Question

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.

Answer 1

Answer: 246

Explanation:

As per given description , we have

Population standard deviation:
`\sigma=16`

Critical value for 95% confidence =
`z_(\alpha/2)=1.96`

margin of error : E= 2

Formula to find the required sample size : -

`n=((z_(\alpha/2)\sigma)/(E))^2\\\\=((1.96*16)/(2))^2\\\\=245.8624\approx246`

Hence, the required minimum sample =246