Statistical inference is the process of making judgment about a population based on sampling properties

An estimator is a statistical parameter that provides an estimation of a population parameter.

A point estimator is a single numerical estimate of a population parameter.

An interval estimator places the unknown population parameter between 2 limits

The level of precision is how sure you want to be about its values.

The credibility is how believable is the estimator.

An unbiased estimator is a statistics that has an expected value equal to the population parameter being estimated.

The sample mean,  is an unbiased estimator of the population mean,.

The sample variance,  is an unbiased estimator of the population variance, .

The sample proportion, P is an unbiased estimator of the population proportion,  .

An efficient estimator consider the reliability of the estimator in terms of its tendency to have a smaller standard error for the same sample size when compared each other.
 

Confidence Interval of the mean

An interval estimator for the mean is given by the following:

or 
 

The Maximum Likelihood Estimator is the most efficient estimator among all the unbiased ones.

A statistics is a consistent estimator of a parameter if its probability that it will be close to the parameter's true value approaches 1 with increasing sample size.

The maximum error of the estimate, E, with level of confidence ., is the error associated with the estimate of the population mean from the sample mean and is given by the formula below:

or 

Hypothesis Testing

Hypothesis testing is a procedure that examines two alternative positions in which a test is made to determine which of the positions may be true within certain level of confidence.
 

(1) The null hypothesis is a statement asserting no change or difference about a population parameter; it is denoted by the symbol H0.

(2) The alternate hypothesis is a statement that rejects the null hypothesis or a statement that might be true if the null hypothesis is not; it is denoted by the symbol Ha. The alternate hypothesis may contain the symbol, >, <,

 

The critical region is the values of the test statistics that provides evidence in favor of the alternate hypothesis. Therefore, a value in the critical region results in a decision to reject the null hypothesis.

Alpha or  is the level of significance of the hypothesis test and it is the probability that the test statistics will fall in the critical region or the red area if the null hypothesis is true.

 

A Type I error is an error in rejecting the null hypothesis when it is true, and this happens if the test statistics falls inside the critical region (red).

 

A Type II error is an error in accepting the null hypothesis when it is false, and this happens if the test statistics falls inside the acceptable region (blue) when it should be fallen in the red region or critical region.

Hypothesis Testing General Procedure

The p-value is the probability of getting the test statistics in support of the alternate hypothesis.