1. WARM UP ONE SAMPLE T-Interval
The average life of an Energy Saving Light bulb, in hours, is unknown. You investigate by randomly testing 9 bulbs and record their lives in the following hours:
Estimate the true mean life of these bulbs using 95% C.I.
ONE SAMPLE
T-Interval
SRS – Stated
Approximately Normal Distribution – SHOW Graph
We can be 95% confident that the true mean hours of bulb life is between and hours.

2. Chapter 23 T- Distribution:z
n = ∞
n = 30
n = 10
n = 2
The following are statements that compare t-distributions to the normal distribution.
I. t distributions are also mound shaped and symmetric.
II. t distributions have more spread than the normal distribution.
III. As degrees of freedom increase, the variance of t distributions becomes smaller.

3. Performing a Test for ONE SAMPLE T-TEST for Means:
1. Define your Parameter μ = true mean…
2. State the Hypothesis; H0: μ = #
Ha: μ < > or ≠ #
3. Name Test and Check assumptions
4. …PHANTOMS
ONE SAMPLE
t-TEST

4. Example1: (continued)
The manufacturer of an Energy Saving Light bulb claims that their bulbs have an average life of 3800 hours . To verify this you randomly test 9 bulbs and record their lives in the following hours:
Is there sufficient evidence at the 0.05 level to contradict the manufacturer’s claim?
ONE SAMPLE
t-TEST
μ = The true population mean hours of life for the energy saving
light bulbs.
SRS – Stated
Approximately Normal Distribution – SHOW Graph
H0: μ = 3800
Ha: μ ≠ 3800
Since the P-Value < 0.05 REJECT H0. There is evidence that the Bulbs do NOT last 3800 hours as claimed.

5. Example 2:
As a Quality Control Specialist for Doritos you feel that the filling machine has malfunctioned and that the average weight is now different. You know that the population mean weight follows a normal distribution with µ = 30g After opening and weighing 12 random bags you find a sample mean of grams with s = Is there evidence that the bags are underfilled?
μ = The true mean weight for a bag of Doritos.
ONE SAMPLE
t-TEST
1- SRS -stated
2- Appr. Norm - stated
Since the P-value of > 0.05, we fail to REJECT H0.
There is no evidence that the true mean weight of the Doritos Bags is less than 30g.

7. HW: Page 544: 25, 26, 31, 32
25 c.)

8. HW: Page 544: 25, 26, 31, 32, 36

9. HW: Page 544: 25, 26, 31, 32, 36

11. WARM – UP
In an attempt you estimate the average Baseball Player salary in 2011 you randomly sample 12 players: (All in Millions of Dollars)
$2.7, 2.9, 1.5, 2.2, 2.5, 2.0, 1.7, 2.9, 2.8, 2.6, 0.8, 2.7
1. Have all the assumptions been met for an Inference?
2. What would be the critical value of t for a 98% Conf. Int.?
3. What is the Standard Error for this sample?
4. What is the Margin of Error for a 98% Confidence Int.?
NO! SRS √’s out, but a histogram of the data reveals gross skewness. (Not Appr. Normal)
| invT (1 – .98)/2 , 11 | =
Standard Error = =
Margin of Error = =

12. In 2007 baseball players made on average $1. 8 million
In 2007 baseball players made on average $1.8 million. Using these randomly sample 12 players (All in Millions of Dollars) from 2011 , Is there evidence that salaries are now different?
$2.7, 2.9, 1.5, 2.2, 2.5, 2.0, 1.7, 2.9, 2.8, 2.6, 0.8, 2.7
μ = The true mean salary for a 2011 baseball player
ONE SAMPLE
t-TEST
H0: μ = 1.8
Ha: μ ≠ 1.8
Since the P-Value < 0.05 we REJECT H0 . There is evidence that Baseball salaries have changed. PWC
SRS – Stated
Approximately Normal Distribution – NO, the shown Graph depicts skewness