WARM - UP Find the P-Value for t ≥ 3.05 with a sample of 19. Find the P-Value for | t | > 3.62 with 15 degrees of freedom. Find the P-Value for t ≤ -0.25 with a sample of 21 tcdf(3.05, E99, 18) = P-Val = 0.0034 2tcdf(3.62, E99, 15) = P-Val = 0.0025 tcdf(-E99, -0.25, 20) = P-Val = 0.4026 4. Find the critical value t* for a t statistic from a SRS of 18 observation with probability of 0.75 to the left. 5. Find the critical value t* for the construction of a 90% confidence interval with a SRS of 10 observation. invT(0.75, 17) = t = 0.6892 invT(0.05, 9) = t = 1.8331

Ch. 23: CONFIDENCE INTERVALS… The confidence level describes the uncertainty associated with a sampling method. A 95% confidence level means that we would expect 95% of the interval estimated from similar samples to include the population parameter. Confidence interval = Sample Statistic + Margin of error Categorical Data (z) = Proportions = Quantitative Data (t) = Means =

One – Sample t –Confidence Interval with t* = Critical Value found on: Table B or t* = | invT( (1 – C)/2, df ) | Degree of Freedom: df = n - 1 t* C% Level

Chapter 23 – Confidence Intervals for MEANS Conditions/Assumptions for the t-test/Interval: 1. SRS – must be Stated 2. Approximately Normal Distribution Checked by just ONE of the following: - Stated, or - Sample size, n ≥ 30 due to C.L.T. , or - Histogram/BoxPlot of the graphed data depicts symmetry. Interpreting a Confidence Interval We are C% confident (sure) that the true mean/average of {insert context here} is between x1 and x2.

P.A.N.I.C. Calculating a t – Confidence Interval: Identify the Parameter. Check the Assumptions/Conditions Name the interval = One Sample t – interval Calculate the Interval using: Write the Conclusion:

EXAMPLE #1 Gas Prices vary from city to city. A random sample of seven gas stations in Richardson, TX was collected. Estimate the population mean gas prices for Richardson in 2016 using: $2.07, 2.11, 2.05, 2.03, 2.05, 2.14, 1.96 Construct a 90% Confidence Interval. One Sample T-Interval “We can be 90% Confident that the true population mean for the Gas Prices in Richardson, TX will be between 2.016 and 2.101.” SRS – Stated Approximately Normal Distribution →

EXAMPLE #2 After opening a bag of Doritos and finding mostly air, you want to know if the population mean weight of the product actually equals the true (printed) mean weight per bag. After opening and weighing 12 random bags you find a sample mean of 28.983 grams, s = 0.36. (Weight Printed on Bag = 30.0 grams) Calculate the 95% Confidence Interval to estimate the true population mean. One Sample T-Interval We can be 95% confident that the true population mean weight for a bag of Doritos is between 28.754 and 29.212 grams. SRS –Stated √ Approximately Normal Distribution X → Unconfirmed PWC

HW: Page 543: 15-18