Hypothesis Testing I:The One-Sample Case

Learning Objectives1.Explain the logic of hypothesis testing.2.Define and explain the conceptual elements involved in hypothesis testing, especially the null hypothesis, the sampling distribution, the alpha level, and the test statistic.3.Explain what it means to reject the null hypothesis or fail to reject the null hypothesis.4.Identify and cite examples of situations in which one-sample tests of significance are appropriate.5.Test the significance of single-sample means and proportions using the five-step model and correctly interpret the results.6.Explain the difference between one- and two-tailed tests and specify when each is appropriate.7.Define and explain Type I and Type II errors and relate each to the selection of an alpha level.

In This PresentationThe basic logic of hypothesis testingHypothesis testing for single sample means (ttest)The Five-Step ModelOther material covered:One- vs. Two- tailed testsType I vs. Type II errorTesting sample proportionsStudent’stdistribution

Significant DifferencesHypothesis testing is designed to detect significant differences: differences that did notoccur by random chance. Hypothesis testing is significance testing.This chapter focuses on the “one sample” case: we compare a random sample (from a large group) against a population.We compare a sample statistic to a population parameter to see if there is a significant difference.

ExampleThe education department at a university has been accused of “grade inflation” so education majors have much higher GPAs than students in general.GPAs of all education majors should be compared with the GPAs of all students.There are 1000s of education majors, far too many to interview. How can the dispute be investigated without interviewing all education majors?

ExampleThe average GPA for allstudents is 2.70. This value is a parameter.The box reports the statistical information for a random sample of education majors= 2.70=3.00s = 0.70N = 117X