 0.5) / 0.05^2 = 384.16

Rounding up to the nearest whole number, we need a sample size of 385 to estimate the percentage of adults who can wiggle their ears with a margin of error of 5 percentage points and a confidence level of 95%.