Question

A random sample of medical files is used to estimate the proportion p of all people who have blood type b.

(a) If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p will be within a distance of 0.07 from p?
______medical files

(b) Answer part (a) if you use the preliminary estimate that about 13 out of 90 people have blood type B.
_______ medical files

Answer 1

Answer:

a) 106

b) 53

Step-by-step explanation:

Minimum required medical files can be found using the formula

n≥ p×(1-p) × $(\frac{z}{ME} )^2$ where

• n is the minimum required medical files

• p is the estimated proportion for blood type b

• z is the corresponding z-score for two tailed 85% confidence level

• ME is the margin of error in the estimation

For the case (a)

If there is no preliminary estimate for p, then it is estimated as p=0.5

corresponding z-score for two tailed 85% confidence level is 1.44

and ME is 0.07.

Putting all in the formula;

n≥ 0.5×0.5 × $(\frac{1.44}{0.07} )^2$  ≈ 106

For the case (b)

The only difference is p=$\frac{13}{90}$≈0.144

n≥ 0.144×0.856 × $(\frac{1.44}{0.07} )^2$  ≈ 53