9. A doctor noticed that many female patients were Vitamin D deficient. She woul

Question

9. A doctor noticed that many female patients were Vitamin D deficient. She would like to determine what proportion of her patients are deficient. She chooses a random sample of 45 medical files of female patients and finds that 37 of these patients are Vitamin D deficient. (Round to 3 decimal places) (Write out all formulas used and show ALL work) a. Find x, n, p, and q. (4 points) b. For a 95% Confidence level, identify and the z,r/2. (2 points) c. Find the margin of error, E for a 95% confidence level. write out the formula for E. (3 points) n struct and interpret a 95% Confidence Interval for the true population proportion of female d. Co patients who are Vitamin D deficient. Write out the formula used for a Confidence Interval for Estimating a Population Proportion p. (4 points)

Explanation / Answer

a)
x = 37
n = 45
pcap = 37/45 = 0.82222
qcap = 1 - pcap = 0.17778

b)
alpha = 0.05
z(alpha/2) = 1.9600

c) and d)

n 45 p 0.82222 z-value of 95% CI 1.9600 SE = sqrt(p*(1-p)/n) 0.05699 ME = z*SE 0.11171 Lower Limit = p - ME 0.71052 Upper Limit = p + ME 0.93393 95% CI (0.7105 , 0.9339 )

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