1 / 9

Probability: Part 2 Sampling Distributions

Probability: Part 2 Sampling Distributions. Wed, March 17 th 2004. Sampling Distribution. A theoretical distribution that allows us to calculate probability of our sample stats Can then generalize from sample  pop Ex) pop of 2,4,6,8  y = 5 (mu = pop mean)

najila
Télécharger la présentation

Probability: Part 2 Sampling Distributions

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. Probability: Part 2Sampling Distributions Wed, March 17th 2004

  2. Sampling Distribution • A theoretical distribution that allows us to calculate probability of our sample stats • Can then generalize from sample  pop Ex) pop of 2,4,6,8 y = 5 (mu = pop mean) Draw random sample of N=2 from that pop and get 4 and 6, ybar = 5 (pretty good representation of pop mean!)… but if we drew 8 and 8, ybar = 8 (not so good) The difference betw sample estimate and population parameter = sampling error

  3. (cont.) • How much confidence should we have in our sample estimate of the pop parameter? • Sampling distribution – gives probabilities of all possible sample values • Found by taking all possible random samples of size N from pop, compute their means plot

  4. example • Can do this for all possible combinations of N=2 (w/replacement) and calculate ybar each time: ybar f 2 1 (1 way to get ybar=2, 2 then 2) 3 2 (could pull 2 then 4, or 4 then 2) 4 3 etc… 5 4 6 3 7 2 8 1 …if you plot this distribution  it is your sampling distribution!

  5. Mean of Sampling Distrib. • Sampling distribution also has a mean and std dev: •  ybar = mean of samp distrib = pop mean • Standard deviation of samp distrib is called the standard error: • ybar =  y / sqrt N …where  y is standard dev of pop (sigma) Represents average distance between pop & sample means

  6. Central Limit Theorem • As N increases, sampling distribution has less variability & looks like a normal curve • As N increases, mean of samp distribution = mean of population • Usually when N> 30 sampling distrib will be normal

  7. (cont.) • Given this, we’ll use the sampling distribution to find out how probable (or improbable/unusual) our 1 sample happens to be • Is it a good representation of the pop or not? Use probability to determine • As N increases, standard error decreases & we’ll be more confident in our sample estimate

  8. Sample Likelihood • Use z scores, now to find the likelihood of a sample mean (rather than an individual score) • 1st find mean & standard error For IQ test, what is prob of group of 9 students has mean >= 112? Pop mean = 100, y = 15 1st, need samp distrib mean & standard error

  9. (cont.) • Ybar (m in lab) = 100 • Ybar (x or s in lab) = 15 / sqrt (9) = 5 Z = ybar -  / ybar Z = 112-100 / 5 = 2.4 Use unit normal table to find probability of z=2.4, p = .0082 So very unlikely (.0082) to get a sample of 9 students w/average IQ of 112 from pop with  = 100

More Related