The parametric test called the t-test provides a statistical inference about the population by testing the sample that has been drawn from that population in such a manner that it represents the population as a whole.
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This parametric test, called the t-test, is based on the student’s t statistic. This statistic in the t-test is based upon the assumption that the samples are drawn from a normal population. It is assumed in the t-test that the mean of the normal population exists. The shape of the distribution of the t-test is a bell shaped appearance.
The t-test is applicable in those cases where the size of the sample is less than 30. If the sample size is more than 30 and the t-test is carried out on it, then the inference drawn would not be valid as the distribution of the t-test and the normal distribution would not be noticeable.
The parametric test called the t-test is called parametric because it consists of the parameters called the mean and the variance. There are chiefly three types of t-tests: one sample t-test, two independent sample t-tests, and paired sample t-test.
The first type of t-test is applicable in those cases where the testing of one sample is done. For example, if the researcher wants to test whether or not at least 65 % of the students of a particular school would pass their 10 standard board exam, he could use this test. To conduct this type of t-test, a suitable null and alternative hypothesis is created by the researcher. The next step for the researcher is to construct the test statistic. In this case, the test statistic would be t-test. An appropriate level of significance would be selected by the researcher to conduct the t-test of the null hypothesis. The appropriate level of significance for conducting t-test is generally 0.05(which is the same in other significant tests as well). The level of significance refers to the probability that there would be a false rejection of the null hypothesis on which the t-test would be carried out.
Now, the comparison of the tabulated value of the t-test and the calculated value of the t-test is done by the researcher. If the calculated value of the t-test is more than the tabulated value, then the null hypothesis is rejected at that level of significance. In the opposite case of t-test, the null hypothesis is accepted.
Similarly, in the case of the second type of t-test, two independent samples are tested by comparing their significances with the help of the t-test. So, all the steps carried out in the previous step would remain the same, except that the hypothesis assumed by the researcher in this case would be for two independent samples.
Similarly, in the case of the paired sample t-test, the paired type of categories are tested and all the steps would remain the same, except that the hypothesis on which the t-test would be conducted will now be formulated according to the third type of t-test.
