Hypothesis Testing and Errors

The video covers AP Statistics Chapter 9, focusing on null and alternative hypotheses, Type 1 and Type 2 errors, and hypothesis testing. It uses examples like courtroom analogies and app profitability to explain concepts. The video also discusses calculating test statistics, p-values, and when to use different statistical tests, including z-tests and t-tests. A sleep study example is used to demonstrate a significance test.

What is the null hypothesis typically set up as in hypothesis testing?

• The parameter is equal to a certain value.

• The parameter is less than a certain value.

• The parameter is greater than a certain value.

• The parameter is not equal to a certain value.

When do you reject a null hypothesis?

• When the p-value is greater than the significance level.

• When the p-value is less than the significance level.

• When the p-value is equal to the significance level.

• When the p-value is not equal to the significance level.

In a court of law analogy, what does a Type 1 error represent?

• Finding a guilty person guilty.

• Finding an innocent person guilty.

• Finding an innocent person innocent.

• Finding a guilty person innocent.

How is the probability of a Type 1 error calculated in the lie detector test example?

• By dividing the number of false positives by the total number of tests.

• By dividing the number of true positives by the total number of tests.

• By dividing the number of false negatives by the total number of tests.

• By dividing the number of true negatives by the total number of tests.

What is the first step in calculating a test statistic for a survey?

• Find the t-value.

• Find the z-value.

• Find the p-hat value.

• Find the standard deviation of the sample.

How do you find the p-value for a test with a given z-value?

• Add the area to the left of the z-value to 1.

• Look at the area to the left of the z-value in Table A.

• Subtract the area to the left of the z-value from 1.

• Look at the area to the right of the z-value in Table A.

What effect does increasing the sample size have on the power of a test?

• It makes the power equal to the significance level.

• It has no effect on the power.

• It increases the power.

• It decreases the power.

In the app profitability case study, what would a Type 1 error imply?

• More than 30% of customers would buy the app when actually fewer would.

• Fewer than 30% of customers would buy the app when actually more would.

• Exactly 30% of customers would buy the app.

• The app would not be profitable.

When is the t-test considered robust?

• When the sample size is less than 30.

• When the sample size is greater than or equal to 30.

• When the data is strongly skewed.

• When there are outliers in the data.

Which test should be used when the population standard deviation is unknown?

• Paired t-test

• One-sample t-test

• One-sample z-test

• One-sample z interval