Question

In a study of government financial aid for coliege students, it becomes nocessary to estmate the percentage of tul-time oolege itivents who earn a bacholor's degree in four ysan or iess. Find the sample sice needed to ostimate that percentage. Use a 0.05 margin of erfor and vis

a contidence level of 95%. Complete pars (a) through (e) below a. Assume that nothing is known about the peroentage to be estimatod. n=365 (Round up in the neareat integer)
b. Assume pror atudies have shown that about B5\% of tustime stiydents eam bacheloris degroon in four years or loss. n=MeO (Rlound up to the nearest integet)

c. Does the added knewiedge in part (b) have much of an offoct on the savple suce?
A. Yes, using the addabanal furvey information from part (b) only sighty increases the savple sion.
B. No, uting the adobina aurvey infomatian from part (b) oely slovily reduces the sample size
C. No, using the adesionsl surver information from part (b) does not change the samyle size
D. You, uning the addoanil suvey infermation fiom pat (b) dranaticaly ieduces the sanple sive

Answer 1

No, using the additional survey information from part (b) does not change the sample size.

The correct option is C.

Step-by-step explanation:

In determining the sample size for estimating a population percentage, the margin of error (E) is influenced by the variability of the population (P) and the confidence level (Z). The formula for the sample size (n) is given by the equation:

`\[ n = (Z^2 * P * (1 - P))/(E^2) \]`

In part (a), where nothing is known about the percentage, we assume a 50% variability (P = 0.5). In part (b), prior studies provide information about the population percentage (P = 0.85). However, since the confidence level and margin of error remain constant, the change in P does not significantly impact the sample size. The formula demonstrates that P and (1 - P) are multiplied by the same factor, so the effect on n is limited.

Therefore, despite having prior knowledge in part (b), the added information about the population percentage does not substantially affect the sample size calculation. The decision to choose option C is based on recognizing that the change in P doesn't result in a dramatic reduction or increase in the required sample size for the given confidence level and margin of error.

The correct option is C.