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Lecture Note, July 28, 2014 Chih-Hsin Hsueh Review Hypothesis testing for population mean σ known Null hypothesis Alternative hypothesis Test statistic Rejection region p-value Decision method (rejection region) Decision method (p-value) 1 σ unknown Example: Consider the same cola bottle sample. Suppose the content of cola bottle is normal with mean µ and standard deviation, σ(µ and σ, both unknown). If the person who suspects that the bottler is underfilling measures the contents of 20 bottles and gets the mean content for this sample x = 298.9 ml. and sample standard deviation, s = 5.2 ml., then carry out a test to see if this is a convincing evidence that the mean content(µ) of cola bottles is less than the advertised 300 ml. Construct a 95% confidence interval for µ, are the test and confidence interval give us same result? 2