One-Sample Hypothesis Test: Confidence Intervals and p-values, Study notes of Statistics

Download One-Sample Hypothesis Test: Confidence Intervals and p-values and more Study notes Statistics in PDF only on Docsity! STAT 301 TA : Lisa Chung lchung@stat.wisc.edu DISCUSSION 10 (Apr. 4. 2004) REVIEW - One Sample Hypothesis Test Example 1. A sample of 40 sales receipts from a university book store has x̄= $ 121 and s =$ 10.2. Use these values to perform a test at level α = 0.05 of H0 : µ = 125 vs. HA : µ 6= 125 Example 2. In the lake population study, the concentration of lead in the upper sedimentary layer of a lake bottom is measured from 25 sediment samples of 1000 cubic centimeters each. x̄=0.38 and s= 0.06 respectively. a. Compute 99% confidence interval for the mean concentration of lead per 1000cm3 of sediment in the lake bottom. 2. Do the data provide strong evidence that the true mean concentration of lead is higher than 0.35? Example 3. According to the ETS, the random variable, X=SAT exam score, in the national high school population is normally distributed with mean µ = 500 points, and standard deviation σ = 100 points, i.e. X N(500, 100). High school administrators test the null hypothesis H0 : µ = 500 vs.H1 : µ > 500 . Using random sample of n=256 students per high school, the following data are collecdted. Calculate p-value of each sample, and use it to arrive at a decision about the null hypothesis for that particular high school, at the α = 0.05 significant level. • High School # 1: Mean SAT score =520 points • High School # 2: Mean SAT score =480 points Example 4. A new subpopulation of a certain species of stag beetle is discovered, whose individuals seem to be significantly larger than the parent species. A small random sample of n=25 specimens is collected, and the length of X (mm) of each is measured. It is found that x̄=75.8mm, with s=62.5mm. Assuming that X is normally distributed in the population. a. Compute the 90% confidence interval for the true population mean length. b. Calculate the p-value of this sample, under the null hypothesis H0 : µ = 50mm of the parent population, vs.H1 : µ 6= 50mm. Office: 1335 MSC, 263-5948 1 Office Hour: Wed.1:00-2:00 and Thurs. 11:00-12:00