1. Example: All vehicles made
Parameter – numerical
summary of the entire
population.
Example: population mean
fuel economy (MPG).
Population – all items
of interest.
Example: All vehicles made
In 2004.
Sample – a
few items from
the population.
Example: 36
vehicles.
Statistic – numerical
summary of the sample.
Example: sample mean
fuel economy (MPG).
Statistical thinking involves knowing the difference between a population and a sample and numerical summaries of populations (parameters) and numerical summaries of samples (statistics). Basically, statistics involves using sample information to make inferences about the population in general.

2. 95% Confidence Interval

3. 95% Confidence Interval

4. Interpretation – Part 1
The population mean fuel economy for cars and trucks made in 2004 could be any value between mpg and mpg.
This locates the center of the distribution.
Draw picture on the blackboard and tie it to the model.

5. Interpretation – Part 2
We are 95% confident that intervals based on random samples from the population with capture the actual population mean.
This is confidence in the process.

6. What is confidence?

8. Testing Hypotheses
Do cars and trucks made in 2004 meet the CAFE standard of 24 mpg, on average?

9. Step 1 - Hypotheses

10. Step 2 – Test Statistic
The denominator of the test statistic is called the standard error of the sample mean. This quantifies the amount of variation in the sample mean we would expect to see and provides a ruler against which we can measure the difference between the sample mean and the hypothesized population mean.

11. Step 3 - Decision
Reject the null hypothesis because the P-value is so small (smaller than 0.05).
There are two parts to the decision. First make a decision, then support that decision statistically.

12. Step 4 – Conclusion
Based on our sample data, cars and trucks in 2004 did not meet the CAFE standard or 24 mpg, on average.
Be sure to state the conclusion within the context of the problem. The difference between our sample mean of and the hypothesized population mean is statistically significant. That is, the difference cannot be explained by chance, random, error alone.

13. CI versus Testing
Note that our CI is consistent with our test of hypothesis.
CI indicates plausible values are between and mpg.
24 is not a plausible value!
Be careful with this. The confidence intervals we create will always be two-sided while test can be one- or two-sided. Sometimes there may appear to be a mismatch if one does a one-sided test and compares it to a two-sided confidence interval.

14. Statistical Inference
So far we have found plausible values for the population mean value and discovered that 24 is not the value of the population mean.

15. What about one vehicle?
Individual vehicles will have fuel economies different from the mean.
How can we quantify the variation we might expect to see in an individual vehicle?

16. 95% Prediction Interval

17. 95% Prediction Interval

18. Interpretation
I am 95% confident that a vehicle chosen at random from those made in 2004 will have a fuel economy between mpg and mpg