Question

1) Explain what inferential statistics is used for

2) Define briefly and in your words the p-value

3) Provide an example where a hypothesis test would be worth doing with a null hypothesis μ1-μ2 = 0, and with an alternative hypothesis of μ1-μ2 ≠ 0

4) Explain why, in confidence intervals, when moving from a case in which the population variance is known to another in which this value is estimated from samples (sample variance), the length of the interval grows - keeping everything else constant.

5) Suppose we have a parameter k that interests me. I establish a null hypothesis that says k = 0, and an alternative hypothesis of k ≠ 0. At the end of my procedure, I have a p-value of 0.0001. What is the conclusion of this analysis?

6) Briefly explain what the central limit theorem consists of.

Answer 1

As per the guidelines I am suggested to answer only one question at a time. Please ask the rest of the questions separately, I will be happy to help.

Answer 1) Inferential statistics is used to make judgements and predictions about the population data by seeing a sample of that population. For example, if we consider a mall, we can take a survey of 100 people in the mall about whether they shopped at Apple store, or not. So we can get an idea about the over all population, and what percentage of overall population shopped at apple. We also use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in a particular study. It is used at many places in our life widely, that is why it is of utmost use.