1 Stat chapter notes by Elaine Jadacki is licensed under CC-BY 4.0Math 117 Z Chapter 7 Notes Hypothesis Testing:making a decision about a parameter(s) based on a statistic(s). Confidence Interval:estimating a parameter(s) based on a statistic(s). Basics of Hypothesis Testing To understand the process of a hypothesis tests, you need to first have an understanding of what a hypothesis is, which an educated guess about a parameter. Once you have the hypothesis, you collect data and use the data to make a determination to see if there is enough evidence to show that the hypothesis is true. However, in hypothesis testing you actually assume something else is true, and then you look at your data to see how likely it is to get an event that your data demonstrates with that assumption. If the event is very unusual, then you might think that your assumption is actually false. If you are able to say this assumption is false, then your hypothesis must be true. This is known as a proof by contradiction. You assume the opposite of your hypothesis is true and show that it can’t be true. If this happens, then your hypothesis must be true. All hypothesis tests go through the same process. Once you have the process down, then the concept is much easier. Let’s look at theexample #7.1.1 in the text on page 229. Definitions a.A null hypothesis 𝑯𝟎is a claim, historical value, or product specification that contains a statement of equality such as =, ≥, ≤ .b.The alternative hypothesis 𝑯𝑨is the complement of the null hypothesis. It is what you want to prove. This is what you want to accept is true when you reject the null hypothesis. *You will always assume the null hypothesis is true until there is significant statistical evidence that contradicts the 𝑯𝟎and supports the 𝑯𝑨. Practice Stating the null and alternative hypotheses a.A car dealership advertises that the mean time to change the oil in your car is 18 minutes. 𝑯?:𝑯𝒂:b.A manufacturer of batteries claims the mean life of a battery is 500 days. 𝑯?:𝑯𝒂:c.According to a recent survey 85% of college students own a smartphone. (Source: 21 Pearson Student Mobile Device Survey: College Students June 2015 𝑯?:𝑯𝒂:

2 Stat chapter notes by Elaine Jadacki is licensed under CC-BY 4.0Definitions