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A statistics student would like to estimate the average age of students at her college. She would like to be 99% confident that her estimate includes the actual college population mean. She did a smaller preliminary survey and found that a reasonable estimate of the population standard deviation was 2 1/2 years. How many people must she survey if she wants to be within 1/2 year of the true population mean?

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Answer:

Step-by-step explanation:

Given that a statistics student would like to estimate the average age of students at her college.

Population std dev =2.5years

For 99% , Z critical = ±2.59

Margin of error =  [tex]±2.59*\frac{2.5}{\sqrt{n} }  \\= \frac{±6.475}{\sqrt{n} } =0.5[/tex]

Simplify to get

[tex]\sqrt{n} =12.95[/tex]

n = 167.70

n=168

She must survey 168 people

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