1. Warm - Up:
Are the SAT Math Scores for Pearce higher than other schools? To Test the population SAT Math average score of 510, you randomly select a sample of 9 PHS student scores:
510, 460, 560, 520, 570, 560, 660, 610, 620
Is there evidence that PHS is a better school.
ONE SAMPLE
t-TEST
μ = The true mean SAT Math score for PHS students.
1- SRS - Stated
2- Appr. Norm - Graph
Since the P-value of less than α = 0.05, REJECT H0. There is evidence that the true mean PHS SAT Math score is higher.

2. t-distributions vs. to the z (normal) distribution
Chapter T- Distribution:
t-distributions vs. to the z (normal) distribution
t - distributions are used for inferences dealing with samples with unknown population standard deviation (σ).
z - distributions are used for inferences dealing with the entire population with the population standard deviation known.

3. Computing Sample Sizes for Means
Solve for n

4. Computing Sample Sizes for Means
Gas Prices vary from city to city. A random sample of several gas stations in Richardson, TX was collected. The average calculated to be $2.059 with standard deviation, $ What sample size must be collected in order to have a margin of error of $0.02 with a 90% Confidence Interval.

5. Computing Sample Sizes for Means
After opening and weighing several bags of Doritos you find a sample mean of grams, s = What sample size must be collected in order to have a margin of error of grams with a 95% Confidence Interval.

6. Decision based on sample
STATISTICAL ERRORS (AGAIN)
Decision based on sample
Reject H0
Fail to Reject H0
H0 is True
H0 is False
Type I Error
POWER
Type II Error
Correct Decision
POWER = Probability of the test to correctly reject a false H0. Increasing the Sample Size, n, or α (sign. Level) increases the Power of a test by decreasing Type II error. Power = 1 – Type II.

7. List the Hypothesis and then Describe the Type I and Type II Error and the Consequences
1. In 2003 the Dept. of Commerce reported that the average American home cost $104,000. A recent slump in the US economy has greatly affected the housing market. You suspect that home prices have significantly decreased. If they have decreased you will buy a home.
H0: μ =
Ha: μ <
TYPE I ERROR = You feel that home prices have dropped, but in fact they remain the same. You buy a home and pay the high price.
TYPE II ERROR = You feel that home prices have remained the same, but in fact they have decreased. You don’t buy a home and lose out on bargain home prices.

8. Page 543: #13d(s=.6824), 14d(s=15), 21, 22, 23
s =
s = 15

10. Power – The Probability that a significance test will correctly reject a false H0.
Power = 1 – β (Type II Prob.)
Increasing sample sizes (n) will decrease Type II error (β) and consequently increase the Power of the test.
Increasing α = (Type I Prob.) will decrease β =(Type II Prob.).
Increasing α = (Type I Prob.) will increase the power. β α
μ μa

11. WARM-UP
You want to estimate how much money Texas teachers in the DFW area make. A random sampling of 32 teachers in this area reveals an average of $52,410 with s = $4580
1. Find the 95% Confidence interval for this estimate.
ONE SAMPLE
T-Interval
We can be 95% confident that the true mean salary for teachers teaching in the DFW area is between $50,759 and $54,061.
SRS – Stated
Approximately
Normal Distribution → n > 30 CLT