For this problem, carry at least four digits after the decimal in your calculati

Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

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 0.04 from p? (Round your answer up to the nearest whole number.)
______ medical files

(b) Answer part (a) if you use the preliminary estimate that about 15 out of 90 people have blood type B.
______ medical files

Explanation / Answer

a)

The margin of error is 0.04

Because the proportions are not given, we have to assume that p equals 0.5
Therefore, 1-p equals 0.5

1-85%=15%

15%/2= 7.5%

Invnorm (0.075, 0, 1) =-1.44

The z value is 1.44 according to the 85% confidence level.

Since,

Margin of error, E = z* sqrt (pq/n)

When all of this is in the formula and solve for n we get,

n   = (z/E) ^2 *P*(1-P)

n   = (1.44/0.04)^2 * 0.5 * 0.5

n   = 324

So 324 medical files should be included in the sample.

b)

p = 15/90 = 0.16667

Margin of error, E = 0.04

The z value is 1.44 according to the 85% confidence level

Margin of error, E = z* sqrt (pq/n)

When all of this is in the formula and solve for n we get,

n   = (z/E) ^2 *P*(1-P)

n   = (1.44/0.04)^2 * 0.16667 * (1- 0.16667)

n   = 180.0029

Minimum sample size = 180 (when rounded up).

So 180 medical files should be included in the sample.

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