2 Parameter Statistic number that describes a population fixed value generally unknownStatisticnumber that describes a samplevalue can change from sample to sampleused as an estimate for the population parameter
3 EXAMPLE 1:A polling agency takes a sample of 1500 American citizens and asks them if they are lactose intolerant. 12% say yes. This is interesting, since it has been shown that 15% of the population is lactose intolerant.12% =15% =Population =Sample =Parameter of interest =StatisticParameterAll American Citizens1500 American CitizensTrue % of American citizensthat are Lactose Intolerant
4 EXAMPLE 2:A random sample of 1000 people who signed a card saying they intended to quit smoking were contacted a year after they signed the card. It turned out that 210 (21%) of the sampled individuals had not smoked over the past six months.21% =Population =Sample =Parameter of interest =StatisticAll smokers1000 smokers that signed the cardTrue % of smokers thatquit smoking
5 Population – All bottles of ketchup produced on Tuesday EXAMPLE 3:On Tuesday, the bottles of tomato ketchup filled in a plant were supposed to contain an average of 14 ounces of ketchup. Quality control inspectors sampled 50 bottles at random from the day’s production. These bottles contained an average of 13.8 ounces of ketchup.14 = =ParameterStatisticPopulation – All bottles of ketchup produced on TuesdaySample – 50 bottles randomly selectedParameter of interest – True average ounces of ketchupin Tuesday’s bottles
6 EXAMPLE 4:An area high school boasts that 85% of all graduating seniors attend college after graduation. A local newspaper polls the next senior class and finds that 74% plan on attending college after graduation.85% = 74% =Population:Sample:ParameterStatisticAll students in the next senior classStudents that were polled (unknown number)
7 EXAMPLE 5:A researcher wants to find out which of two pain relievers works better. He takes 100 people and randomly gives half of them medicine #1 and the other half medicine #2. 17% of people taking medicine 1 report improvement in their pain and 20% of people taking medicine #2 report improvement in their pain.17% = _________ 20% = __________Population? Sample? Parameter of interest?
8 Statistic Parameter Measures? Different Symbols…Statistic Parameter Measures?proportion/percentmeans/averages
9 p. 223 Read through Example 5.8Answer the questions.Pop: All adults; P.I. = % that had bought a lottery ticketp = 60%SRS of 100 adults% that had bought a lottery ticket. 46%1000 samplesThe sample proportions for all 1000 samplesSymmetric, unimodal, centered around .6 and ranges from .44 to .72
10 8. Sample size is 15239. The sample proportions for 1000 samples10. Symmetric, unimodal, centered around 60, and ranges from 0.56 to 0.6411. The second has much less spread than the first one.12. Both are unimodal and symmetric. Also both are centered around 0.6013.
11 * Different samples give us different results SAMPLING VARIABILITY* Different samples give us different results* Different size samples give us different results* Bigger samples are better!!* If we take lots of random samples of the same size, the variation from sample to sample follows a predictable pattern = they make a good graph!True parameter
12 Larger samples give smaller variability: * Variability = spread/width of graphLarger samples give smaller variability:Lots of samples of size 100Lots of samples of size 1000True parameterTrue parameter
13 Bias vs Variability Bias is the accuracy of a statistic Variability is the precision of a statistic
14 Label each as high or low for bias and variability High BiasLow VariabilityTrue parameterTrue parameterLow BiasHigh Variability
15 Label each as high or low for bias and variability High BiasHigh VariabilityTrue parameterTrue parameterLow BiasLow Variability
16 Another vocab word… Unbiased Estimator: - When the center of a sampling distribution (histogram) is equal to the true parameter.True parameterTrue parameter
17 * To reduce bias… use random sampling * To reduce variability… use larger samples!