Answer to Question #250504 in Statistics and Probability for smilynne

Question

Getting acquainted with the essential terms and concepts on testing the difference between two independent sample means using t-test, it is now time for you to explain thoroughly your answers to the following questions.

1. Explain the role of the following statistical terms in testing the difference of two independent samples using t-test.

a. Hypotheses (Null and Alternative Hypotheses)

b. Test of significance (One Tailed Test and Two Tailed Test)

c. Level of significance 

d. Critical region 

e. Critical value 

f. Test value 

Answer 1

a. Hypotheses: Hypotheses define relationship between two variables. Null hypothesis is used to assume no difference between two independent sample means. Alternative hypothesis is used as no relationship between two samples. Both hypotheses are used as basis to test relationship between two independent sample means.

b. Test of significance: It is referred as a formal procedure for comparing observed data with the well defined hypotheses. Under this, hypothesis test can be classified as either one-tailed test (right tail), two-tailed test or one-tailed test (left tail). Test of significance can be useful to determine whether relationship is statistically significant.

c. Level of significance: The level of significance is also also denoted as alpha or α that represents the probability of rejecting the null hypothesis when it it true. The most common significance level is α = 0.05 that is used to find critical value for t-test.

d. Critical region: It is also known as rejection region for which the null hypothesis is rejected. In hypothesis testing, critical region provides a set of values that can use to determine whether null hypothesis is true.

e. Critical value: The role of critical value is to determine whether it is greater than test statistic. For example, significance level is 0.05 and degrees of freedom is 19 then critical value is 2.093.

It is assumed that test statistic is 6.70. These values show the critical value is less than test statistic, so we can reject the null hypothesis.

f. Test value: The formula for the t-test is as follows:

$t=\frac{\tilde{x-\mu}}{\frac{s}{\sqrt{n}}}$

In t-test, the calculated value can be used to test the original hypotheses and determine statistical significance. The role of test value is to provide final conclusion based on its comparison with critical value.