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.

Figure 

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)

10%

5%

1%

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

-1.28

-1.64

-2.33

Critical values for Right-tailed tests

1.28

1.64

2.33

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
Large Sample Test for Mean A random sample of size n (n > 30) has a sample mean    . To test the hypothesis that the population mean μ has a specified value  μ 0  let us formu

Try different numbers of clusters in your program (K=2...15) and build a plot that shows the dependency between number K and value of RSS function on the last iteration. What is th

You will recall the function pnorm() from lectures. Using this, or otherwise, Dteremine the probability of a standard Gaussian random variable exceeding 1.3.  Using table(), or

There exists an unclassified data set with hidden data structures in it. The task in this assignment is to perform comprehensive Cluster Analysis in order to reveal the structures

the president of a certain firm concerned about the safety record of the firms employee sets aside $50 million a year for safety education. the firms accountant believes that more


To determine the proportion of people in your town who are smokers, it has been decided to poll people at one of the following local spots: (a) the pool hall; (b) the bowling alley

why we use dummy variable

solve problems

Schedule Schedule is also used for the collection of primary data. A schedule is a list of question. it is a device of obtaining answer to the questions in a form which is fill