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# Or Classical Decision Theory - Preliminaries Inferential...

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Preliminaries Inferential Statistics is concerned with estimating the true value of population parameters using sample statistics. The 2 types Of Estimates are:- Point Estimate Interval Estimate

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Point Estimate :- Single sample statistic that is used to estimate the true value of a population parameter. Interval Estimate :- This interval will have a specified confidence or probability of estimating the true value of the population parameter.
Level Of Confidence :- Is symbolised by (1-α)x 100%, where α is the proportion in the tails of the distribution that is outside the confidence interval. The proportion in the upper tail of the distribution is α/2 and the proportion in the lower tail is also α/2.

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Introduction Formulate Questions Structure observations and experiments to gather data (measurements) (Hypothesis) Formally test the hypothesis (Accepting or rejecting it) Reach tentative conclusions based on one or more formal tests Acceptance of a hypothesis doesn’t mean it is proven!! (Hypothesis is just supported by available knowledge)
A statistical hypothesis Null Hypothesis (H 0 ) :A hypothesis that we want to test . It is always expressed in the form of mathematical statement which includes the sign(≤ , = ,≥). Alternative Hypothesis ( H 1 ) : It is the counter claim made against the value of the particular population parameter. i.e. the alternative hypothesis states that specific population parameter value is not equal to the value stated in the null hypothesis

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In General statistical Hypothesis is a claim about an unknown population parameter value. One Tailed Test: If H 0 :µ ≤ µ 0 and H 1 :µ > µ 0 , then this is a right tailed test If H 0 :µ ≥ µ 0 and H 1 :µ < µ 0 , then this is a left tailed test. Two Tailed Test : If H 0 :µ = µ 0 and H 1 :µ ≠ µ0 , then in this case we have a two-tailed test.
Parametric hypothesis Suppose that the nature of the distribution of the random variable is known. A hypothesis consisting of a statement about some or all the parameters of the relevant distribution is called a parametric hypothesis Example: X~ N (µ, σ 2 ), Hypothesis (i) µ = 40 (ii) µ > 40 (iii) µ = 25, σ = 2

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Distributional hypothesis A hypothesis which states the nature of the distribution of a random variable is called a distributional hypothesis Example (i) X follows a normal distribution (ii) X follows a poisson distribution with mean λ = 8
Distribution-free nonparametric hypothesis A hypothesis which is neither distributional nor parametric.

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Or Classical Decision Theory - Preliminaries Inferential...

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