## In a study of government financial aid for college​ students, it becomes necessary to estimate the percentage of​ full-time college students

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 0.02 margin of error and use a confidence level of 99​%. Complete parts​ (a) through​ (c) below.
a. Assume that nothing is known about the percentage to be estimated.n = ________b. Assume prior studies have shown that about 55% of​ full-time students earn​ bachelor’s degrees in four years or less.n = _______c. Does the added knowledge in part​ (b) have much of an effect on the sample​ size?

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1 week 2021-10-11T16:31:10+00:00 1 Answer 0

(a) The sample size required is 2401.

(b) The sample size required is 2377.

(c) Yes, on increasing the proportion value the sample size decreased.

Step-by-step explanation:

The confidence interval for population proportion p is: The margin of error in this interval is: The information provided is:

MOE = 0.02 (a)

Assume that the proportion value is 0.50.

Compute the value of n as follows: Thus, the sample size required is 2401.

(b)

Given that the proportion value is 0.55.

Compute the value of n as follows: Thus, the sample size required is 2377.

(c)

On increasing the proportion value the sample size decreased.