1. WARM - UP
The following represents snowfall amounts for 8 random winters in Detroit.
78” 130” 140” 120” 108” 120” 156” 101”
1. Fill in all four variables for the one sample 80% Confidence Interval formula:
2. What is the Margin of Error?
3. Have the Assumptions been met?
SRS – Stated
Approximately Normal Distribution
- Stated ?
- n> 30 = CLT ?
- Graph ?

2. CHAPTER 24 - COMPARING TWO MEANS The Two Sample t-Procedures
Comparing two means is the most common situation in statistical practice.
The Two Sample t-Procedures
The Parameters and Statistics:
μ1 = the true mean response in the first group or population .
μ2 = the true mean response in the second group or population.
and = the mean and standard deviation from each sample.
The Conditions:
- The set of data must have been collected randomly.
. - The Data of both groups must be Approximately Normal The two samples must be 100% independent of each other

3. Margin of Error

4. Critical Value t *= from the t-distribution Table
The Two Sample t – Confidence Interval
The Mechanics:
-t* t* C%
The Conservative
Degree of freedom:
df = n(smallest) – 1
Critical Value t *= from the t-distribution Table
“We can be C% confident that the true Difference in the means of the two populations is between a and b.”

5. Just Say NO to Pooled SRS – Both Stated
Is it a good idea to listen to music when studying for a test? In a study, 49 random student were assigned to listen to Rap or Mozart while attempting to memorize many objects pictured on a page. Find the 95% Confidence Interval for the mean difference in the number of objects each group could recall.
Rap
Mozart
Mean
10.72
11.81
S.Dev.
3.99
3.19 n 29 20
TWO Sample
t – Conf. Int.
SRS – Both Stated
Approximately Normal Distribution – NO because both sample sizes are less than 30 for [Central Limit Theorem] = FAILS
Independent
We can be 95% confident that the true difference in the mean number of objects students can recall listening to Rap(μ1) – Mozart(μ2) is between and
Just Say NO to Pooled

6. NO – Zero IS in the interval = Rap(μ1) – Mozart(μ2) = 0 → μ1 = μ2
Mean
10.72
11.81
S.Dev.
3.99
3.19 n 29 20
TWO Sample
t – Conf. Int.
We can be 95% confident that the true difference in the mean number of objects students can recall listening to Rap(μ1) – Mozart(μ2) is between and
Is there evidence that Mozart listeners recalled MORE objects then Rap listeners?
NO – Zero IS in the interval =
Rap(μ1) – Mozart(μ2) = → μ1 = μ2
IF Zero was NOT in the interval =
Rap(μ1) – Mozart(μ2) ≠ → μ1 ≠ μ2

7. HW - PAGE 566: 1, 2, 5, 6
Zero in interval = No significant difference.
Zero NOT in interval significant difference.

8. In Repeated sampling…

11. t – Confidence Interval
WARM - UP
I want to estimate the average amount of snow fall in Buffalo, NY. Use an SRS of the following 8 Buffalo winters to set up the EQUATION used to construct a 95% Confidence Interval. Do not find the actual interval.
78” 130” 140” 120” 108” 120” 156” 101”
One Sample
t – Confidence Interval

12. Warm – Up
“Freshman – 15” An average incoming freshman weighs 120lbs. Many people believe that students gain a significant amount of weight their freshman year of college. Is there enough evidence at the 5% level to support that there is an increase in weight? Use the weights of 6 randomly chosen students measured at the end of the 1st semester.
μ = The true mean Weight in pounds of students at the end of 1st Semester.
End 1
168 2
111 3
136 4
119 5
155 6
106
H0: μ = 120
Ha: μ > 120
ONE Sample
t – Test.
Since the P-Value > α = there is NO evidence to REJECT H0 . The belief that Freshman gain weight is not supported.
SRS – Stated
Approximately Normal Distribution – Graph
FAILED