Question

#9 find the minimum sample size for the following. you wish to estimate 90% confidence and within 3% of the true population, the proportion of senior citizens that need to be treated for heart disease. there is no initial estimate for p-hat (Hint: think half and half) Show all work.

#10 using the data from #9 - if there was an initial estimate of 30%, what would be the minimum sample size?

Answer 1

Solution:

9 ) Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3% = 0.03

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= (1.645 / 0.03)2 * 0.5 * 0.5

= 751.54

= 752

n = sample size = 752

10 ) Given that,

= 0.3

1 - = 1 - 0.3 = 0.7

margin of error = E = 3% = 0.03

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= (1.645 / 0.03)2 * 0.3 * 0.7

= 631

n = sample size = 631