Question

For these three questions you will need to determine the necessary sample size. Notice these all use the same confidence level. Round this value to three decimal places and use that for all calculations. Using the full critical value can cause incorrect answers. What sample size is needed to be 93% confident that the sample proportion is off by no more than 2.5% if we don't have an estimate for ˆ p ? n = What sample size is needed to be 93% confident that the sample proportion is off by no more than 2.5% if a previous study showed that ˆ p = .39 ? n = What sample size is needed to be 93% confident that the sample mean is off by no more than 3 is we know that σ = 15 ? n =

Answer 1

Solution,

Given that,

1) = 0.39

1 - = 1 - 0.39 = 0.61

margin of error = E = 0.025

At 93% confidence level

= 1 - 93%

= 1 - 0.93 =0.07

/2 = 0.035

Z/2 = Z0.035  = 1.812

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

= (1.812 / 0.025)2 * 0.39 * 0.61

= 1249.77

sample size = n = 1250

2) Z/2 = Z0.035 = 1.812

sample size = n = [Z/2* / E] 2

n = [1.812 * 15 / 3 ]2

n = 82.06

Sample size = n = 83