lecture_6_2 - Introduction to inference Tests of...

Info icon This preview shows pages 1–6. Sign up to view the full content.

    Introduction to inference   Tests of significance IPS chapter 6.2 © 2006 W.H. Freeman and Company
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Objectives (IPS chapter 6.2) Tests of significance Null and alternative hypotheses One-sided and two-sided tests The P -value Tests for a population mean The significance level α Confidence intervals to test hypotheses
Image of page 2
We have seen that the properties of the sampling distribution of x bar help us estimate a range of likely values for population mean μ . We can also rely on the properties of the sample distribution to test hypotheses. Example: You are in charge of quality control in your food company. You sample randomly four packs of cherry tomatoes, each labeled 1/2 lb. (227 g). The average weight from your four boxes is 222 g. Obviously, we cannot expect boxes filled with whole tomatoes to all weigh exactly half a pound. Thus, Is the somewhat smaller weight simply due to chance variation? Is it evidence that the calibrating machine that sorts cherry tomatoes into packs needs revision?
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Null and alternative hypotheses A test of statistical significance tests a specific hypothesis using sample data to decide on the validity of the hypothesis. In statistics, a hypothesis is an assumption or a theory about the characteristics of one or more variables in one or more populations. What you want to know: Does the calibrating machine that sorts cherry tomatoes into packs need revision? The same question reframed statistically: Is the population mean µ for the distribution of weights of cherry tomato packages equal to 227 g (i.e., half a pound)?
Image of page 4
The null hypothesis is a very specific statement about a parameter of the population(s). It is labeled H 0 . The alternative hypothesis is a more general statement about a parameter of the population(s) that is exclusive of the null hypothesis. It is labeled H a .
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern