Q10) 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?

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. ____________

 

1. Sample size for September is 335
2. Sample size for October is 553
3. Sample size for November is 1083
4. Sample size for pre-election day is 3007

P=0.5

Q =1-p

=1-0.5

=0.5

Confidence level=90%

Level of significance α =1-0.9

=0.1

α/2=0.1/2

=0.05

Z _α/2=1.645 (From z table)

Formula of sample size is given by,

S=(Z _α/2²_*P*Q)/E²

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

S=(Z _α/2²_*P*Q)/E²

=(1.645²*0.5*0.5)/0.045²

=334.0771605

Sample size for September is 335

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

S=(Z _α/2²_*P*Q)/E²

=(1.645²*0.5*0.5)/0.035²

=552.25

Sample size for October is 553

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

S=(Z _α/2²_*P*Q)/E²

=(1.645²*0.5*0.5)/0.025²

=1082.41

Sample size for November is 1083

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

S=(Z _α/2²_*P*Q)/E²

=(1.645²*0.5*0.5)/0.015²

=3006.694444

Sample size for pre-election day is 3007