Question

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

1. One-tailed vs two-tailed :

When we want to test whether a certain parameter's value is equal to a prespecified value, we use two-tailed test. But if we want to test if a certain parameter's value is greater than a prespecified value (or less than a prespecified value), we use one-tailed test. When rejection of null hypothesis is the final outcome of a test, then One tailed test gives more information than two-tailed test because in two-tailed test, alternate hypothesis is that parameter's value is not equal to prespecified value.

2. Importance of stating hypothesis:

It ensures that the procedure carried out for the conclusion purpose is directed towards our final objective. For. eg. once we state the hypothesis, we can decide what sample statistic to be used.

3. Type I error

Type I error is committed when we reject null hypothesis when actually null is TRUE. This error is the one that we want to avoid committing as much as possible because in the absence of any sample data, we fall back to the null hypothesis. It is similar to the statement in court of law : "In the absence of any evidence, the accused is innorcent." So fundamental requirement is that innocent should not be punished eventhough it may allow a criminal to go unpunished.

4. p-value

If p-value > significance level than we accept null hypothesis. If p-value<significance level, we reject null hypothesis.