Question

According to the Central Limit Theorem, the probability distribution of the sum or average of a large random sample drawn with replacement will be roughly normal, regardless of the distribution of the population from which the sample is drawn. Question 4.4. Note the statement about the sample being large and random. Is this sample large and random

Answer 1

Answer:

Step-by-step explanation:

The specific sample is not given but the key point is to know if the sample is large and random.

In other words, the inquiry that applies here is: "How to identify a large sample and a random sample"

A large sample is one which has a large number of elements or observations or values.

In a large sample size, N (the number of observations or values) is either equal to 30 or greater than 30.

A random sample is a sample which is drawn randomly from a population. A population is the whole body of items or individuals which the researcher's 'torchlight' is focused on. A sample is usually drawn from a population to make the work of the researcher to be possible or feasible.

We say a sample is drawn randomly from a population IF there is no bias or preference for particular items or individuals in the population.

If a sample is drawn with replacement, it means that after picking an item to derive data from, the researcher replaces the item in the population space BEFORE picking another item to derive data from.

Hence, all through the sample creation process, the population size stays constant.

Now, the Central Limit Theorem (which you have already defined) says "... regardless of the distribution of the population from which the sample is drawn".

This means "... whether the distribution of the population is negatively skewed, normal, or positively skewed.

So once the sample is large (gives a wide representation of the population), random, and drawn with replacement of items; the Central Limit Theorem applies!