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 0.0157 less than α = 0.05, REJECT H0. There is evidence that the true mean PHS SAT Math score is higher.

t-distributions vs. to the z (normal) distribution Chapter 23 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.

Computing Sample Sizes for Means Solve for n

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, $0.06. What sample size must be collected in order to have a margin of error of $0.02 with a 90% Confidence Interval.

Computing Sample Sizes for Means After opening and weighing several bags of Doritos you find a sample mean of 28.983 grams, s = 0.36. What sample size must be collected in order to have a margin of error of 0.01 grams with a 95% Confidence Interval.

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.

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 = 104000 Ha: μ < 104000 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.

Page 543: #13d(s=.6824), 14d(s=15), 21, 22, 23 s = 0.6824 s = 15

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 μ0 μa

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