Understanding Hypothesis Testing

The video introduces hypothesis testing, focusing on null and alternative hypotheses. It explains how to set up and interpret these hypotheses using examples, such as a real estate scenario. The video also covers decision-making using alpha and p-values, and draws an analogy between hypothesis testing and legal trials to illustrate the concept of proving an alternative hypothesis.

What is the primary goal of a hypothesis test?

• To calculate the mean of a sample

• To prove the null hypothesis

• To make a claim about a sample statistic

• To make a claim about a population parameter

Which symbol is used to denote the null hypothesis?

• H₀

• Hₐ

• p

• μ

In the context of hypothesis testing, what does the null hypothesis typically claim?

• The parameter is not equal to a claimed value

• The parameter is less than a certain value

• The parameter is greater than a certain value

• The parameter equals a claimed value

What is the alternative hypothesis trying to prove?

• The parameter is always smaller than the claimed value

• The parameter is always larger than the claimed value

• The parameter is different, smaller, or larger than the claimed value

• The parameter is equal to a claimed value

What type of test is it when the alternative hypothesis claims the parameter is either smaller or larger than the claimed value?

• Left-tailed test

• Right-tailed test

• Two-tailed test

• One-tailed test

In hypothesis testing, what is alpha (α)?

• The largest probability where we still believe the null hypothesis is true

• The probability of accepting the alternative hypothesis

• The smallest probability where we still believe the null hypothesis is true

• The probability of rejecting the null hypothesis

What does a small p-value indicate in hypothesis testing?

• The null hypothesis is true

• There is not enough evidence to reject the null hypothesis

• There is enough evidence to reject the null hypothesis

• The alternative hypothesis is false

If the p-value is larger than alpha, what decision should be made?

• Fail to reject the null hypothesis

• Accept the null hypothesis

• Accept the alternative hypothesis

• Reject the null hypothesis

In the analogy with legal trials, what does the null hypothesis represent?

• The person is innocent

• The person is guilty

• The person is not guilty

• The person is not equal to innocent

What can we never prove in hypothesis testing?

• The alternative hypothesis

• The null hypothesis is false

• The null hypothesis is true

• The p-value is smaller than alpha