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?

(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.

answer for #1 is c

answer for #2 is d

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