## What is Hypothesis Testing?

A hypothesis is a specific statement regarding population parameters, and hypothesis testing determines whether a hypothesis is consistent with the sample data. Testing a hypothesis about a population parameter starts by specifying a null hypothesis and an alternative hypothesis. The null hypothesis is an assumption about the population parameter. The alternative hypothesis specifies the population parameter values (i.e., the critical values) where the null hypothesis should be rejected. These essential values are determined by:

- The distribution of the test statistic when the null hypothesis is true, and
- The size of the test, which reflects our aversion to rejecting a null hypothesis that is, in fact, true.

## Example

There are six parts to a hypothesis test:

- The null hypothesis defines a value for a parameter that is presumed to be true.
- The alternative hypothesis specifies the range of values below which the null hypothesis must be rejected.
- The test statistic has a known distribution when the null hypothesis is true.
- The test size reflects the willingness to make a mistake and incorrectly reject a true null hypothesis.
- The crucial value, which is a number that is compared to the test statistic to see if the null hypothesis should be rejected; and
- The decision rule uses the test statistic and critical value to determine if the null hypothesis should be rejected.

A regression model estimated using 46 observations has β=0.76 and Sb=0.33

Determine if the slope coefficient is statistically significantly different from zero at a 5% significance level. The critical t-value for a sample size of 46 and 5% l.o.s is 2.02.

$ t=\frac{\beta-\beta _{\beta } }{S_{b}} \frac{0.76-0}{0.33}=2.30 $

Critical t-value = 2.02

Because 2.30> 2.02, we reject the null hypothesis and conclude the alternative hypothesis (the slope coefficient is not equal to zero).

## Why is hypothesis testing important?

Using sample data, Hypothesis Testing could be used to understand and draw inferences about the population. A Hypothesis Test aids in determining which of the two mutually exclusive statements about the population is supported by sample data.