The same sample of 25 seniors from the urban school district with the mean and standard deviation N (450, 100). A 95% confidence interval for µ for the population of seniors with a margin of error of ± 25 is used. What is the smallest sample size we can take to achieve this same margin of error?

The margin of error of a sample is given by:

B = z (α/2) σ/√n; where B is the margin of error = 25, z (α/2) is the level of significant = 1.96, σ is the standard deviation = 100 and n is the sample size.

25 = 1.96 (100/√n)

100/√n = 25/1.96 = 12.76

√n = 100/12.76 = 7.84

n = (7.84) ^2 = 61.47

Therefore, the smallest sample size required is 62 seniors.