Final answer:
We use the formula for constructing a confidence interval for a population proportion to calculate a 98% confidence interval for the proportion of left-handed golfers. We need the sample proportion, the Z-score for the 98% confidence level, and the sample size for the calculation.
Step-by-step explanation:
To create a 98% confidence interval for the proportion of golfers that are left-handed, we would use the formula for a confidence interval for a population proportion: CI = p ± Z*(√p(1-p)/n), where p is the sample proportion, Z is the Z-score corresponding to the confidence level, and n is the sample size.
The sample proportion of left-handed golfers is calculated as p = 381/2450. The Z-score for a 98% confidence level is approximately 2.326 (this can be found using a standard normal distribution table or calculator). The formula can then be applied to find the margin of error and thus the confidence interval.
Once the calculations are completed, the confidence interval for the proportion of left-handed golfers is obtained and should be rounded to three decimal places as specified in the question.