A doctor would like to know what proportion of their patients are vitamin D deficient. They choose a random sample of 30 patients and find that 23 of them are vitamin D deficient. What is the margin of error with 95% confidence? Round your answer to the nearest hundredth.(1 point)
To calculate the margin of error with 95% confidence, we can use the formula:
Margin of error = Z * sqrt((p*(1-p))/n)
Where:
Z = Z-score for 95% confidence level, which is approximately 1.96
p = proportion of vitamin D deficient patients in the sample (23/30 = 0.7667)
n = sample size (30)
Plugging in the values:
Margin of error = 1.96 * sqrt((0.7667*(1-0.7667))/30)
Margin of error = 1.96 * sqrt((0.2332)/30)
Margin of error = 1.96 * sqrt(0.007773)
Margin of error = 1.96 * 0.08813
Margin of error ≈ 0.17
Therefore, the margin of error with 95% confidence is approximately 0.17.