Answer to Question #278461 in Statistics and Probability for love

Question

Getting acquainted with the essential terms and concepts on testing the difference between two dependent sample means, 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 dependent samples.

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 :

Null hypothesis denoted by H_O ,it is a hypothesis that is subject to research, when the p-value of a data is less than the significance level of the test, the null hypothesis is rejected indicating the test result are significant ,however if the p-value of the data is higher than the significant value we fail to reject the null hypothesis. While an Alternative hypothesis provide the researchers with direction and clarification of the problem, it provide a chance of discovering new theories that can disprove an existing one that might not be supported by evidence.

b).Test of significance (one tailed and two tailed)

Test of significance for a one tailed test provide more power to detect an effect on one direction ,one tailed test will either be a right or left tailed test, in a right tailed test the mean of data is significantly greater than x while in a left tailed test the mean of the data is less than x. Two tailed test is for the test of hypothesis and null is written as H_o ;X=20 and H₁ is not equal to, this implies that it is testing the exact value or the difference.

c).Level of Significance:

The level of significance is the probability of rejecting the null hypothesis or failing to reject the null hypothesis ,one can choose what level of significance he/she wants to use such as 0.05 this implies that 5% risk of concluding that a difference exist when there is no difference.

d).Critical region

This region has a set of values for test statistics for which the null hypothesis is rejected, hence the critical region is the rejection region.

e).Critical value

The critical value of the test statistics which defines the upper and lower bounds of confidence interval ,they are usually read from the statistical tables with respect to the kind of test one was using such as t-values and z-score .

f).Test value

The test values are test statistics values that is calculated from sample data during a hypothesis test.