Question

If all possible random samples of size N are drawn from a population with a mean of mu and a standard deviation of sigma, then as N becomes larger, the sampling distribution of sample means becomes approximately normal with a mean of muy(bar) and a standard deviation of sigmay(bar). This statement is known as the:

Answer 1

"Central limit theorem" is the right answer.

Explanation:

A hypothesis essentially claims that whenever there seems to be a small variance throughout the big confidence intervals, the sampling is based on averages as well as the sampling distribution (mean) usually nearly the same as the public's median.

When,

• Mean =
  `\mu_y`
• Standard deviation =
  `\sigma_y`
• Sample size = N

is sufficiently larger than
`\bar Y \sim N(\mu_y, \sigma_y)`

Thus, the above is the right answer.