Question

In the planning stage, a sample proportion is estimated as pˆ = 30/50 = 0.60. Use this information to compute the minimum sample size n required to estimate p with 95% confidence if the desired margin of error E = 0.07. What happens to n if you decide to estimate p with 90% 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
95%
90%

Answer 1

Given that,

sample proportion = 30/50 = 0.60

Margin of error (E) = 0.07

We want to find, the sample size for the following confidence level,

i) A 95% confidence level has significance level of 0.05 and critical value is,

Therefore, required sample size is 188

ii) A 90% confidence level has significance level of 0.10 and critical value is,

Therefore, required sample size is 133

NOTE : if wr reduced the confidence level from 95% to 90% then then required sample size gets reduced.