Examples thinking about power in significance tests | AP Statistics | Khan Academy

TL;DR

Lowering the significance level increases the probability of making a type II error and decreases both the power of the test and the probability of making a type I error.

Transcript

• [Instructor] A significance test is going to be performed using a significance level of 5/100. Suppose that the null hypothesis is actually false. If the significance level was lowered to 1/100, which of the following would be true? So pause this video and see if you can answer it on your own. Okay, now let's do this together. Let's see, they're ... Read More

Key Insights

• ✊ Lowering the significance level decreases the power of the test and increases the probability of making a type II error.
• ✊ Increasing the sample size increases the power of the test.
• ✊ The true proportion of the population affects the power of the test.
• ✋ The further the true proportion is from the null hypothesis proportion, the higher the power of the test.
• ⚾ Hypothesis testing involves making decisions based on statistical significance levels.
• 🎚️ The significance level determines the threshold for accepting or rejecting the null hypothesis.
• 🅰️ Type I error refers to incorrectly rejecting the null hypothesis, and type II error refers to incorrectly failing to reject the null hypothesis.

Questions & Answers

Q: What happens to the power and probability of type II error when the significance level is lowered?

When the significance level is lowered, the power of the test decreases, and the probability of making a type II error increases. The opposite is true when the significance level is increased.

Q: How can Asha increase the power of her test?

Asha can increase the power of her test by selecting a larger sample size. The higher the sample size, the higher the power of the test.

Q: Does the true proportion of customers who would buy coffee affect the power of Asha's test?

Yes, the true proportion of customers who would buy coffee affects the power of Asha's test. The larger the difference between the true proportion and the null hypothesis proportion, the higher the power of the test.

Q: Can Asha control the true proportion of customers who would buy coffee to increase the power of her test?

No, Asha cannot control the true proportion of customers who would buy coffee. The true proportion is a population parameter and cannot be changed. She can only control the sample size to increase the power of her test.

Summary & Key Takeaways

• Lowering the significance level decreases the probability of making a type I error but increases the probability of making a type II error.

• Increasing the significance level increases the power of the test and the probability of not making a type II error.

• The sample size and the difference between the true proportion and the null hypothesis proportion affect the power of a test.