What is statistical inference, Advanced Statistics

What is statistical inference?

 Statistical inference can be defined as the  method of drawing conclusions from data which are subject to random variations. This is based on the mathematical laws of probability. Probability is the branch of statistics, where we make inferences from a finite set of observations to an infinite set of new observations. The finite set of observations is called as Samples and the infinite set is called as populations. Suppose let us consider tossing a few coins. Here the total number of outcomes i.e., getting the heads and tails are called as the sample space. The new observation that is getting particularly heads or tails is the population.

Solutions to statistical inference:

There are two kinds of statistical inferences. One is the estimation, where we use the sample and sample variables to predict the population variables. The second is the hypothesis testing. Here we use the samples and sample variables to test the population and the population variables.

Estimation:

 Estimation can be divided into two types. One is point estimation and the other is interval estimation.  In the point estimation we use the sample variable to estimate the parameter ?, whereas in the interval estimation we use the samples variable to construct an interval which is equated to p where p is the confidence level adopted.

The most common method adopted for point estimation is the maximum likelihood estimation (MLE) which consists of choosing the estimate that maximizes the probability of the statistical material. MLE is the best solution if the statistical material is large. Special cases of MLE are the sample mean dented as E(X) and the relative frequency denoted by P(X=x).

Illustrations  of MLE:

A game is played with a single fair die. A player wins Rs.20 if a 2 turns up and Rs.40 if a 4 turns up, and he losses if a 6 turns up. While he neither wins nor loses if any other face turns up. Find the expected sum of money he can win.

Let X be the random variable denoting the amount he can win. The possible values are 20,40,-30,0

P[X=20] = P(getting 2) = 1/6

P[x=40] = P( getting 4 = )1/6

P[X = -30] = P(getting 6] = 1/6

The remaining probability is ½.

Hence the mean is E(X) = 20(1/6) + 40(1/6) + (-30)(1/6) +0(1/2) = 5.

Hence the expected sum of money he can win is Rs.5

Hypothetical Testing:

A statistical hypothesis is a statement of the numerical value of the population parameter.

The steps involved in solving a statistical hypothesis is

1.       State the null hypothesis Ho

2.       State the alternative hypothesis Ha

3.       Specify the level  of significance α

4.       Determine the critical regions and the appropriate test statistic.

5.       Compute the equivalent test statistic of the observed value of the parameter.

6.       Take the decision either to reject Ho or accept Ho.

Posted Date: 7/21/2012 9:16:51 AM | Location : United States







Related Discussions:- What is statistical inference, Assignment Help, Ask Question on What is statistical inference, Get Answer, Expert's Help, What is statistical inference Discussions

Write discussion on What is statistical inference
Your posts are moderated
Related Questions
Models which make use of the smoothing techniques such as locally weighted regression to identify and represent the possible non-linear relationships between the explanatory and th

sales per day for a product are as follows: x= 10, 11, 12, 13 (p)= 0.2, 0.4, 0.3, 0.1 obtain mean and variance of daily sale. if the profit is described by the following equation p

Obuchowski and Rockette method  is an alternative to the Dorfman-Berbaum-Metz technique for analyzing multiple reader receiver operating curve data. Instead of the modelling the ja

Profile plots  is a technique of representing the multivariate data graphically. Each of the observation is represented by a diagram comprising of a sequence of equispaced vertical

1. You are interested in investigating if being above or below the median income (medloinc) impacts ACT means (act94) for schools. Complete the necessary steps to examine univariat

It is the art of attempting to exchange something quite small and certain, for something which are large and uncertain. Gambling is big business; in the US, for instance, it is at

Oracle property is a name given to techniques for estimating the regression parameters in the models fitted to high-dimensional data which have the property that they can correctl

Bayesian confidence interval : An interval of the posterior distribution which is so that the density of it at any point inside the interval is greater than that of the density at

Technically the multivariate analogue of the quasi-likelihood with the same feature that it leads to consistent inferences about the mean responses without needing specific supposi

The Null Hypothesis - H0: β 1 = 0 i.e. there is homoscedasticity errors and no heteroscedasticity exists The Alternative Hypothesis - H1: β 1 ≠ 0 i.e. there is no homoscedasti