Question

Consider an x distribution with standard deviation o = 34.

(a) If specifications for a research project require the standard error of the corresponding distribution to be 2, how
large does the sample size need to be?
B) If specifications for a research project require the standard error of the corresponding x distribution to be 1, how large does the sample size need to be?

Answer 1

Part (a)

The standard error (SE) formula is

`\text{SE} = (\sigma)/(√(n))\\\\`

where n is the sample size. We're given SE = 2 and sigma = 34, so,

`\text{SE} = (\sigma)/(√(n))\\\\2 = (34)/(√(n))\\\\2√(n) = 34\\\\√(n) = (34)/(2)\\\\√(n) = 17\\\\n = 17^2\\\\n = 289\\\\`

So we need a sample size of n = 289 to have an SE value of 2.

Answer: 289

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Part (b)

We'll use SE = 1 this time

`\text{SE} = (\sigma)/(√(n))\\\\1 = (34)/(√(n))\\\\1*√(n) = 34\\\\√(n) = 34\\\\n = 34^2\\\\n = 1156\\\\`

Because we require greater precision (i.e. a smaller SE value), the sample size must be larger to account for this. In other words, as SE goes down, then n must go up, and vice versa.

Answer: 1156