Question

A simple random sample of 1100 males aged 12 to 17 int he United States were asked whether they played massive multiplayer online role-playing games (MMORPGs); 775 said that they did. Construct a 95% confidence interval to estimate the proportion of all U.S. males aged 12 to 17 who play MMORPGs. Using Scenario 2, if you wanted to have a margin of error of LaTeX: \pm 2% with 99% confidence, would your sample have to be larger, smaller, or the same size as the sample in the previous question

Answer 1

`n' = 2212` (larger)

Explanation:

From the question we are told that

Initial sample size n=1100

Sample range 5

Sample Proportion
`\hat P= x/n=>775/1100=>0.704`

99% confidence

Margin for error
`E=\pm2 \%=>0.02`

Generally at confidence level 99%

Level of significance
`\alpha =1-0.99=>0.01`

`\alpha /2 =(0.01)/(2) =0.005`

Therefore

`Z_\alpha_ /_2=Z_0_._0_0_5=2.576`

`Z_\alpha_ /_2=2.576`

Generally sample size is mathematically given by

`n' = (Z_\alpha_/_2 / E )^2 * \hat P * (1 - \hat P )`

`n' = (2.576) / 0.025)^2 * 0.704 * (1 - 0.704)`

`n' = 2212.463274`

`n' = 2212`

Therefore the new sample will be larger