1. How many days until thanksgiving15 16 17 18 19 20

2. Upcoming in Class Quiz #6 this Wednesday HW #12 due Sunday
Exam #2 next Wednesday
Data Project Due by 5pm Thursday December 5th via or my department mailbox.

3. Chapter 20
Comparing Means

4. Comparing Two Means
Comparing two means is not very different from comparing two proportions.
This time the parameter of interest is the difference between the two means, 1 – 2.
Examples,
Height of black vs. height of whites
SAT scores of men vs SAT scores of women
Sugar content in Children’s cereal vs. Sugar content in Adult’s cereal

5. Two-Sample t-Interval
When the conditions are met, we are ready to find the confidence interval for the difference between means of two independent groups.
The confidence interval is
where the standard error of the difference of the means is
The critical value depends on the particular confidence level, C, that you specify and on the number of degrees of freedom, which we get from the sample sizes and a special formula.

6. Degrees of Freedom
The special formula for the degrees of freedom for our t critical value is a bear:
Because of this, we will let technology calculate degrees of freedom for us!

7. Route To School
A student takes two routes to class. Route A and Route B. Each day she randomly selects a route until she has walked each route 20 times.
Route A
Mean = 44
St.D.= 5
Route B
Mean =47
St. D. 4
Create a 95% confidence interval for the difference between the routes, and interpret it.

8. We are 95% confident the true difference between Route A and Route B is in the interval (0.09, 5.91). Which route is faster?
Route A
Route B
Our data shows no difference.

9. Testing the Difference Between Two Means
We test the hypothesis H0:1 – 2 = 0, where the hypothesized difference, 0, is almost always 0, using the statistic
The standard error is
When the conditions are met and the null hypothesis is true, this statistic can be closely modeled by a Student’s t-model with a number of degrees of freedom given by a special formula. We use that model to obtain a P-value.

10. Comparing different teaching methods

12. Is the new method better than the traditional method
Is the new method better than the traditional method? What is the appropriate hypothesis test?
Ho: μ1-μ2=0 Ha: μ1-μ2≠0
Ho: μ1-μ2=0 Ha: μ1-μ2>0
Ho: μ1-μ2=0 Ha: μ1-μ2<0

13. What is your conclusion based on the data?
Reject null. There is sufficient evidence that the new activities are better
Reject null. There is NOT sufficient evidence.
Fail to reject null. There is NOT sufficient evidence.
Fail to reject null. There is sufficient evidence that the new activities are better.

14. Find the P-value and compare your test resultsml
homework.com/statistics_tables/statistics_tables. html
Calculators
ocuments/ComparingMeans_001.pdf

15. Comparing sports leagues

16. Interpret your interval. We are 90% confident that…
the points scored per game in both leagues will fall in the interval
the amount by which the points scored in League 2 games exceed the points scored in League 1 games will fall in the interval
the amount by which the points scored in League 1 games exceed the points scored in League 2 games will fall in the interval

17. Does the interval suggest that the two leagues differ in average number of points scored per game?
No, because the interval does not contain zero
Yes, because the interval contains zero
No, because the interval contains zero
Yes, because the interval does not contain zero

18. Comparing TV Programs

19. What is the best conclusion? Test using a 95% CI.
Viewer’s memory are different, since we reject the null
Viewer’s memory are not different, since we reject the null
Viewer’s memory are different, since we do not reject the null
Viewer’s memory are not different, since we do not reject the null

20. Based on our data and CI, what could you say about the two programs.
Program A helps viewers remember commercials better than Program B.
Program B helps viewers remember commercials better than Program A.
There is no statistical difference between Program A and Program B. Viewers remember the commercials just the same.

21. Runner’s Problem
In a certain running event, preliminary heats are determined by random draw, so it would be expected that the abilities of runners in the various heats are about the same, on average.
There are 7 runners in each race, but due to an outlier in heat 2, we only have 6 observations for heat 2.

22. Runner’s Problem The statistics for heats 2 and 5 are below. Heat 2
Mean: seconds
SD: 0.635
N=6
Heat 5
Mean: seconds
SD: 0.961
N=7

23. Is there any evidence that the mean time to finish is different for the heats? What is the appropriate hypothesis test?
Ho: μ2-μ5=0 Ha: μ2-μ5≠0
Ho: μ2-μ5=0 Ha: μ2-μ5>0
Ho: μ2-μ5=0 Ha: μ2-μ5<0

24. Determine the test statistics
-0.198
0.435
-0.45
0.662

25. At the 0.05 significance level, test the hypothesis that the heats have different average times.
Do reject the null hypothesis. There is not sufficient evidence to support the claim that the mean running times in heat 2 and 5 are different.
Do reject the null hypothesis. There is sufficient evidence to support the claim that the mean running times in heat 2 and 5 are different.
Do not reject the null hypothesis. There is not sufficient evidence to support the claim that the mean running times in heat 2 and 5 are different.
Do not reject the null hypothesis. There is sufficient evidence to support the claim that the mean running times in heat 2 and 5 are different.

26. Upcoming in Class Quiz #6 this Wednesday HW #12 due Sunday
Exam #2 next Wednesday
Data Project Due by 5pm Thursday December 5th via or my department mailbox.