Flashcards in The normal distribution and estimation Deck (12)

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1

## What is the relative frequency density graph?

### Like a histogram but y axis is now density. the area under the histogram is 1. density is defined as the proportion of observations per unit interval of the x-axis

2

## What is probability density function?

###
With an increasing sample size the width intervals on the histogram - with an infinite sample size the line is smooth.

The area under the curve is one

The AUC can be used to calculate the probability within a range of values of interest

3

## What is the normal distribution?

### Describes a family of bell-shaped probability functions which are totally specified by two parameters

4

## What are the parameters of normal distribution?

### mean value and standard deviation

5

## What is variance?

### SD squared

6

## What happens with an N(0,1) distribution?

### the x-axis is usually labelled z and the cumulative distribution function (c.d.f) denoted ... is the probability that a value chosen at random from N(0,1) distribution is less than or equal to z

7

## How do you assess the normality of data?

###
the mean and median should be approximately equal

the box plot should be symmetric

95% of the data should lie within 2SDs of the mean and almost all within 3SDs

Normal probability plot should be linear

8

## What is the standard error?

### SE = (population SD) / square root (n)

9

## How do we estimate the population mean?

### If we assume that the distribution of the sample means in Normal, then we expect 95% of the sample means to lie within 1.96 standard errors of the true population mean

10

## What is the 95% confidence interval?

### the sample mean +/- (1.96 X SE) and will contain the population mean in 95% of the samples

11

## What can we say about a 95% confidence interval?

### The limits of a 95% confidence interval contain the true population parameter with 95% confidence

12