Two-tailed and one-tailed tests, Applied Statistics

Assignment Help:

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.


Related Discussions:- Two-tailed and one-tailed tests

Population variance, Examining the Population Variance Business decisio...

Examining the Population Variance Business decision making does not limit itself to setting up the hypothesis to test for the equality of more than two means or proportions sim

Descriptive Statistics, To determine the proportion of people in your town ...

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

Small sample test for mean, If the sample size is less than 30, then we nee...

If the sample size is less than 30, then we need to make the assumption that X (the volume of liquid in any cup) is normally distributed. This forces    (the mean volume in the sam

Predict higpa using a logistic regression, In this problem, we use the CSDA...

In this problem, we use the CSDATA data set, which is available in 'CSDATA.txt'. We do ne an indicator variable, say HIGPA, to be 1 if the GPA is 3.0 or better and 0 other- wise. S

Find the conditional distribution of turning diameter, 1. Assume the random...

1. Assume the random vector (Trunk Space, Length, Turning diameter) of Japanese car is normally distributed and the unbiased estimators for its mean and variance are the truth. For

Evaluate standard deviation, Consider an MBA program as a processing networ...

Consider an MBA program as a processing network where the flow unit consists of a student in the program.  Suppose the organizations that hire and promote MBAs are considered to be

Stratified sampling, Stratified Sampling Stratified Sampling is ...

Stratified Sampling Stratified Sampling is generally used when the population is heterogeneous. In this case, the population is first subdivided into several parts (or s

Break-even analysis, a. How can break-even analysis be used in selecting a ...

a. How can break-even analysis be used in selecting a new plant site? b. What are potential advantages and disadvantage of locating a production facility in foreign country i

PERCENTAGES, CALCULATE THE PERCENTAGE OF REFUNDS EXPECTED TO EXCEED $1000 U...

CALCULATE THE PERCENTAGE OF REFUNDS EXPECTED TO EXCEED $1000 UNDER THE CURRENT WITHHOLDING GUIDELINES

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd