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Hypothesis Testing: Upper, Lower, and Two Tailed Tests

Hypothesis testing helps to evaluate the two mutually exclusive statements about the population. The statement is used to determine which one statement is the best supported by the sample data. The test of the hypothesis is based on the information and investigator belief about the parameters of a population. The testing process involves two competing hypotheses, the first one is the null hypothesis and the second one is the alternative hypothesis.


In the testing procedure, critical values indicate the acceptance and rejection region to make the decisions. For convenience, you can give an account to the critical values calculator that allows you to determine the critical values of any tail.


The procedure of Hypothesis:

The procedure of hypothesis testing is based on the ideas; firstly we need to state the hypothesis as null or alternative. Select the random samples on the basis of a population of interest and summary statistics. After that, we can determine whether the sample data is supportive of the null or alternative hypothesis or not. The procedure is summarized into four simple steps:

Step # 1: In the first step of statistical hypothesis testing, set up the hypothesis, and choose the significance level Alpha, which is denoted by α. The significance level is an important factor in the statistical hypothesis test. If you know the level of confidence, then simply give a try to the left and right critical values calculator to calculate the critical values of different distributions.

Step # 2: Select the appropriate test statistic for the distribution. The test statistic is said to be a single number, which is used to summarize the sampling information.  Z-statistic is the example of the test statistic, which is calculated by using the formula:


If the size of the sample is small, in this situation we use a t-statistic. In statistical testing, the critical value is a point on the distribution, which is compared with the test statistic to check whether the null hypothesis is accepted or rejected. By using the t & z critical value table, you can find the critical values of the distribution. For ease, you can also use the critical value calculator to the critical value of the t, z, f, and chi-square distribution.


Step # 3: Make a decision for your hypothesis. The decision rule is a type of statement that specifies factors that helps to reject the null hypothesis. The decision rule is based on specific values of the test statistics. The decision for a particular test depends on three factors and they’re alternative hypothesis, test statistic, and level of significance.

Hypothesis testing is important for any business to make a decision. A critical value plays a vital role in a business that specifies the acceptance and rejection region. Give an account to the left and right critical values calculator that calculates the critical values with its left and right tail.

Step # 4: computing the test statistic is also a very important part of the hypothesis testing. The test statistic is computed by substituting the observed sample data.

Step # 5: The last step of the test is making a conclusion about the hypothesis. The final decision is made by comparing the test statistic with the decision rule. In the final conclusion, the null hypothesis is rejected or accepted. The hypothesis is rejected if the hypothesis is true and the hypothesis is accepted when the sample data is not very unlikely.

The null hypothesis is represented by H0 and the alternative hypothesis is represented by HA. Critical values in the statistical tests are considered as the main factor and it helps to check the validity of the hypothesis. These values are complex to calculate. So, use the critical value formula or critical value calculator online that evaluates the critical values of one and two-tailed tests.

Types of Error:

There are two types of error used in hypothesis testing and they’re:

Type one Error:

The type one error occurs when the p-value of the distribution is less than your significant level, the result is statistically significant. However, the supposed effect might not exist in the population. Type one error is also called false positive.

Type two Error:

The researcher failed to reject the null hypothesis when it is actually false, in this situation type two error occurs. The probability of making the type two error is β that depends on the power of the statistic test. If the test has enough power, then the risk of committing the type two error can be reduced.

Ending Words:

A hypothesis is said to be the rule that helps to specify whether the claim about the population is accepted or rejected. It depends on the evidence generated by the sample data. The test examines the opposing hypothesis, the first one is the null hypothesis and the second one is the alternative hypothesis.

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