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consider a normal population with u= 75 and o= 10. a sample of at least which size needs to be obtained in order to achieve a standard error or om= 2.00 or less.

Consider A Normal Population With U 75 And O 10 A Sample Of At Least Which Size Needs To Be Obtained In Order To Achieve A Standard Error Or Om 200 Or Less class=

Sagot :

Answer: Choice C)

n = 25

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Explanation:

The standard error formula for the mean is

[tex]\sigma_{M} = \frac{\sigma}{\sqrt{n}}\\\\[/tex]

Since we want this 2.00 or less, this means,

[tex]\sigma_{M} \le 2.00\\\\\frac{10}{\sqrt{n}} \le 2.00\\\\10 \le 2.00\sqrt{n}\\\\2.00\sqrt{n} \ge 10\\\\\sqrt{n} \ge \frac{10}{2.00}\\\\\sqrt{n} \ge 5\\\\n \ge 5^2\\\\n \ge 25\\\\[/tex]

The sample size needs to be n = 25 or larger.

In other words, the sample size needs to be at least 25.

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