You will still reject the null hypothesis of no difference, if the class sample is either much higher or much lower than our population mean of 75.Īs distinguished from the two-tailed test, we canĪpply a directional - one sided i.e. If we consult the table of areas under the normal curve (table - 2), we find the acceptance region of 0.495 ( (one half of. Suppose you want to reduce the risk of committing a Type I error, reduce the size of the rejection region. Otherwise if it falls into area 0.475 corresponds to 1.96 S.E. You will reject the null hypothesis on the basis that the sample mean falls into the area beyond 1.96 S.E. 2.5% or 0.25 in the upper tail and 2.5% or 0.25 in the upper tail and 2.5% or 0.25 in the lower tail since your hypothesis gives only a difference and not a direction. Now this rejection region is divided between both the tails of the distribution ( see figure 1 ) i.e. Both tests have the rejection (or critical) region of 5% i.e. Now our pre-determined probability level is 95% i.e. The alternative (or research) hypothesis is :ħ5 while the null hypothesis is : H o : m The national mean score in this test was found to be 75. Thus in two-tailed test the rejection (critical) region is located in both the tails.įor example, suppose you suspect that a particular 6th grader’s performance on a test in Mathematics is not a true representative of the students who have appeared. A two-tailed test of hypothesis will reject the null hypothesis H o, if the sample statistic is significantly higher than or lower than the hypothesized population parameter. The test for such a hypothesis is non-directional or two-sided or two-tailed. That is, we did not want sample statistic ( say mean ) to be away from the population parameter (say mean) in either direction. In the previous tests the critical region lay along both the tails of the distributions. While testing a hypothesis, we often talk of two-tailed tests and one-tailed tests. Your browser does not support the IFRAME tag.
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