Lecture 6 Notes

10 and n 10 30 100 and 300 what happens as n

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: q qqq q qqq 4 qqqq qqqq qqqq qqqq qq qqqqqq qqqqq qqqqq qqqqq qqq qq qq 2 q qqqq qqqqq qq 2 q qq −2 −1 n = 10 5 Sample Quantiles Sample Quantiles q 10 40 35 30 25 20 q q −2 −1 0 0 1 2 n = 30 qq q q qq q qqq qqq qqq qqq qq qq qq qqq qqq qqq qqq qq qqq qqq qqq qq qq q qqq qqq qqq qqq qqq qqq qq qq qq q qqq qq qq q qqqq qqq q q q qq 15 Users in our sample pressed the like button next to friends’ content an average of 14 times, but had their content “liked” an average of 20 times qqqqq qqqqq qqqqq qqqq qq q 1 2 q q q qq qq q q q q qq qq qq q qq qq qq qq q q q q qq qq q q q q q q q q qq q q q q qq q q q q q q q q q q qq qq q q q qq qq q q q qq qq qq q qq qq q q q q q q q q qq q q −2 n = 100 −1 0 1 q Users sent 9 personal messages, but received 12 q 12% of users tagged a friend in a photo, but 35% were themselves tagged in a photo Any guesses for how this pattern can be explained? 2 n = 300 In general - if np ≥ 10 and n(1 − p ) ≥ 10 then normal approximation is reasonable. Sta102/BME102 (Colin Rundel) A recent study found that “Facebook users get more than they give”. For example: 40% of Facebook users in our sample made a friend request, but 63% received at least one request q 6 0 q qq qqqqqqqq q qqqqqqq qqqqq qqq q Basics Lec 6 Normal Approximation to the Binomial February 5, 2013 13 / 23 Basics http:// www.pewinternet.org/ Reports/ 2012/ Facebook-users/ Summary.aspx Sta102/BME102 (Colin Rundel) Lec 6 Normal Approximation to the Binomial February 5, 2013 14 / 23 Basics Facebook cont. Normal approximation to the binomial This study found that approximately 25% of Facebook users are considered power users. The same study found that the average Facebook user has 245 friends. What is the probability that the average Facebook user with 245 friends has 70 or more friends who would be considered power users? When the sample size is large enough, the binomial distribution with parameters n and p can be approximated by the normal model with parameters µ = np and σ = np (1 − p ). In the case of the Facebook power users, n = 245 and p = 0.25. √ µ = 245 × 0.25 = 61.25 σ = 245 × 0.25 × 0.75 = 6.78 We are given that n = 245, p = 0.25, and we are asked for the probability P (X ≥ 70). Binom(n...
View Full Document

This note was uploaded on 04/06/2014 for the course STA 102 taught by Professor Staff during the Spring '08 term at Duke.

Ask a homework question - tutors are online