Take this statement as an example. A study found that the average urban Indian between the ages of 18- 24 checks their phone 74 times per day.

Here a Scientist expected a doubt about the average of 74 times.

Note that the scientist did not say it is high or low!

Hence, Our null hypothesis, H sub-zero Mu is equal to 74.

In this scenario, anything more than 1.74 standard deviations from the mean in either direction, would mean we could reject our null hypothesis. Hence this is a 2 tail test.

Hypothesis testing allows us to examine results from a sample of people, and make inferences about the total population.

Significance tests ask: Given the differences observed in our sample, what are the odds that there are no true differences in the population?

## Perform Hypothesis Testing

Hypothesis testing can be performed using these 4 steps:

1. Design a test statistic

2. Design a null hypothesis

3. Determine the p-value

4. Compare the p-value to the Significance Level

Take one detailed example of comparing the effectiveness of two groups of students one using Online Videos and other Textbooks for preparing for the exams. We have the data and we want to conclude which one is better.

The average score for the online video group was 2.1 questions higher than that of the textbook group

Let’s begin by setting up our two hypotheses. Our Null hypothesis will be that the online video and the textbook are equally effective. There is no difference in their ability to prepare the students for this exam. In other words, the difference between the population means of these two groups would be 0.

For this Hypothesis Test let’s use a 1% significance level, or, an Alpha value of 0.01.  This is because they really want to make sure the evidence is strong before they declare the online video as being a more effective learning tool.

This means that we reject that the online video and textbook were equally effective in preparing students, which means we feel there is strong support for the alternative hypothesis. It does seem that the online video is more effective than the textbook in preparing students for the exam.

Our two samples, though, revealed that the video group scored 2.1 questions higher than the textbook group.  Our Hypothesis Test has a 1% significance level. This means that if our outcome, 2.1, has less than a 1% chance of occurring we will reject the Null hypothesis.

This means that if our outcome, 2.1, has less than a 1% chance of occurring we will reject the Null hypothesis

to make sure the evidence is strong before they declare the online video as being a more effective learning tool, we need a z score that is associated with 0.99. On a z distribution chart, we find that that z score would be 2.33. So if our outcome of 2.1 is more than 2.33 Standard deviations from 0, then we will reject our Null hypothesis.

After doing the calculation, the z score is 4.54. The threshold to reject the Null hypothesis was that – 2.10 would be more than 2.33 Standard deviations from the center of our distribution, 0. Well, as we just saw, we are far beyond 2.33 Standard deviations from the mean. We are 4.54 Standard deviations from the mean. This puts us in the zone where we can reject our Null hypothesis. This means that we reject that the online video and textbook were equally effective in preparing students.

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