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icang [17]
3 years ago
12

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?
Mathematics
1 answer:
kvv77 [185]3 years ago
3 0
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.
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