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 first need to find the standard error.
The formula for the standard error is:
SE = √(p * (1-p) / n)
where:
p = sample proportion (23/30 = 0.767)
n = sample size (30)
SE = √(0.767 * 0.233 / 30)
SE = √(0.178311 / 30)
SE = √0.0059437
SE ≈ 0.0771
Next, we calculate the margin of error using the formula:
ME = z * SE
where z is the z-score corresponding to 95% confidence level, which is 1.96.
ME = 1.96 * 0.0771
ME ≈ 0.1515
Therefore, the margin of error with 95% confidence is approximately 0.15.