Question

This week, we consider how to conduct hypotheses test on one sample data. Discuss the concepts associated with these tests. Consider the following:

• The difference between a one tail and a two tailed test.
• The importance of stating the null and alternative hypotheses before conducting the test.
• The importance of a type one error (p) in conducting the test  
• The relationship between the p value and our decision to accept or reject the null hypothesis

Answer 1

Solution:

The difference between one tail and a two-tailed test.

Answer: A one-tailed test is one in which the alternative hypothesis has only one direction like < or >.

A two-tailed test is one in which the alternative hypothesis has two directions like

The importance of stating the null and alternative hypotheses before conducting the test.

Answer: The null and alternative hypotheses need to be set before conducting the test because while finding the p-value, we need to know whether the test is one-tailed or two-tailed and that will be determined if we have null and alternative hypotheses set up.

The importance of a type one error (p) in conducting the test  

Answer: The type one error also called the significance level is very important because we need it while finding the critical value and while making a decision using the p-value.

The relationship between the p-value and our decision to accept or reject the null hypothesis

Answer: The relationship between the p-value and our decision to accept or reject the null hypothesis is that:

If the p-value is less than the significance level, we, reject the null hypothesis.

If the p-value is more than the significance level, we, fail to reject the null hypothesis.