Idea behind hypothesis testing | Probability and Statistics | Khan Academy

TL;DR

The probability of obtaining accurate results from a test, with a 99% chance of accuracy per test, decreases significantly as the number of tests increases.

Transcript

• [Voiceover] Let's say that you have a cholesterol test, and you know, you somehow magically know that the probability that it is accurate, that it gives the correct results is 99, 99%. You have a 99 out of 100 chance that any time you apply this test, that it is going to be accurate. Now let's say that you, and you just magically know that, we're... Read More

Key Insights

• 🏆 The probability of obtaining accurate results decreases as the number of tests increases, even if each test has a high chance of accuracy.
• 🏆 It is more likely to get slightly fewer accurate results compared to getting all tests accurate, given a high individual test accuracy probability.
• 🏆 The probability of accurate results decreases significantly when the number of accurate tests decreases.
• 🏆 The observed outcome of a test can be used to assess the hypothesis and make decisions regarding the test's accuracy.
• 😫 Thresholds are often set to determine when to reject a hypothesis based on the probability of obtaining a certain outcome.
• 👶 The probability analysis can be applied in hypothesis testing to evaluate the accuracy of a new test.

Questions & Answers

Q: How likely is it to get accurate results when applying a test that has a 99% chance of accuracy 100 times?

The probability of getting accurate results for all 100 tests is approximately 36.6%. However, there is also a chance of getting fewer accurate results due to randomness.

Q: What is the probability of getting 99 accurate results out of 100 tests?

The probability of obtaining 99 accurate results out of 100 tests is approximately 37%. This outcome is slightly more likely than getting all 100 accurate results.

Q: How likely is it to get only 98 accurate results out of 100 tests?

The probability of getting 98 accurate results out of 100 tests is approximately 18.5%. This outcome is less likely compared to getting 99 or 100 accurate results.

Q: Can the probability of accurate results decrease even further?

Yes, the probability of accurate results decreases as the number of accurate tests decreases. For example, the probability of getting only 97 accurate results out of 100 tests is approximately 6%.

Summary & Key Takeaways

• The probability of getting accurate results from applying a test 100 times, with each test having a 99% chance of accuracy, is approximately 36.6%.

• As the number of accurate tests decreases, the probability of obtaining accurate results also decreases significantly.

• The probability of getting 99 accurate results out of 100 tests is approximately 37%, while the probability of getting 98 accurate results out of 100 tests is approximately 18.5%.