Question

In a study of government financial aid for college students

Answer 1

6,766

Explanation:

Given:

• Margin of error = 0.01

,

• Confidence Level = 90%

We want to find the sample size needed to estimate the percentage of full-time students who earn a bachelor's degree in four years or less.

In order to determine the sample size, we use the formula below:

`n=\left((z^(*))/(M)\right)^(2) \tilde{p}(1-\tilde{p})`

• Because there is no estimate of the proportion given, take ,p=0.5,.

,

• For a 95% confidence interval, z=1.645

Substitute these values into the formula:

`\begin{gathered} n=\left((1.645)/(0.01)\right)0.5(1-0.5) \\ =6765.0625 \\ n\approx6,766 \end{gathered}`

The sample size is 6,766.