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If we desired to estimate the average mechanical aptitude of a large population of workers, how large a random sample would we need to be able to assert with a probability of 0.95 that the sample mean will be within 2 points of the population (true) mean? Assuming that it is known from past experience with similar data that σ = 16.

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JeanaShupp

Answer: 246

Step-by-step explanation:

As per given description , we have

Population standard deviation: [tex]\sigma=16[/tex]

Critical value for 95% confidence = [tex]z_{\alpha/2}=1.96[/tex]

margin of error : E= 2

Formula to find the required sample size : -

[tex]n=(\dfrac{z_{\alpha/2}\sigma}{E})^2\\\\=(\dfrac{1.96\times16}{2})^2\\\\=245.8624\approx246[/tex]

Hence, the required minimum sample =246

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