1. Statistics 201 – Lecture 24

2. 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

3. 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:

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

5. 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

6. Example
Hypotheses:
Test Statistic
P-value
Conclusion

7. 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?

8. Example
Hypotheses:
Test Statistic
P-value
Conclusion