Hypothesis testing tests Essay

Hypothesis testing tests could be a test statistic got from the data is more than or less than a critical value. Depending on the relation to the critical value, you either reject or accept the null hypothesis. Control charts function in a similar way. The control limits are equivalent to critical values. If a point plots outside of the control limits, then you could reject the hypothesis that the process is in statistical control.
A statistical hypothesis is an expression of facts about the amount of the parameter of a probability distribution. For instance, suppose we think that the mean outside of the diameter of a pipe is 10.00 mm. This statement can be expressed as following
State of hypothesis
H_0 mu=10.00 null hypothesis( process in control)
H_1 mu10.00 alternative hypothesis (process out of control)
H_1 specifies value of the mean diameter which could be more than 10.00 mm or less than 10.00.
That is called a two-sided hypothesis.
Various one-sided alternative hypothesis could be appropriate that depends on the problem. Two kinds of errors may be committed when testing hypothesis. One is Type I error () which happens if the null hypothesis is rejected when it is not false. The second is Type II error () occurs if the null hypothesis is admissible when it is incorrect. The probabilities of these two types of errors are represented as
Sometimes it is more convenient to work with the power of a statistical test, where
Power = 1 = P(reject H0 |H0 is false)
Thus, the power is the chance of correctly rejecting H0. In quality control work is called the producer's risk, because it signifies the probability that a good probability will be rejected, or the probability that a process producing suitable amount of a specific quality characteristic will be rejected as performing unsatisfactorily. In addition, is sometimes called the consumer's risk, because it indicates the probability of accepting a lot of poor quality, or allowing a process that is operating in a poor manner relation to some quality characteristic to continue in operation.
The general procedure in hypothesis testing
Specify a value of the probability of type I error ().
Design a test procedure, then we get small value of the probability of type II error ().
That means directly the () risk can be chosen or controlled. The () risk is generally a function of sample size (n) and is controlled indirectly. The larger is the sample size(s) used in the test, the smaller is () risk.
= P(type I error) = P(reject H0|H0 is true = P(type II error) =P(fail to reject H0|H0 is false)
Statistical inference
*errors H_0 mu=mu_0 where mu_0 is cost
H_1 mumu_0 Hypothesis Study
Type Ireject H_(0 ) mumu_0 Actually H_(0 ) is true
Type IIfail to reject H_(0 ) H_(0 ) is false
= P(type I error) = P(reject H0|H0 is true = P(type II error) =P(fail to reject H0|H0 is false)