Answer to Question #138210 in Statistics and Probability for Joseph Se

Question

A.  Describe a normal distribution.

B.  State and explain the Empirical Rule.

C.  State and explain the Central Limit Theorem

D. What is Correlation Analysis?

E. How is correlation measured and how is it interpreted?

Answer 1

A) The normal distribution is a probability function that describes how the values of a variable are distributed. It is a symmetric distribution where most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions.

B) The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.

C) The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed

D) Correlation analysis is a statistical method used to evaluate the strength of relationship between two quantitative variables. A high correlation means that two or more variables have a strong relationship with each other, while a weak correlation means that the variables are hardly related. In other words, it is the process of studying the strength of that relationship with available statistical data. 

E) In statistics, the correlation coefficient r measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of r is always between +1 and –1. To interpret its value, see which of the following values your correlation r is closest to:

• Exactly –1. A perfect downhill (negative) linear relationship
• –0.70. A strong downhill (negative) linear relationship
• –0.50. A moderate downhill (negative) relationship
• –0.30. A weak downhill (negative) linear relationship
• 0. No linear relationship
• +0.30. A weak uphill (positive) linear relationship
• +0.50. A moderate uphill (positive) relationship
• +0.70. A strong uphill (positive) linear relationship
• Exactly +1. A perfect uphill (positive) linear relationship