Question

A1.) A population proportion is estimated to be 0.0283 < p < 0.0373 at 95% confidence level. Using 4 decimal places for z_c find the least sample size required to ensure this estimate.
N=

B1.) A population proportion is estimated to be within 0.0035 of p^= 0.3832 at 99% confidence level. Using 4 decimal places for z_c, find the least sample size required to ensure this estimate.
N=

A2.) A population proportion is estimated to be 0.0323 < p < 0.0443 at 92% confidence level. Using 4 decimal places for z_c, find the least sample size required to ensure this estimate.
N=

B2.) A population proportion is estimated to be within 0.0035 of p^=0.3812 at 90% confidence level. Using 4 decimal places for z_c, find the least sample size required to ensure this estimate.
N=

Answer 1

Answer:

A1.

Given,

0.0283 < p < 0.0373

alpha = 1 - 0.95

= 0.05

Critical value at Z(alpha/2) = Z(0.025)

= 1.96

sample proportion p^ = (0.0283 + 0.0373)/2

= 0.0656/2

= 0.0328

Margin of error E = (0.0373 - 0.0283)/2

= 0.009

Confidence interval = sample proportion +/- margin of error

= 0.0328 +/- 0.009

Sample size n = p^(1-p^)*(z/E)^2

substitute values

= 0.0328*(1-0.0328)*(1.96/0.009)^2

= 1504.6

= 1505

B1)

Margin of error = 0.0035

p^ = 0.3832

Confidence interval = 99%

alpha = 1 - 0.99

= 0.01

Critical value z = 2.58

consider,

n = p^(1-p^)*(z/E)^2

substitute values

= 0.3832*(1-0.3832)*(2.58/0.0035)^2

= 128431.9832

n = 128432