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 95%. Complete parts (a) through (c) below. a. Assume that nothing is known about the percentage to be estimated. (Round up to the nearest integer.) b. Assume prior studies have shown that about 60% of full-time students earn bachelor's degrees in four years or less (Round up to the nearest integer.) c. Does the added knowledge in part (b) have much of an effect on the sample size? O A. Yes, using the additional survey information from part (b) dramatically reduces the sample size. OB. No, using the additional survey information from part (b) does not change the sample size. O C. No, using the additional survey information from part (b) only slightly reduces the sample size. OD. Yes, using the additional survey information from part (b) only slightly increases the sample size.

Answer 1

whenever population proportion(percentage) is unknown, we assume it to be 0.5(50%)

2 Zx2 formula for sample sine needed to estimate population proportion is P(1-P) where pis population propretim E2 here margin of error E = confidence level (1-2) 1006 = 95% |-2=0.95 K 30.05 > 2/2=0.025 2<, = Zoºd 2 s =g6 0.02 il-p=0.5 >> 9.) pis unknown assume P=0.5 (96²x0.500.5 (0:02)2 12401 b) p is en known P=60% = 0.6 => 1-P = 0.4 2 ins (196) X0:6X0.4 (0:02) n= 2 304.96 n = 12305 © © V NO, using additional survey information from part o only slightly reduces sample size