## Hypothesis Testing

The goal of statistical hypothesis testing is to determine that a claim made for a particular parameter of the population can be supported or rejected on the basis of information obtained from the sample data.

This method involves using the theory you learned from previous topics. However, it justifies introduction of some
definitions here:

*Null and Alternative hypothesis:*When our goal is to support the claim made based on the information from the sample, the rejection of the claim is null hypothesis 'H_{0}', and the claim itself is alternative hypothesis H_{a}. Some literature uses H_{1}to denote alternative hypothesis.*Type I error:*Rejecting H_{0}when H_{0}is true.

α is the probability of making type I error.*Type II error:*Not rejecting H_{0}when H_{1}is true.*Test Statistic:*The random variable, such as 'z';, whose value we use to test the hypothesis.

**One important tip is to remember that when you formulate hypothesis, always include equality sign (≤, =,
or ≥) into the null hypothesis H _{0}. This means that your alternate hypothesis should include (<, ≠,
or >)sign.**

The hypothesis testing could be one sided or two sided. One sided tests involves rejecting H

_{0}, if the test statistic falls in the rejection region on one side of the normal distribution curve. Two sided test involves rejecting H

_{0}, if the test statistic falls in the rejection region on either side of the normal curve.

**Example:**

A company XYZ wants to claim that it's weightloss program helps reduce on an average 20 lbs in 4 weeks. In the footprint it will state that the claim is based on the results from 50 participants losing an average of 22 lbs in 4 weeks of study period with the standard deviation of 7 lbs. You job as a statistician is to verify this claim with a 95% confidence level and endorse the claim. Would you endorse it ??

*Solution:* First, we need to formulate the hypothesis. The claim is that X (weightlost)>20. Therefore, our
job is to test if the information from study supports the claim or not.

The rejection of the claim is null hypothesis. Therefore, H_{0}: µ = 20. Alternatively,
H_{a}:µ>20.

The sample size n = 50; α=0.05. The test statistic is Z and you want to check if it is greater than
Z_{0.05}. If that's the case then, you can support the claim and reject H_{0}.

From the normal distribution table, you found that Z_{0.05}=1.645. Using the formula above, you found that:

Z=(22-20)/(7/√50)=2.02. Since this Z > Z_{0.05}, you can reject H_{0} and endorse the claim!