Normal Distribution

The most celebrated of the continuous distributions and plays an important role in statistical inference because of primarily two reasons

◦ It has properties which help generalize inferences by taking samples to the entire population

◦ The Normal Distribution comes closest to fitting the actual observed frequency distributions of many phenomena including human characteristics (Height, Weight etc) and physical processes (Rainfall) and other measured of interest to Managers

Characteristics

The curve is smooth and is bell shaped

It has a single peak and is unimodal

The mean lies at the centre and the curve is symmetric about the mean

Mean=Median=Mode and they all lie at the centre

The tails of the curve extend indefinitely in both directions from the centre and although they get closer and closer to the horizontal axis, they never quite touch it

Sampling methods

Use of lottery

Use of Random numbers

Systematic sampling/ quasi random sampling

Stratified Random sampling

Disproportionate stratified sampling

Cluster sampling

Multistage sampling

Area sampling

ANOVA

ANOVA will enable us to test for the significance of the differences among more than two sample means.

Situations where it can be used :

Analysis of variance is useful in such situations as comparing the mileage achieved by five different brands of gasoline , testing which of four different training methods produces the fastest learning record.

Assumptions

The samples are independently ( or randomly) drawn from the population

All the population from which samples have been drawn are normally distributed

The variances of all the population are equal.

Central Tendency

Central Tendency may be defined as the parameter in a series of statistical observation, which reflects a central value of the same series.

Major characteristics of an entire series of data reflected by a parameter called CENTRAL TENDENCY

Properties of a Measure of Central Tendency

It should be well defined.

It should be easy to compute

It should be easy to understand.

It should be based on all observations.

It should be capable of further mathematical treatment.

It should not be affected by extreme observations.

It should not be affected much by fluctuations of sampling.

Basic steps of hypothesis testing

• Formulating the hypothesis

• Calculating the std error of the mean

• Find the z value or t value

• Interpreting the probability- associated with this difference

• The decision maker’s role in formulating hypothesis

• Risk of rejection