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 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
Generalized principal components analysis: The non-linear version of the principal components analysis in which the goal is to determine the non-linear coordinate system which is

Weighted least squares  is the method of estimation in which the estimates arise from minimizing the weighted sum of squares of the differences between response variable and its pr

The number of passengers arriving at an airport terminal average 1200 each hour. To process passengers (check in, take luggage, etc) take an average of 6 minutes each. There are

Incidental parameter problem is a problem which sometimes occurs when the number of parameters increases in the tandem with the number of observations. For instance, models for pa

The phrase first spoken by one of the witches in Macbeth. Now this is used to describe the exponential rise in the number of possible locations in the multivariate space as dimensi

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

The Null Hypothesis - H0: There is no first order autocorrelation The Alternative Hypothesis - H1: There is first order autocorrelation Durbin-Watson statistic = 1.98307

Model is the description of the supposed structure of a set of observations which can range from a fairly imprecise verbal account to, more commonly, a formalized mathematical exp

Intercropping experiments are the experiments including growing two or more crops at same time on the same patch of land. The crops are not required to be planted nor harvested at

I need help solving a problem using excel.