Statistical inference is that branch of statistics
Statistical inference is that branch of statistics which is concerned with using probability concept to deal with uncertainty in decision-making. The field of statistical inference has had a fruitful development since the latter half of the 19th century.
It refers to the process of selecting and using a sample statistic to draw inference about a population parameter based on a subset of it-the sample drawn from the population statistical inference treats tow different classes of problems:
1. Hypothesis testing, i.e., to test some hypothesis about parent population from which the sample is drawn.
2. Estimation, i.e., to use the statistics' obtained from the sample as estimate of the unknown
'Parameter' of the population from which the sample is. Drawn.
In both these cases the particular problem at hand is structured in such a way that inferences about relevant population values can be made from sample data.
Hypothesis testing
Hypothesis testing begins with an assumption, called a hypothesis that we make about a population parameter. A hypothesis is a supposition made as a basis for reasoning. According to prof. Morris Hamburg,
''a hypothesis in statistics is simple a quantitative statement about a population,'' palmer o Johnson has beautifully described hypothesis as ''islands in the uncharted seas of thought to be used as bases for consolidation and recuperation as we advance into the unknown''.
There can be several types of hypotheses. For example, a coin may be tosses 200 time and we may get heads 80 times and tails 120 times. We may now be interested in testing the hypothesis that the coin is unbiased. To take another example we may study the average weight of the 100 students of a particular college and may get the result as 110 ib. we may now be interested in testing average weight 115 ib. Similarly, we may be interested in testing the hypothesis that the variable in the population are uncorrelated.
Tests for number of successes:
The sampling distribution of the number of successes follows a binomial probability distribution. Hence its standard error is given by the formula:
S.E. of no. of successes = √npq
p = size of sample
q = (1 - p), i.e. probability of failure.
Illustration: a coin was tossed 400 times and the head turned up 216 times. Test the hypothesis that the coin is unbiased.
Solution: let us take the hypothesis that the coin is unbiased. On the basis of this hypothesis the probabiolity of getting head or tail would be equal, i.e. ½ hence in 400 throws of a coin we should expect 200 heads and 200 tails.
Observed number of heads = 216
Difference between observed number of heads and expected number of heads = 216 - 200 = 16
S.E. of no. of heads = √npq
n = 400, p =q = ½
S.E. = √400 × ½ × ½ = 10
Difference/S.E. = 16/10 = 1.6
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