Question

The Central Limit Theorem states that:

When the population distribution is normal, the sampling distribution will also be normal.
the t statistic is the distance from x to μ .
There are many t-distribution curves, but only one standard normal curve.
When n is sufficiently large (n ≥ 30) , the sampling distribution of x is approximately normal, even if the population distribution is not normal.

Answer 1

The correct statements are (1) and (4).

Explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n ≥ 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normal.

Then, the mean of the distribution of sample means is given by,

`\mu_(\bar x)=\mu`

And the standard deviation of the distribution of sample means is given by,

`\sigma_(\bar x)=(\sigma)/(√(n))`

And if the population is Normally distributed, then irrespective of the sample size the sampling distribution of the sample mean will be approximately normal.

Thus, the correct statements are (1) and (4).