In: Statistics and Probability
Rejecting and Failing to Reject the Null Hypothesis. What is the difference between failing to reject the null hypothesis and having evidence to support the alternative hypothesis?
Solution:-
In Hypothesis testing you have H0: The Null Hypothesis and Ha: The Alternate Hypothesis.
We direct the test (z test, t test, chi square and so on) and discover the estimation of the comparing test measurement.
We contrast this test measurement and the basic esteem found at some predetermined noteworthiness level(default is 95%).
In light of this examination, we either Reject H0, or Fail to dismiss H0
The examinations are as per the following
a) test measurement is > basic incentive for a privilege followed test, Reject H0
b) test measurement is < - basic incentive for a left followed test, Reject H0
c) test measurement is > basic esteem or test measurement is < - basic incentive for a two followed test, Reject H0
Essentially it implies in the event that your test staistic falls inside the noteworthiness level(critical esteem) district, at that point it has entered the dismissal locale and subsequently it must be rejected, i.e the H0 must be rejected and we have adequate proof to help the substitute theory. For eg test detail = 2.3 and basic esteem is 1.645(for \alpha = 0.05) for a privilege followed test. It implies your test detail has gone too far of the basic district (2.3>1.96) and has entered the dismissal locale. Also for a left followed test, your test detail is - 2.3 and basic esteem is - 1.645. again your test detail has entered the dismissal district (- 2.3 is < - 1.96)
Similary if the H0 falls outside the dismissal area, subsequently we don't dismiss H0, as it outside the basic locale. Eg your test detail is 1.2 for a 2 followed test at 95% centrality level(\alpha = 0.05). Consequently the basic qualities = +1.96 and - 1.96. Since your test detail is neither < - 1.96, nor > 1.96, that is ilies between the 2 basic qualities, it isn't in the dismissal area. It is protected, and subsequently, we neglect to dismiss H0.