Question

In the planning stage, a sample proportion is estimated as pˆ = 49/70 = 0.70. Use this information to compute the minimum sample size n required to estimate p with 99% confidence if the desired margin of error E = 0.15. What happens to n if you decide to estimate p with 95% confidence? (You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places and "z" value to 3 decimal places. Round up your answers to the nearest whole number.)

Confidence Level	N
99%
95%

Answer 1

Given in the planning stage, a sample proportion is estimated as pˆ = 49/70 = 0.70. Now the minimum sample size n required to estimate p with 99% confidence if the desired margin of error E = 0.15 is calculated as:

where Zc is critical score at the given confidence level which is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.995), thus the Zc is computed as 2.576.

now the minimum sample is computed as:

again at 95 % confidence level the Zc is computed using the excel formula for normal distribution which is =NORM.S.INV(0.975), thus the Zc is computed as 1.960.

now the minimum sample is computed as: