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miskamm [114]
3 years ago
6

Suppose we want to determine the minimum sample size required to give us a 95% confidence interval that estimates, to within $50

0, the average salary of a state employee. Also, suppose that from a previous experiment, we know that the population standard deviation is $6300. What is the minimum sample size required
Mathematics
1 answer:
Firlakuza [10]3 years ago
4 0

Answer:

The minimum sample size is 610.

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 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.

Population standard deviation is $6300, so \sigma = 6300

Suppose we want to determine the minimum sample size required to give us a 95% confidence interval that estimates, to within $500, the average salary of a state employee.

This is n when M = 500. So

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

500 = 1.96*\frac{6300}{\sqrt{n}}

500\sqrt{n} = 1.96*6300

\sqrt{n} = \frac{1.96*6300}{500}

(\sqrt{n})^{2} = (\frac{1.96*6300}{500})^{2}

n = 609.89

Rouding up

The minimum sample size is 610.

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