Statistics 201 – Lecture 24

Back to Significance Testing… Four Basic Steps: State hypothesis (in terms of pop. parameter) Calculate test statistics Find p-value (WILL NOT DO RECTION REGION) State Conclusion in terms of real problem at hand

Z-Test for a Population Mean (Known Standard Deviation) Data: random sample x1, x2, …, xn from a N(m, s) population Mean, m, is unknown Standard deviation, s, is known For testing the hypothesis H0: m=m0 Test Statistic:

Z-Test for a Population Mean (Known Standard Deviation) Computing p_value depends on the alternate hypothesis:

Example A student group claims that first year students at a university study 2.5 hours per weeknight A skeptical statistics professor claims that this is waaaay too high A random sample of 269 university students found an average study time of the students to be 137 minutes Suppose that the study times follow a normal distribution with standard deviation of 65 minutes Using these data test the prof’s hypothesis with a sig. level of 0.01

Example Hypotheses: Test Statistic P-value Conclusion

Example IQ test scores of 7th grade girls in the Midwest USA follow a normal distribution with standard deviation of 15 A random sample of 31 7th grade girls from a Midwest school district is taken and their IQ’s measured…giving a sample mean of 104 IQ’s in the broad population supposed to have an average of 100 Is there evidence at a 0.05 level that the mean in this district is different from the mean in the general population?

Example Hypotheses: Test Statistic P-value Conclusion