Hypothesis Testing (Critical Value Approach)


In order to make the decisions about the population whether to support or reject the null hypothesis. The decision is based on test statistics, there are two approaches used to make decisions in hypothesis testing. If the test statistic of the statistical test is more extreme than the critical value, then in the favor of an alternate hypothesis the null hypothesis is rejected. For ease, you can use the online critical values calculator that helps to find the critical values of z, t, chi-square, and f distribution.

Here, we are going to describe the four important steps involved in the critical value approach to conduct the test of the hypothesis is:

Step # 1: Define the hypothesis:

State the hypothesis as a null hypothesis or as an alternate hypothesis.

Step # 2: Set the criteria:

By using the sample data set, assume the null hypothesis to be true, and calculate the test statistic value. We use the t critical value test, to conduct the hypothesis test for the population mean and the mean is expressed as μ. Here, the t-statistic follows the t-distribution with n – 1 degree of freedom.

Step # 3: Test statistic:

Calculate the t critical value by finding the value of the known distribution of the test statistic and it is the probability of making the type 1 error. The type one error is denoted by a greek letter alpha (𝝰) and it is known as the level of significance of the test.

Step # 4: Drawing conclusions:

Compare the test statistic by the critical value of the distribution. If the test statistic is extreme in the direction of the alternative hypothesis then we reject the null hypothesis to favor the alternate hypothesis. On the other side, we don’t reject the hypothesis, if the test is less extreme than the critical value.

Right tailed:

To conduct the right-tailed test H0, the critical value will be μ = 3 VS HA is μ> 3. This is the t critical value, which is denoted by t α, n – 1, and the probability on its right side is Alpha (α). The probability can be shown by using the t critical value table. That is why we reject the null hypothesis in the favour of alternative hypotheses. You need not worry about how to find the critical value of the distribution. Simply use an online t critical value that helps to find the t value at one click.

Left-Tailed:

To conduct the left tailed test, the critical value is H0: μ = 3 VS HA: μ < 3. It is the critical value of the distribution, which is denoted by -t (α, n - 1). So, the probability to the left of it is Alpha, which is denoted by α. You can find the values by using the statistical table for example t & z critical value table or you can simply use an online critical value calculator that allows you to find critical values of t & z. We reject the null hypothesis in the favour of the alternative hypothesis.

Two-tailed:

There are two critical values for the two-tailed test H0: μ = 3 VS HA: μ ≠ 3. One of the critical values of the left tailed test is denoted by t(α/2, n – 1) and the second one for the right-tailed is denoted by t(α/2, n – 1). The probability to the left of the distribution is α/2 because of t-value -t(α/2, n – 1) and the other t-value is t(α/2, n – 1) and its probability to the right side is α/2. If the test statistic is less than or greater than the critical value, then we reject the null hypothesis H0: μ = 3 to favor the alternative hypothesis HA: μ ≠ 3. You can find the critical values by using the statistical tables and you can also use the t critical value calculator that measures the chi-square, t, z, and f values.

End-Words:

Hypothesis testing is a process that is generally used to check the validity of the claim or idea with the help of a certain confidence level. In statistical testing, the critical values of a statistical test are said to be the boundaries of the acceptance region of the test. The acceptance region has a set of values of the test statistic and on this base, the null hypothesis is rejected. There can be one or more than one critical value and it depends on the acceptance region. So, you can simply use an online critical value calculator that helps to determine the critical values of chi-square, t, z, and f distribution according to the significance level and degree of freedom.




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