The p-value Method: Examples


Let’s revisit an example we looked at earlier.

Let’s say you work at a pharmaceutical company that manufactures an antipyretic drug in tablet form, with paracetamol as the active ingredient. An antipyretic drug reduces fever. The amount of paracetamol deemed safe by the drug regulatory authorities is 500 mg. If the value of paracetamol is too low, it will make the drug ineffective and become a quality issue for your company. On the other hand, a value that is too high would become a serious regulatory issue.

There are 10 identical manufacturing lines in the pharma plant, each of which produces approximately 10,000 tablets per hour.

Your task is to take a few samples, measure the amount of paracetamol in them, and test the hypothesis that the manufacturing process is running successfully, i.e., the paracetamol content is within regulation. You have the time and resources to take about 900 sample tablets and measure the paracetamol content in each.

Upon sampling 900 tablets, you get an average content of 510 mg with a standard deviation of 110. What does the test suggest if you set the significance level at 5%? Should you be happy with the manufacturing process, or should you ask the production team to alter the process? Is it a regulatory alarm or a quality issue?

Solve the following questions in order to find the answers to the questions stated above.

One thing you can notice here is that the standard deviation of the sample of 900 is given as 110 instead of the population standard deviation. In such a case, you can assume the population standard deviation to be the same as the sample standard deviation, which is 110 in this case.

Here’s another exercise set to consolidate your learning.

A nationwide survey claimed that the unemployment rate of a country is at least 8%. However, the government claimed that the survey was wrong and the unemployment rate is less than that. The government asked about 36 people, and the unemployment rate came out to be 7%. The population standard deviation is 3%.

Before we move on to the last topic of this session, let’s hear from Kalpana on how hypothesis testing can be very useful in making business decisions in the industry.

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