Question

1. What is a Sampling Distribution?

2. How is a Sampling Distribution created?

3. Explain the Central Limit Theorem in terms of having a normal Sampling Distribution.

4. Why is having a normal Sampling Distribution important?

5. How do we calculate the mean for a Sampling Distribution?

6. How do we calculate the standard deviation for a Sampling Distribution?

7. How is the mean and standard deviation for a Sampling Distribution affected as the sample size increases?

8. How do we determine if an outcome is unusual using z-scores or using probability?

9. What is a standard normal distribution and how is it used?

Answer 1

1. When a sample is taken from a population, the sample information can be used to infer things about the population. A population quantity could be it's mean or variance. If we were to keep taking samples from the same distribution and keep calculating the mean and variance of the sample, we would find that the mean and variance results form distributions as well.

2. The distributions of the sample mean and variance are called sampling distributions. They are used to construct confidence intervals and carry out hypothesis tests.

3. The central limit theorem is used to obtain the distribution of the sample mean. Due to the central limit theorem, inference concerning a population mean can be considered (Normal) without specifying the form of the population, provided the sample size is large enough.

5 . Mean of a sampling distribution: sum of all the variables/total no of variables

6. Variance = S^2 (calculated again like the sample variance, it is an unbiased estimator of the population variance)

8. The z-score should lie between -3 to +3. So if the z score of a variable does not lie within the given interval we will know that it is unusual.