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Morgarella [4.7K]
2 years ago
5

If you want to be 95​% confident of estimating the population mean to within a sampling error of plus or minus3 and the standard

deviation is assumed to be 20​, what sample size is​ required? The sample size required is
Mathematics
1 answer:
Aleksandr [31]2 years ago
5 0

Answer:

The sample size required is at least 171

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

What sample size is​ required?

A samle size of at least n is required, in which n is found when M = 3, \sigma = 20

So

M = z*\frac{\sigma}{\sqrt{n}}

3 = 1.96*\frac{20}{\sqrt{n}}

3\sqrt{n} = 20*1.96

\sqrt{n} = \frac{20*1.96}{3}

(\sqrt{n})^{2} = (\frac{20*1.96}{3})^{2}

n = 170.7

Rouding up

The sample size required is at least 171

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