95% Confidence Interval for Left-Handed Proportion: Calculation and Interpretation

To calculate the confidence interval for the proportion of the whole population, we can use the formula:
CI = p̂ ± Z * √(p̂(1-p̂)/n)
Where:
p̂ is the sample proportion (33/300 = 0.11)
Z is the Z-score for a 95% confidence interval (1.96 for a 95% confidence interval)
n is the sample size (300)
Plugging in the values:
CI = 0.11 ± 1.96 * √(0.11(1-0.11)/300)
Calculating the values inside the square root:
CI = 0.11 ± 1.96 * √(0.0979/300)
CI = 0.11 ± 1.96 * 0.0167
CI = 0.11 ± 0.0327
Taking the upper and lower limits of the confidence interval:
Lower limit = 0.11 - 0.0327 = 0.0773
Upper limit = 0.11 + 0.0327 = 0.1427
Therefore, the 95% confidence interval for the proportion of the whole population which is left-handed is (0.0773, 0.1427).
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