1. Lecture #24 Thursday, November 10, 2016 Textbook: 13.1 through 13.6
Statistics 200
Lecture #24 Thursday, November 10, 2016
Textbook: through 13.6
Objectives:
• Formulate null and alternative hypotheses involving population means (cont’d from lecture #23)
• Calculate T-statistics (for means) instead of Z-statistics (for proportions); determine correct degrees of freedom.
• Determine correct test procedure from context of problem.
• Relate a hypothesis test to a confidence interval’s coverage of the null value.

2. Hypothesis Tests: One Sample
Response
Variable
Categorical
Quantitative
Population
Parameter
Sample
Estimate
Inferential
Procedure
one-proportion Z
one-sample t
Test statistic
Chapter 12 13
P-value
Z table
T table with df = (n – 1) because σ is unknown

3. Hypothesis Tests: Two independent samples
Response
Variable
Categorical
Quantitative
Population
Parameter
Sample
Estimate
Inferential
Procedure
two-proportion Z
two-sample t
Test statistic
Chapter 12 13
P-value
Z table
T table with df = min{(n1–1), (n2–1)} because σ1 and σ2 are unknown

4. Which procedure should we use?
What kind of data do we have?
What kind of research question do we have?
Show something specific
Estimate a population parameter
Categorical
(binomial)
Quantitative
Pop. mean:
Hypothesis
Test
Confidence interval
Pop. proportion: p

5. Example:
Researchers at Penn State are interested in estimating the percentage of underage students who drink alcohol at least once a month. They should…
Construct a confidence interval for a population proportion
Perform a hypothesis test for a population proportion
Construct a confidence interval for a population mean
Perform a hypothesis test for a population mean

6. What is the average number of texts that a STAT 200 student receives on a weekday? To answer this question we should…
Construct a confidence interval for a population proportion
Perform a hypothesis test for a population proportion
Construct a confidence interval for a population mean
Perform a hypothesis test for a population mean

7. Do more than 30% of Penn State students binge drink at least once a month on average? To answer this question we should…
Construct a confidence interval for a population proportion
Perform a hypothesis test for a population proportion
Construct a confidence interval for a population mean
Perform a hypothesis test for a population mean

8. Relationship between tests and CIs
If a 2-sided 95% CI contains the null value…
…we fail to reject H0 at the 0.05 level.
If a 2-sided 95% CI does not contain the null value…
…we reject H0 at the 0.05 level.

9. If you understand today’s lecture…
13.23, 13.25, 13.63(a), 13.67(a and d), 13.71, 13.73, 13.99
Objectives:
• Formulate null and alternative hypotheses involving population means (cont’d from lecture #23)
• Calculate T-statistics (for means) instead of Z-statistics (for proportions); determine correct degrees of freedom.
• Determine correct test procedure from context of problem.
• Relate a hypothesis test to a confidence interval’s coverage of the null value.