Question

you want to obtain a sample to estimate a population mean age of the incoming fall term transfer students. based on previous evidence, you believe the population standard deviation is approximately . you would like to be 90% confident that your estimate is within 2.1 of the true population mean. how large of a sample size is required?

Answer 1

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.