Question

1) margin of error: 0.025; confidence level: 99%; p = .25.  The minimum sample size is n =  .

2) margin of error: 0.04; confidence level 98%; p = .7. The minimum sample size is n =  .

3) margin of error: 3%; confidence level 95%; p = .5. The minimum sample size is n =  .

4) margin of error 2%; confidence level 97%; p = .15. The minimum sample size is n =  .

5) margin of error 1.5%; confidence level 96%; p = .66. The minimum sample size is n =  .

Answer 1

Solution,

Given that,

= 0.25

1 - = 1 - 0.25 = 0.75

margin of error = E = 0.025

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576

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

= ( 2.576 / 0.025 )2 * 0.25 * 0.75

= 1990.73

Sample size = n = 1991

( 2 )

= 0.7

1 - = 1 - 0.7 = 0.3

margin of error = E = 0.04

At 98% confidence level

= 1 - 98%  

= 1 - 0.98 = 0.02

/2 = 0.01

Z/2 = Z0.01  = 2.326

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

= ( 2.326 / 0.04 )2 * 0.7 * 0.3

= 710

Sample size = n = 710

( 3 )

= 0.5

1 - = 1- 0.5 = 0.5

margin of error = E = 3% = 0.03

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= (1.96 / 0.03 )2 * 0.5 * 0.5

= 1067

Sample size = n = 1067

( 4 )

= 0.15

1 - = 1 - 0.15 = 0.85

margin of error = E = 2% = 0.02

At 97% confidence level

= 1 - 97%  

= 1 - 0.97 = 0.03

/2 = 0.015

Z/2 = Z0.015  = 2.170

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

= ( 2.170 / 0.02 )2 * 0.15 * 0.85

= 1500.96

Sample size = n = 1501

( 5 )

= 0.66

1 - = 1 - 0.66 = 0.34

margin of error = E =  1.5% = 0.015

At 96% confidence level

= 1 - 96%  

= 1 - 0.96 = 0.04

/2 = 0.02

Z/2 = Z0.032  = 2.054

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

= ( 2.054 / 0.015 )2 * 0.66 * 0.34

= 4207.67

Sample size = n = 4208