Understanding Significance Tests and Power

The video tutorial covers significance tests, focusing on the relationship between significance levels, type 1 and type 2 errors, and the power of a test. It explains how decreasing the significance level affects these factors. The tutorial also includes a practical example involving a car wash owner, Asha, who uses hypothesis testing to decide on purchasing a vending machine. The example illustrates how sample size and true population proportion impact the power of a test.

What is the primary purpose of a significance test?

• To calculate the sample size needed

• To assess the evidence against the null hypothesis

• To determine the probability of a Type 1 error

• To prove the null hypothesis is true

What happens to the probability of a Type 1 error when the significance level is decreased?

• It decreases

• It remains the same

• It becomes zero

• It increases

If the significance level is lowered, what happens to the power of the test?

• It remains unchanged

• It decreases

• It becomes zero

• It increases

Which choice correctly describes the relationship between Type 2 error probability and test power?

• Both increase together

• Both decrease together

• They are unrelated

• One increases while the other decreases

In the car wash example, what is Asha's null hypothesis?

• The proportion of coffee buyers is unknown

• Less than 30% of customers will buy coffee

• Exactly 30% of customers will buy coffee

• More than 30% of customers will buy coffee

What factor is under Asha's control to increase the power of her test?

• The true proportion of coffee buyers

• The price of coffee

• The sample size

• The significance level

How does increasing the sample size affect the power of a test?

• It decreases the power

• It has no effect on the power

• It increases the power

• It makes the power unpredictable

Why is a higher sample size preferred in hypothesis testing?

• It decreases the significance level

• It increases the power of the test

• It reduces the cost of the test

• It increases the probability of a Type 1 error

What is the relationship between the true proportion and the null hypothesis proportion for maximizing power?

• They are unrelated

• The true proportion should be further from the null hypothesis

• The true proportion should be closer to the null hypothesis

• They should be equal

In the context of the video, what does a high power indicate?

• A high probability of making a Type 1 error

• A low probability of making a Type 2 error

• A high significance level

• A low sample size