Final answer:
The student's question involves calculating a sample size needed to estimate the proportion of left-handed scientists with a specific confidence level and margin of error, which can be done using a formula that incorporates the Z-value for the confidence level, the estimated proportion, and the desired margin of error.
Step-by-step explanation:
The student is interested in determining how large a sample size is needed for a pollster to estimate the number of left-handed scientists with a 98% confidence level and a margin of error no greater than 4%. Given that a previous study indicates the proportion of left-handed scientists is 8%, we can calculate the required sample size using the formula for the sample size of a proportion:
n = (Z² * p * (1-p)) / E²
Where:
- Z is the Z-value corresponding to the confidence level desired (2.33 for 98% confidence),
- p is the estimated proportion of the attribute present in the population (0.08 in this case),
- E is the desired margin of error (0.04).
Plugging these values into the formula gives us:
n = (2.33² * 0.08 * (1-0.08)) / 0.04²,
After calculating, we can determine the minimum sample size needed for the pollster's confidence interval regarding the proportion of left-handed scientists.