Question

1)What does the Central Limit Theorem say, and why is it so important to inferential statistics?

2) Why would someone want to know whether a sample had more than 30 observations?

3) What is the continuity correction?

4) What is a sampling distribution?

5) What are the basic distinctions between situations in which the binomial, poisson, and hypergeometric distributions apply?

6) Suppose you have a population with mean ? and standard deviation ?. What can you say about the sampling distribution of the sample mean for samples of size 20?

7) What are the three primary distributions we are interested in when dealing with a quantitative random variable, and what symbol do we use to indicate the mean and standard deviation of each.

8) We needed to make sure that np>15 and n(1-p)>15 in order to use the normal distribution in two situations. What are those situations, and why do they both involve the same rule?

9) Suppose someone tells you that no matter what they do, when they combine the fact that P(A|B)=P(A?B)/P(B) with the rule that P(A?B) always equals P(A) times P(B), they always find events A and B to be independent. Where did they go wrong in their analysis of independence?

Answer 1

1. Central limit theorem says that when the sample size is sufficient large, distribution of sample mean is normal even though population distribution is not normal.

As we know that for inferential statistics, it is recommended to have normal distribution. Using central limit theorem we get that for sufficient large sample distribution of sample mean is normal if original distribution is not normal.

2. As per central limit theorem, if n>30 distribution of sample mean is normal even if population is not normal. So it is important to know whether sample size is more than 30.

3. To approximate discrete distribution by continuous distribution we make some adjustments and that is called continuity correction.

4. Sampling distribution is the probability distribution of the large samples which are obtained from the population.