Question

-PLEASE SHOW ALL WORK-

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.

(i) 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 p̂ will be within a distance of 0.03 from p? (Round your answer up to the nearest whole number.)

_______ medical files

(ii) Answer part (i) if you use the preliminary estimate that about 11 out of 90 people have blood type B.

_______ medical files

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.03

At 85% confidence level the z is ,

= 1 - 85% = 1 - 0.85= 0.15

/ 2 =0.075

Z_/2 = Z_0.075 = 1.44 ( Using z table  

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.44/ 0.03)² * 0.5 * 0.5

= 576

n=576 medical files

(B)

Solution :

Given that,

= x/n=11/90=0.122

1 - = 1 - 0.122= 0.878

margin of error = E = 0.03

At 85% confidence level the z is ,

= 1 - 85% = 1 - 0.85= 0.15

/ 2 =0.075

Z_/2 = Z_0.075 = 1.44 ( Using z table  

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.44/ 0.03)² * 0.122 * 0.878

= 247

n=247 medical files