Critical Region

Critical Region

    • The testing of statistical hypothesis involves the choice of a region on the sampling distribution of statistic. If the statistic falls within this region, the null hypothesis is rejected: otherwise it is accepted. This region is called critical region.Let the null hypothesis be Ho: µ1 = µ2 and its alternative be H1: µ1 ≠ µ2. Suppose Ho is true. Based on sample data it may be observed that statistic a follows a normal distribution given by
    z
    • We know that 95% values of the statistic from repeated samples will fall in the range a±1.96 times SEa . This is represented by a diagram.
    Critical Region
    • The border line value ±1.96 is the critical value or tabular value of Z. The area beyond the critical values (shaded area) is known as critical region or region of rejection. The remaining area is known as region of acceptance.If the statistic falls in the critical region we reject the null hypothesis and, if it falls in the region of acceptance we accept the null hypothesis.In other words if the calculated value of a test statistic (Z, t, χ2 etc) is more than the critical value in magnitude it is said to be significant and we reject Ho and otherwise we accept Ho. The critical values for the t and are given in the form of readymade tables. Since the criticval values are given in the form of table it is commonly referred as table value. The table value depends on the level of significance and degrees of freedom.
      • Example: Z cal < Z tab -We accept the Ho and conclude that there is no significant difference between the means

Last modified: Sunday, 18 March 2012, 4:25 PM