BINOMIAL, POSSION AND STATISTICAL ESTIMATION IN BUSINESS FINANCE

BINOMIAL

To identify Binomial question;

1. It has small figures in the question
2. The figures should not up to 30, it is always 5, 4, 9 etc.
3. Probability of success and failure is always equal to one     
4. There are always two possible events i.e success or failure    

POISSON

To identify a Poisson question, it will be mentioned in the question

STATISTICAL ESTIMATION

Note: To identify statistical estimation question, you will be asked to test the confidence limit for the mean of a sample taken from unknown population i.e testing 95% = 1.96, 99%=2.58 and 90%=1.64.

Formula   S

X ± Z x √ n

HYPOTHESIS

A hypothesis is a statement about a population in which are then used to check the reasonableness of the statement.

Hypothesis testing: it is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement.

TYPES OF HYPOTHESIS

1.            Null (negative) Hypothesis

2.            Alternative (positive) hypothesis

Null hypothesis: it is a statement about the value of a population parameter.  It is represented by Ho

Alternative hypothesis:  It is a statement that is accepted if the sample data provide enough evidence that the null hypothesis is false.

Type 1 error:  Rejecting the null hypothesis (HO) when it is true

Type 2 error: accepting the null hypothesis (HO) when it is false

Question Five:

A  random sample of 400 householders is classified by two characteristics whether they own a colour television and by what type of householder.  (i.e – owner –occupier, private tenant, council tenant).  The results of this investigation are given below:

	ACTUAL FREQUENCIES
	Owner Occupier	Council tenant	Private tenant	Total
Colour TV	150	60	20	230
No Colour TV	45	68	57	170
Total	195	128	77	400

It is required to test at 5% level, the following hypotheses using chi-square:

Ho: the two classifications are independent (i.e no relation between classes of householders and colour TV ownership)

	Accept Ho where X2 < X2 Reject Ho where X2 > X2

 

H1:  The classifications are not independent.

Solution:

Step I.

H_o:     The two classifications are independent

H₁:     The classifications are not independent