Question

A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%

A. If no preliminary estimate is available

B. If a recent survey indicated that 43% of the population suffers from high blood pressure.

Answer 1

Solution,

Given that,

a) =  1 - = 0.5

margin of error = E = 0.05

At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05  = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.05)2 * 0.5 * 0.5

= 270.60

sample size = n = 271

b) = 0.43

1 - = 1 - 0.43 = 0.57

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.05 )2 * 0.43 * 0.57

= 265.29

sample size = n = 266