what is the difference between the critical value of z and the observed value of z?

Question

what is the difference between the critical value of z and the observed value of z

Answer 1

They are related. A critical value is a pre-determined value, say 1.5% whereas the observed value is what you calculate. You compare to decide if you want to accept or reject the null hypothesis.

Answer 2

From Wikipedia, the free encyclopedia

In statistical hypothesis testing, the p-value is the probability of obtaining a result at least as extreme as that obtained, assuming the truth of the null hypothesis that the finding was the result of chance alone. The fact that p-values are based on this assumption is crucial to their correct interpretation.


More technically, the p-value of an observed value tobserved of some random variable T used as a test statistic is the probability that, given that the null hypothesis is true, T will assume a value as or more unfavorable to the null hypothesis as the observed value tobserved. "More unfavorable to the null hypothesis" can in some cases mean greater than, in some cases less than, and in some cases further away from a specified center.

A critical value is used in significance testing. It is the value that a test statistic must exceed in order for the the null hypothesis to be rejected. For example, the critical value of t (with 12 degrees of freedom using the 0.05 significance level) is 2.18. This means that for the probability value to be less than or equal to 0.05, the absolute value of the t statistic must be 2.18 or greater. It should be noted that the all-or-none rejection of a null hypothesis is not recommended

Answer 3

In hypothesis testing the significant concentration is the acute area. If the try statistic falls in this area we reject the hypothesis H0, if not we do not reject H0. If it is composed of accurate one-tailed z-try, the acute area is on the right end, separated with techniques from the acute fee. The severe area is of the style {Z>z}. For a 5% try, P{Z>z}=0.05, and this z is the acute fee for this try element. look on the z line (horizontal), all factors to the right of z make up the acute area. This z is the tabulated z-fee. Now you calculate the try z-fee, a fee you get from the samples. If this calculated z is contained in the acute area reject H0, else do not reject H0, at 5%. For left tail you follow a similar way, and also for 2-tailed - save in ideas the style {|Z|>z} as severe area for 2-tailed. although, for the 5% one-tailed accurate, look at P{Z>z} the position z is the calculated try statistic. it is termed p-fee for this try. comparing both z values, we see that if p-fee is smaller than 5%, then z-calculated is more advantageous than z-tabulated; and z-cal is contained in the acute area. Draw the horizontal z line and mark both values, and have a glance at to ensure out the corresponding parts lower than the z-curve. the end results of the try is both: Reject H0,or do not reject H0 (Fail to reject H0). At stepped ahead element we suggested at length in this theory.