statistics - year 2

correlation, conditional probability and normal distribution

total area under normal curve

1

points of inflection on normal curve

at μ + σ and μ - σ

the parameters for normal distribution

population mean ( μ ) and population variance ( σ ² )

effect of curve being symmetrical

mean = median = mode

notation for X is normally distributed

X ~ N(μ, σ ²)

parameters for standard normal distribution

population mean = 0 and population variance = 1

how to code X to use standard normal distribution

Z = (X - μ)/σ

when can normal distribution be used to approximate binomial distribution?

• sample size is large

• p is close to 0.5 (because normal distribution is symmetrical)

range of values for PMCC

-1 ≤ r ≤ 1

what does r = 1 indicate

perfect positive linear correlation

what does r = -1 indicate

perfect negative linear correlation

what does r = 0 indicate

no linear correlation

steps to carry out a hypothesis test for zero correlation

• state null and alternative hypotheses

• the null hypothesis is always that correlation is 0

• find critical value in PMCC table (for the given significance level and sample size)

• reject null hypothesis if observed r value is in critical region

what is the meaning of the gradient of the regression line:

y = a + bx

the change in y for each unit change in x

making a prediction based on a value from inside the range of the given data

interpolation

making a prediction based on data from outside the range of the given data

extrapolation

the controlled variable

independent/explanatory variable

the effected/measured variable

dependent/response variable