Final answer:
Assuming the population standard deviation to be the same as provided in the examples (15 years), a sample size of 138 transfer students is required to estimate the mean age within a 2.1 year margin of error with 90% confidence.
Step-by-step explanation:
To determine the sample size needed to estimate the population mean age of the incoming fall term transfer students with a specified level of confidence, we use the formula for calculating sample size in a confidence interval for a mean when the population standard deviation is known:
n = (Z*σ/E)^2
Where n is the sample size, Z is the Z-value corresponding to the desired level of confidence, σ is the population standard deviation, and E is the margin of error (the desired maximum difference between the sample mean and the population mean).
We were given:
The level of confidence: 90%, which corresponds to a Z-value of approximately 1.645 (from Z-tables)
The margin of error (E): 2.1 years
However, the population standard deviation (σ) is not provided in the question. Assuming the population standard deviation is the same as in the examples provided (σ = 15 years), we can calculate the sample size as follows:
n = (1.645*15/2.1)^2
Calculating this gives us:
n = (24.675/2.1)^2
n = (11.75)^2
n = 137.5625
Since we cannot have a fraction of a sample, we would round up to ensure the sample size is adequate. Therefore, a total of 138 transfer students would be required to meet the criteria set for the confidence interval.