Question

In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who can earn a bachelor's degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.1 margin of error and use a confidence level of 90%.

Answer 1

The sample size needed to estimate the percentage is 68

The margin of error is calculated using the relation:

• Error = Zcritical * √(p(1 - p)/n)
• Error = 0.1
• Zcritical at 90% = 1.645

Since, we don't know anything about the proportion, we use : p = 0.5

Now we have:

0.1 = 1.645 × √(0.5(1 - 0.5)/n)

0.1 = 1.645 × √0.25/n

0.1/1.645 = √0.25/n

0.0607902736 = √0.25/n

Take the square of both sides

0.00369545 = 0.25/n

0.00369545n = 0.25

n = 0.25/0.00369545

n = 67.65

Hence, the required sample size is 68.