The Central Limit Theorem Answer true or false to each of th

The Central Limit Theorem

Answer true or false to each of the following statements:

1. The larger a sample you take, the more the population looks like a normal distribution.

2. The larger a sample you take, the closer the sample is to being normally distributed.

3. The larger a sample you take, the more the sample looks like the population.

4. The larger a sample you take, the closer the sample mean is likely to be to the mean of the population.

5. The theoretical collection of all possible different sample means that could be obtained forms an approximately normal distribution

Solution

Answer to the question)

Statement 1- The central limit theorem comments on the sample , it does not state about the population. Thus this statement is FALSE, because it says that the population looks like normal

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Statement 2 - This is statement is TRUE. The larger the sample , the more closer is the sample to normal distribution

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Statement 3 - This statement is not true , the reason is pretty simple. If suppose the population is skewed. Now if we take a larger sample , as per the central limit theorem the sample follows normal distribution , thus it fails to look like the population

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Statement 4 - Yes this statement is true , for a larger sample , sample mean is equal to population mean

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Statement 5 - This statement is not correct. Normal distribution is not obtained by theoretical collection of samples. It is obtained by including all the sampling units in one single sample , and making it a large sample.