Question

In a study of government financial aid for college​ students, it becomes necessary to estimate the percentage of​ full-time college students who earn a​ bachelor's degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.04 margin of error and use a confidence level of 95​%. Complete parts​ (a) through​ (c) below. a. Assume that nothing is known about the percentage to be estimated.

Answer 1

Solution :

a) The sample size needed to estimate the population percentage at 95% confidence level is given as follows :

Where, n is sample size, E is margin of error, p̂ is point estimate of population percentage, q̂ = 100 - p̂ and Z(0.05/2) is critical z-value at 95% confidence level.

We have, E = 0.04 = 4%

If nothing is known about the percentage to be estimated, then we assume that point estimate of population percentage is 50%.

Hence, p̂ = 50%,  q̂ = 100 - 50 = 50%

Using Z-table we get, Z(0.05/2) = 1.96

Hence, the required sample size is,

On rounding to nearest whole number we get,

n = 600

The sample size needed to estimate the percentage is 600.

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