Hypothesis Testing About Samples.

**Highlight:**

- Hypothesis
- Region of acceptance and rejection
- Decision taking
- Steps In Hypothesis Testing

Hypothesis is a statement showing the relationship between two or more population parameter. it is referred to as an intelligent guess of a solution to a problem. there are two kinds of hypothesis;

- Research Hypothesis
- Statistical Hypothesis

Research hypothesis shows the relationship between variables in such a way that the relationship is not testable. for example, introducing a new teaching method and claiming the teaching method will be effective.

Statistical hypothesis focus on relationship between tow or more variables such that the variables are presented in a measurable form. statistical hypothesis can be tested because it is measurable.

These hypothesis is grouped into;

- Null hypothesis
- Alternate hypothesis

Null hypothesis is a hypothesis of no significance, no relationship, or no difference. it entails no relationship exist or no significant difference exist between two relationship. Hypothesis are tested in or at null form.

Alternate hypothesis is the hypothesis that the researcher always uphold when the null hypothesis is rejected. under this, we have; non directional/ two – tailed, which is a hypothesis that do not specify the direction of expected difference or change.

Directional/ one – tailed, which is a hypothesis that specify the direction of expected difference or change. At a point of testing a hypothesis, we are expected to take decision which is guided by the level of significance. This level of significance in social science is 5%( this shows the error tolerance).

The level of significance guides decision under two concepts;

- Critical/ table value
- Probability value

**Using Critical or Table Values**

in doing this, if the calculated value is greater than the critical or table value, then the null hypothesis will be rejected, otherwise we fail to reject the null hypothesis.

**Using the Probability Value**

This is called the ‘p-value’ and it is employed when we are running analysis in statistical software like the R, R- foundation, SPSS and so on. p-value value is the measure of strength in support or favor of the null hypothesis.

If the p-value(sig) is less than 0.05, the null hypothesis is rejected, implying there is a significant difference, similarly if the p-value is greater than 0.05, the null hypothesis will not be rejected, implying that there is no significant difference or there exist no significant difference.

in taking decision, a researcher can make one of the below decisions;

- reject a true null hypothesis
- accept a true null hypothesis
- reject a false null hypothesis
- accept false null hypothesis

Errors one can commit here includes,

**Type I Error: **This is when a researcher reject a true null hypothesis. it is related to level of significance.

**Type II Error: **This is when a researcher fails to reject a false null hypothesis. it is related to power of a test.

Power of a test is the ability of a test statistics to accurately reject a null hypothesis.

**Rejection and Acceptance Region**

Acceptance region implies the region of the normal distribution curve where those values which when the null hypothesis is true and the alternate hypothesis is false are likely to be found.

Rejection region is the region where those values of the test statistics are likely to be found if our null hypothesis is false. Critical value is the minimum value or statistical value that is required in order to reject a null hypothesis.

**Steps In Hypothesis Test**

- Formulate your null hypothesis
- state the criteria for rejection(level of significance)
- state the appropriate statistical tool to use. for example when t-test is used it means a researcher is interested in testing the difference between the two groups( male and female) and because the sample size is less than 30.
- compute the test statistics
- find the critical value
- decision taking
- draw inference and conclusion

Examples on testing hypothesis about samples(one and two samples) can be found here