Sampling and Procedure of Hypothesis Testing – Geography – UGC NET – Notes

• Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.
• Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Such data may come from a larger population, or from a datagenerating process. The word “population” will be used for both of these cases in the following descriptions.

$$Z\;=\;\frac{\widehat{P\;}\;-\;P}{\sqrt{\displaystyle\frac{pq}n}}$$

• Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data.
• The test provides evidence concerning the plausibility of the hypothesis, given the data.
• Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analyzed.

How Hypothesis Testing Works

• In hypothesis testing, an analyst tests a statistical sample, with the goal of providing evidence on the plausibility of the null hypothesis.
• Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analyzed. All analysts use a random population sample to test two different hypotheses: the null hypothesis and the alternative hypothesis.
• The null hypothesis is usually a hypothesis of equality between population parameters; e.g., a null hypothesis may state that the population mean return is equal to zero. The alternative hypothesis is effectively the opposite of a null hypothesis; e.g., the population mean return is not equal to zero. Thus, they are mutually exclusive, and only one can be true. However, one of the two hypotheses will always be true.

Four Steps of Hypothesis Testing

All hypotheses are tested using a four-step process:

• The first step is for the analyst to state the two hypotheses so that only one can be right.
• The next step is to formulate an analysis plan, which outlines how the data will be evaluated.
• The third step is to carry out the plan and physically analyze the sample data.
• The fourth and final step is to analyze the results and either reject the null hypothesis, or state that the null hypothesis is plausible, given the data.

Real-World Example of Hypothesis Testing

• If, for example, a person wants to test that a penny has exactly a 50% chance of landing on heads, the null hypothesis would be that 50% is correct, and the alternative hypothesis would be that 50% is not correct.
• Mathematically, the null hypothesis would be represented as Ho: P = 0.5. The alternative hypothesis would be denoted as “Ha” and be identical to the null hypothesis, except with the equal sign struck-through, meaning that it does not equal 50%.
• A random sample of 100 coin flips is taken, and the null hypothesis is then tested. If it is found that the 100 coin flips were distributed as 40 heads and 60 tails, the analyst would assume that a penny does not have a 50% chance of landing on heads and would reject the null hypothesis and accept the alternative hypothesis.
• If, on the other hand, there were 48 heads and 52 tails, then it is plausible that the coin could be fair and still produce such a result. In cases such as this where the null hypothesis is “accepted,” the analyst states that the difference between the expected results (50 heads and 50 tails) and the observed results (48 heads and 52 tails) is “explainable by chance alone.”

Steps of Hypothesis

There is a proper four-step method in performing a proper hypothesis test:

• Write the hypothesis
• Create an analysis plan
• Analyze the data
• Interpret the results

Let’s take a look. But first, let’s meet Sam. Sam has a hypothesis that he wants to test. Sam works as a researcher with the National Food Administration. He is the one that goes out and tests the food that we eat to make sure that it is safe. Let’s see how he follows the four-step method.

Step One: Hypothesis

• The first step is that of writing the hypothesis. You actually have two hypotheses to write. One is called the null hypothesis. This is the hypothesis based on chance. Think of this as the hypothesis that states how you would expect things to work without any external factors to change it. The other hypothesis is called the alternative hypothesis. This is the hypothesis that shows a change from the null hypothesis that is caused by something.
• In hypothesis testing, we just test to see if our data fits our alternative hypothesis or if it fits the null hypothesis. We don’t worry about what is causing our data to shift from the null hypothesis if it does. Keep in mind, when writing your null hypothesis and alternative hypothesis, they must be written in such a way so that if the null hypothesis is false, then the alternative hypothesis is true and vice versa.
• What does Sam do here? Sam’s null hypothesis is that all meat that is sold to supermarkets is less than 48 hours old. Sam’s alternative hypothesis is that all meat that is sold to supermarkets is more than 48 hours old. As you can see, if the null hypothesis is false, then the alternative hypothesis is true.

Step Two: Analysis Plan

• The second step is to create an analysis plan. This involves deciding how to read your results to know whether your null hypothesis is true or your alternative hypothesis is true. Usually, this involves analyzing just one single test statistic.
• There are two ways to read your results: P-value method and the region of acceptance method. The P-value is the probability of observing the desired statistic. If this P-value is less than the significance level, then the null hypothesis is not valid. The significance level is the probability of making the mistake of saying that the null hypothesis is not valid when it actually is true. The region of acceptance is a chosen range of values that results in the null hypothesis being stated as valid.
• For this step, Sam decides to analyze his data using the region of acceptance. The statistic that Sam decides to use is the number of hours the meat is at that is being sold to supermarkets. Sam goes to various meat providers and checks to see the age of the meat that is being sold.
• He then analyzes this statistic to see how many meat providers are shipping meat out under 48 hours. The region of acceptance is 99% or higher. This means that if 99% or more of the meat producers ships out their meat in time, then the null hypothesis is valid.

Step Three: Data Analysis

• The third step is that of analyzing the data. It is the putting step two into action. It is in this step that the data is analyzed and either a P-value is found, or the data’s region is found.
• It is in this step that Sam checks his data to see how many of his meat producers are shipping out their meats within 48 hours. Sam looks at his data and sees that 99.9% of the meat producers are shipping out their meats within 48 hours.

Step Four: Interpretation

• The fourth step involves interpreting the results. It is in this step that the data is compared to the region of acceptance or the significance level. If the P-value is less than the significance level, then the null hypothesis is not valid. If the data is within the region of acceptance, then the null hypothesis is valid.
• Sam looks at this data. His data shows that the data’s region is at 99.9%. He compares it to his acceptable 99%. Is 99.9% higher than 99% ? It is. This means that his data is within the region of acceptance. This tell is Sam that he can say that the null hypothesis is valid. Now, he has the data to prove his null hypothesis statement. This is what he wanted to happen. He wanted to be able to tell people that his meat producers are shipping out fresh meat that is less than 48 hours old.