数据库文化基础 (18).pdf

Statistics I10thweek/Probability and Statistics(IV)Objectives of This WeekUnderstand the concepts of random sampling,and statisticsUnderstand the concepts of confidence interval,-value,and hypothesis testsPractice statistical tests with RRandom Sampling The average height of adults can be approximated from randomly chosen n adults Random samples:independent and identically distributed RVs from the same population3Sample 1:1Sample 2:2Sample 100:100the whole populationStatistic A statistic is a value calculated from the observed random samples to say something about the whole population=(1,2,3,)4Sample 1:1Sample 2:2Sample 100:100the whole populationSample Mean True mean(population mean):the average of the whole population Sample mean Average of the observed samples Representing the true mean,but not equal=1=15Sample Variance True variance(population variance)Var:the variance of the whole population Sample variance Variance of the observed samples Representing the true variance,but not equal2=11=126Confidence Interval Confidence in how close the sample mean is to the population mean Depends on the sample size()and standard deviation of the population()If standard deviation of the population is unknown,will use the sample standard deviation Estimated standard error is/7Confidence Interval of Sample Mean The sample mean is a common estimator of the true mean We are interested in(px100)%confidence interval=Pr +=Pr /The prob.that the true mean is within this interval is By the CLT,/(0,1)8Confidence Interval of Sample Mean Example:samples are 1.40,0.44,1.90,1.05,0.04=0.23,=1.28,/=0.57The prob.that the true mean between-0.80 and 0.24 is 68%95%confidence interval is-1.35 to 0.889T-statistics If n is not large enough,=/is not normal Instead,T(1),-distribution https:/en.wikipedia.org/wiki/Student%27s_t-distribution100.000.100.200.30-4-2042()0.050.150.250.350.40=1=2=5=+