1 / 22

AP Statistics

AP Statistics. 9.1 Sampling Distribution. Learning Objectives. Know the difference between a statistic and a parameter Understand that the value of a statistic varies between samples Be able to describe the shape, center and spread of a given sampling distribution

fergal
Télécharger la présentation

AP Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. AP Statistics 9.1 Sampling Distribution

  2. Learning Objectives • Know the difference between a statistic and a parameter • Understand that the value of a statistic varies between samples • Be able to describe the shape, center and spread of a given sampling distribution • Understand how bias and variability of a statistic affects the sampling distribution

  3. Parameter - a number that describes the population (usually it’s unknown) • Statistic - a number computed from the sample data

  4. Examples • Is the boldfaced number a parameter or a statistic? 1. 60,000 members of the labor force were interviewed of whom 7.2% were unemployed   statistic

  5. 2. A lot of ball bearings has a mean diameter of 2.5003 cm. A 100 bearings are selected from the lot and have a mean diameter of 2.5009 cm. 2.5003- parameter 2.5009- statistic

  6. 3. A telemarketing firm in Los Angeles randomly dials telephone numbers. Of the first 100 numbers dialed 48% are unlisted. This is not surprising because 52% of all Los Angeles residential phones are unlisted. 48%- statistic 52%- parameter

  7. Sampling Variability • Sample proportion: (“p hat”) • Example: A poll found that 1650 out of 2500 randomly selected adults agreed with the statement that shopping is frustrating. What is the proportion of the sample who agreed? =1650/2500

  8. Sampling variability – the value of a statistic varies with repeated sampling • Applet: http://www.rossmanchance.com/applets/Reeses/ReesesPieces.html

  9. Sampling Distribution  the distribution of values taken by the statistic in all possible samples of the same size from the same population.

  10. Describing Sampling Distributions • 1. the overall shape is symmetric (normal) • 2. there are no outliers or other important deviations from the overall pattern • 3. the center of the distribution is the true value p • 4. the values of have a large spread

  11. Unbiased Statistic • a statistic is unbiased if the mean of the sampling distribution is equal to the true value of the parameter being estimated

  12. Variability of a statistic • 1. Is described by the spread of its sampling distribution. • 2. This spread is determined by the sampling design and the size of the sample. • 3. Larger samples give smaller spread.

  13. High bias; Low bias; low variability high variability High bias; Low bias; high variability low variability

  14. Example • 60% of people find clothes shopping frustrating. • Find the proportion of people that fall within 2 standard deviations of the mean for samples of size • n =100 (0.502,0.698)

  15. n = 2500 (0.5804 and 0.6196)

  16. Why does the size of the population have little influence on how statistics from a random sample behave? The larger the sample size, the smaller the standard deviation.

  17. Ch 9.2 Sample Proportions Learning Objectives: • Know the characteristics of the sampling distribution of • Know when to use the normal approximation for • Be able to solve problems using the normal approximation for

  18. Sampling distribution of • Choose an SRS of size n from a large population, then: • 1.  the sampling distribution of is approximately normal. (closer to a normal dist. when n is large) • 2. the mean of the sampling dist. is exactly p • 3.

  19. Assumption 1 The standard deviation p for __ can only be used when the population is at least 10 times as large as the sample • Assumption 2 We can say that the sampling distribution of is approximately normal when np>10 and n(1-p)>10. *(some books use np>5)

  20. Example • There are 1.7 million first-year college students of those, 1500 first-year college students are asked whether they applied for admission to any other college. In fact 35% of all first-year students applied to a college other than the one they are attending. What is the probability that your sample will give a result within 2 percentage points of this true value?

  21. Assumptions: -random sample -population is at least 10X the sample -(1500)(0.35)> 10 525>10 -(1500)(0.65)>10 975>10

  22. Complete 9.15 pg. 477 • Assumptions: -SRS -population is at least 10X the sample -(1540)(0.15)> 10 231>10 -(1540)(0.85)>10 1309>10

More Related