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 95%. 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=

Does the added knowledge in part (b) have much of an effect on the sample size?

A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.
B. No, using the additional survey information from part (b) only slightly reduces the sample size.
C. No, using the additional survey information from part (b) does not change the sample size.
D. Yes, using the additional survey information from part (b) only slightly increases the sample size.

a.   n=2401 students

b.   n=2377 students

c.   B. No, using the additional survey information from part (b) only slightly reduces the sample size.

Step-by-step explanation:

a. The sample size for a sample proportion about the mean is calculated using the formula:

Where p is the proportion and E is the margin of error.

-If nothing is known about the proportion to be studied, we use p=0.5:

Hence, the required sample size is 2401

b. If the proportion to be estimated is given, we substitute it for p in the formula.

-Given p=0.55, the required sample size can be calculated as:

Hence, the required sample size for a given proportion of 55% is approximately 2377 students

c. The added information in b had a reducing effect on the sample size:

-The sample size slightly reduces by 24 students.

Hence, No, using the additional survey information from part (b) only slightly reduces the sample size.

30005

yes ok                                            

a28=58

step-by-step explanation:

a1=a1+(n-1)d

a28= 4+ (28-1)2

a28=4+(27)(2)

a28=4+54

a28=58