Two-tailed and one-tailed tests, Applied Statistics

If the test is two-tailed, H1:  μ ≠  μ0 then the test is called two-tailed test and in such a case the critical region lies in both the right and left tails of the sampling distribution of the test statistic, with total area equal to the level of significance as shown in diagram.

If the test is one-tailed either right-tailed or left-tailed), then the test is called a one-tailed test.

For example, to test whether the population mean   μ =  μ0  , we may have the Alternative Hypothesis H1 given by H1:  μ <  μ0 (Left-tailed) or H1:  μ > μ0  (Right-tailed). In this case, the test is a single-tailed or one-tailed test. In the right-tailed test where H1: 

μ >  μ0  , the critical region (or rejection region) z > zα lies entirely in the right tail of the sampling distribution of sample statistic with area equal to the level of significance a.  Similarly, in the left-tailed (H1:  μ < μ0  ), the critical region z < -  zα  lies entirely in the left tail of the sampling distribution of q with area equal to the level of significance α is shown.


2342_one tailed and two tailed test.png

The type of the tests to be applied depends on the nature of the Alternative Hypothesis H1. We apply one-tailed or two-tailed test accordingly as Alternate Hypothesis is one-tailed or two-tailed.

Critical values of z for both two-tailed and one-tailed tests at 10%, 5% and 1% level of significance are given below.

Critical Values of Z

Level of significance (a)




Critical values for Two-tailed tests

   850_one tailed and two tailed test1.png  1.64

   850_one tailed and two tailed test1.png  1.96

   850_one tailed and two tailed test1.png 2.58

Critical values for Left-tailed tests




Critical values for Right-tailed tests




For large samples (n > 30), the sampling distributions of many statistics are approximately normal distribution. In such cases, we can use the results of the table given above to formulate decision rules. We will focus primarily on large samples.

Posted Date: 9/15/2012 3:43:50 AM | Location : United States

Related Discussions:- Two-tailed and one-tailed tests, Assignment Help, Ask Question on Two-tailed and one-tailed tests, Get Answer, Expert's Help, Two-tailed and one-tailed tests Discussions

Write discussion on Two-tailed and one-tailed tests
Your posts are moderated
Related Questions
The file Midterm  Data.xls has a tab labeled "National Grid vs. Alcoa" which presents historical price data for two stocks.  Using the National Grid price as the X-value and the Al

Factor analysis (FA) explains variability among observed random variables in terms of fewer unobserved random variables called factors. The observed variables are expressed in

For the following claim, find the null and alternative hypotheses, test statistic, P-value, critical value and draw a conclusion. Assume that a simple random sample has been selec

In reduced rank regression (RRR), the dependent variables are first submitted to a PCA and the scores of the units are then used as dependent variables in a series of

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

TYPE I AND II Errors If a statistical hypothesis is tested, we may get the following four possible cases: The null hypothesis is true and it is accepted; The

discuss the mathematical test of adequacy of index number of formulae. prove algebraically that the laspeyre, paasche and fisher price index formulae satisfies this test. What is

As we stated above, we start factor analysis with principal component analysis, but we quickly diverge as we apply the a priori knowledge we brought to the problem. This knowled

what do we mean by critical region

A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - on a student's achievement in a mathemati