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Stat 350 Lab Session GSI: Yizao Wang Section 016 Mon 2pm30-4pm MH 444-D Section 043 Wed 2pm30-4pm MH 444-B Today’s Agenda • • • • In-lab review: Sampling Distributions Exams Returned Confidence Interval Review Module 5, Activity 2 CI for a Population Mean Sampling Distribution Review • Sample statistics are random variables, e.g., p-hat, X-bar • The probability distribution of the sample statistics is called its sampling distribution. • The sampling distribution will depend on the distribution of original parent population as well as the sample size. Sampling Distribution Review • If the parent population X ~ N(μ,σ) the sample mean X-bar ~ N(μ,σ/sqrt(n)) • (CLT) If the parent population X has arbitrary distribution with mean μ and s.d. σ, approximately, when n>30, the sample mean X_bar ~ N(μ,σ/sqrt(n)) Midterm Exam 1 Summary • Mean scores 63.0 lab 016 / 60.5 lab 043 (58.3 all labs) • How to get the letter grade: 1, divide the score by 75 2, find the percentage on the grading scale (available on Ctools) • Deadline for questions about grading: Friday, March 5th Confidence Interval Review • Basic structure for any confidence interval: Estimate ± multiplier × standard error • Example: we are 95% confident that the true parameter value lies inside the confidence interval [a, b]. • Dilemma between the accuracy (interval width) and the confidence level. Never 100% CI with very narrow interval. Module 5 Activity 2 • Attention.sav from Ctools • Questions on p29-p30 • P35 example exam questions The 95% CI is (17.04, 24.66). What are the essential ideas in the interpretation of the confidence interval? Choose all that apply... The numbers (17.04, 24.66) The idea of repeated sampling Reference a collection of CIs Range of reasonable estimates The words "population mean" Yes or No Can you say whether the population mean is in your interval that you just computed? Yes or No Is it correct to say there is a 95% probability that the interval you just computed contains the population mean? The 95% CI is (17.04, 24.66). What are the essential ideas in the interpretation of the confidence level? Choose all that apply... The numbers (17.04, 24.66) The idea of repeated sampling Reference a collection of CIs Range of reasonable estimates The words "population mean" A jar is supposed to contain 16oz of peanuts. 50 jars are randomly sampled from the production line to see if the filling machine is on target. 95% CI for popul. mean is (15.4,16.8). What is the value of the sample mean? A) B) C) D) 16 oz 16.1 oz Any number between 15.4 and 16.8 The value is not known A jar is supposed to contain 16oz of peanuts. 50 jars are randomly sampled from the production line to see if the filling machine is on target. 95% CI for popul. mean is (15.4,16.8). What is the value of the population mean? A) B) C) D) 16 oz 16.1 oz Any number between 15.4 and 16.8 The value is not known 95% CI for popul. mean ounces of peanuts in a jar is (15.4,16.8). Is 16oz a reasonable estimate for the population mean? A) Yes B) No C) Can’t tell Extra Credit Opportunity • Complete the CAOS assessment between February 18 and 22 (by NOON) and you will receive 2 additional points added to your first midterm score – This may be enough to move you up to the next letter grade • Look for the link on Ctools > Lab Info: – First CAOS Extra Credit (Feb 18-22)