5.2 Notes

Parameter Statistic number that describes a population fixed value generally unknown Statistic number that describes a sample value can change from sample to sample used as an estimate for the population parameter

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 = Statistic Parameter All American Citizens 1500 American Citizens True % of American citizens that are Lactose Intolerant

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 = Statistic All smokers 1000 smokers that signed the card True % of smokers that quit smoking

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 = 13.8 = Parameter Statistic Population – All bottles of ketchup produced on Tuesday Sample – 50 bottles randomly selected Parameter of interest – True average ounces of ketchup in Tuesday’s bottles

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: Parameter Statistic All students in the next senior class Students that were polled (unknown number)

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?

Statistic Parameter Measures? Different Symbols… Statistic Parameter Measures? proportion/percent means/averages

p. 223 Read through Example 5.8 Answer the questions. Pop: All adults; P.I. = % that had bought a lottery ticket p = 60% SRS of 100 adults % that had bought a lottery ticket. 46% 1000 samples The sample proportions for all 1000 samples Symmetric, unimodal, centered around .6 and ranges from .44 to .72

8. Sample size is 1523 9. The sample proportions for 1000 samples 10. Symmetric, unimodal, centered around 60, and ranges from 0.56 to 0.64 11. The second has much less spread than the first one. 12. Both are unimodal and symmetric. Also both are centered around 0.60 13.

* 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

Larger samples give smaller variability: * Variability = spread/width of graph Larger samples give smaller variability: Lots of samples of size 100 Lots of samples of size 1000 True parameter True parameter

Bias vs Variability Bias is the accuracy of a statistic Variability is the precision of a statistic

Label each as high or low for bias and variability High Bias Low Variability True parameter True parameter Low Bias High Variability

Label each as high or low for bias and variability High Bias High Variability True parameter True parameter Low Bias Low Variability

Another vocab word… Unbiased Estimator: - When the center of a sampling distribution (histogram) is equal to the true parameter. True parameter True parameter

* To reduce bias… use random sampling * To reduce variability… use larger samples!