Hypothesis notes ppt
Hypothesis
It is an assumption or proposition whose tenability ( capability of being justified ) is to be tested on the basis of its implications with empirical evidence and with the previous knowledge. It is the presumptive statement of a proposition or a reasonable guess, based upon the available evidences, which the researchers seeks to prove through his study
OR
In other words, an idea or explanation for something that is based on known facts but has not yet been proven.
Sources of Hypothesis:-
- Creativity and experience of the researcher helps in deriving and adequate hypothesis.
- Background information about the topic is necessary, a rich background of knowledge enables the researcher to locate the key association among the variables. Hence, literature review is a major step of research.
Characteristics of hypothesis:
Hypothesis must possess the following characteristics:
(i) Hypothesis should be clear and precise. If the hypothesis is not clear and precise, the inferences drawn on its basis cannot be taken as reliable.
(ii) Hypothesis should be capable of being tested. In a swamp of untestable hypotheses, many a time the research programmes have bogged down. Some prior study may be done by
researcher in order to make hypothesis a testable one. A hypothesis “is testable if other deductions can be made from it which, in turn, can be confirmed or disproved by observation.”1
(iii) Hypothesis should state relationship between variables, if it happens to be a relational hypothesis.
(iv) Hypothesis should be limited in scope and must be specific. A researcher must remember that narrower hypotheses are generally more testable and he should develop such hypotheses.
(v) Hypothesis should be stated as far as possible in most simple terms so that the same is easily understandable by all concerned. But one must remember that simplicity of hypothesis has nothing to do with its significance.
(vi) Hypothesis should be consistent with most known facts i.e., it must be consistent with a substantial body of established facts. In other words, it should be one which judges accept as being the most likely.
(vii) Hypothesis should be amenable to testing within a reasonable time. One should not use even an excellent hypothesis, if the same cannot be tested in reasonable time for one cannot spend a life-time collecting data to test it.
(viii) Hypothesis must explain the facts that gave rise to the need for explanation. This means that by using the hypothesis plus other known and accepted generalizations, one should be able to deduce the original problem condition. Thus hypothesis must actually explain what it claims to explain; it should have empirical reference.
Null Hypothesis:-
If we are to compare method A with method B about its superiority and if we proceed on the assumption that both methods are equally good, then this assumption is termed as the null hypothesis.. The null hypothesis is generally symbolized as Ho.
Alternative hypothesis:-
If we may think that the method A is superior or the method B is inferior, we are then stating what is termed as alternative hypothesis. The alternate hypothesis is generally symbolized as Ha.
Which test to use:-
If population size is greater than 30 or Standard deviation is known, then Z-Test will be performed.
If population size is less than 30 or Standard deviation is not known, then T-Test will be performed.
To check the compatibility of observed and expected frequency, then chi- square test will be performed.
For sample variance, F- Test will be used.
Steps in Hypothesis testing:-
- Set up Null and Alternate Hypothesis
- Set up Level of significance ( 5% or 1% )
- Decide which test to use
- Find out the value
- Find out the table value of test decision ( generally value for 5% is 1.96 and for 1% it is 2.58 )
- If computed value is less than table value, then accept the null hypothesis
- Or if computed value is greater than the table value, then reject the hypothesis.
Z – Test :-
In the z – test, the sample is assumed to be normally distributed. A z- score is calculated with population parameters such as ” population mean” and population standard deviation” and is used to validate a hypothesis that the sample drawn belongs to the same population.
Basically, it is used to find significant difference between population mean and sample mean
z = ( x – µ ) / (σ / √ n )
Where:-
x = Sample Mean
µ = Population Mean
σ / √ n = Population Standard Deviation.
OR
z = ( x̅ – µ0 ) / (σ / √ n )
Where:-
x̅ = Mean of Sample
µ0 = Mean of Population
σ = Standard deviation of population
n = no. of observations.
Example :- A sample of 400 male students is found to have a mean height 67.47 inches. Can it be reasonably regarded as a sample from a large population with mean height 67.39 inches and standard deviation 1.30 inches? Test at 5% level of significance.
Solution :-
Given data is
by applying null hypothesis H0 = 67 39
x̅ = 67.47
µ0 = 67.39
σ = 1.30
n = 400
Assuming the population to be normal, we can work out the test statistic z as under:
z = ( x̅ – µ0 ) / (σ / √ n )
Z = ( 67.47 – 67.39 ) / ( 1.30 / √ 400 ) = 0.08 / 0.065 = 1.231
The observed value of Z is 1.231 and the table value of Z is 1.96. The observed value of Z is less than table value of Z. Hence, Null hypothesis is accepted.
Case 2:-
If number of observations ( or number of units are larger ) but observed number is smaller from larger units, then the formula for calculating Z Test becomes
z = ( x̅ – µ0 ) / [ (σp / √ n ) x √ ( N – n ) / (N-1)]
Where :-
x̅ = Mean of Sample
µ0 = Mean of Population
σp = Standard deviation of population
N = Total no. of observations.
n = Small numbers of observation out of total numbers of observations
Example:-
Suppose we are interested in a population of 20 industrial units of the same size, all of which are experiencing excessive labour turnover problems. The past records show that the mean of the distribution of annual turnover is 320 employees, with a standard deviation of 75 employees. A sample of 5 of these industrial units is taken at random which gives a mean of annual turnover as 300 employees. Is the sample mean consistent with the population mean? Test at 5% level.
Solution :- Taking the null hypothesis that the population mean is 320 employees.
H0 = 320
Given Data:-
x̅ = 300 , µ0 = 320 , σp = 75 , n =5 , N = 20
Assuming the population is to be normal, we can work out the test statistics z as under
z = ( x̅ – µ0 ) / [ (σp / √ n ) x √ ( N – n ) / (N-1)]
Z = 300 – 320 / ( 75 / √ 5 ) x √ ( 20 -5 ) / (20 – 1)
= – 20 / ( 33.54 -0.888 ) = -0.67
The observed value of Z is -0.67 and the table value of Z is 1.96. The observed value of Z is less than table value of Z. Hence, Null hypothesis is accepted.