Statistics 301: Estimation and Hypothesis Testing for Population Median and Mean, Study notes of Statistics

Download Statistics 301: Estimation and Hypothesis Testing for Population Median and Mean and more Study notes Statistics in PDF only on Docsity! STATISTICS 301 TA: Perla E. Reyes DISCUSSION 11 Pag. 1 Review 1. Estimation of Population Median • The Point Estimator for the population median is the sample median x̃. • Confidence Interval for the population median, – If n ≤ 20, the exact C.I. can be obtained from Table A.7 (page 656). – If n > 20 1. Find z according to the confidence level from Table A.3 (page 652). 2. Compute k′ = n+12 − z √ n 2 3. Round k′ down to the next integer to get k. 4. The approximate C.I. is [x(k), x(n+1−k)] 2. Estimation of Population Mean • The Point Estimator for the population mean is the sample mean x̄. • Confidence Interval for the population mean, Gosset’s confidence interval, 1. Compute the sample mean x̄ and sample standard deviation s. 2. Find t according to the confidence level and n − 1 degrees of freedom from Table A.6 (page 655). Remember when the number of degrees of freedom is greater than 30, go directly to the ∞ row of Table A.6. 3. The C.I. then is x̄± t s√ n • Hipotesis Testing for the population mean, Step 1. Null hypothesis: H0 : µ = µ0. There are 3 choices for the alternative hypothesis : ( > ): H1 : µ > µ0. ( < ): H1 : µ < µ0. ( 6= ): H1 : µ 6= µ0. Step 2. Test Statistic t = √ n(x̄− µ0) s Step 3,4. The p-value. ( > ): P= P (tn−1 ≥ t), which is the area under t-curve with n− 1 degrees of freedom to the right of t. ( < ): P= P (tn−1 ≤ t), which is the area under t-curve with n− 1 degrees of freedom to the right of −t. ( 6= ): P= 2P (tn−1 ≥ |t|), which is twice the area under t-curve with n− 1 degrees of freedom to the right of |t|. Practice Problems 1. Section 15.4 Extra Homework, problems 46, 47, 49 and 52. reyes@stat.wisc.edu. www.stat.wisc.edu/∼reyes/ B248MSC, MW 11:00-12:00