Question

Closer to the November election, better precision and smaller margins of error are desired. Assume the following margins of error are requested for surveys to be conducted during the electoral campaign. Assume a planning value of p^* = 0.50 and a 90% confidence level. What is the recommended sample size for each survey? Show work

1. For September, the desired margin of error is 0.045. ____________

2. For October, the desired margin of error is 0.035. ____________

3. For early November, the desired margin of error is 0.025. ____________

4. For pre-election day, the desired margin of error is 0.015. ____________

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5  

1)

margin of error = E = 0.045

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= (1.645 /0.045 )² * 0.5*0.5

= 334.077

sample size = 335

2)

margin of error = E = 0.035

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

= (1.645 /0.035)² * 0.5*0.5

= 552.25

sample size = 553

3)

margin of error = E = 0.025

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

= (1.645 /0.025 )² * 0.5*0.5

= 1082.41

sample size = 1083

4)

margin of error = E = 0.015

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

= (1.645 /0.015)² * 0.5*0.5

= 3006.69

sample size = 3007