Data Analysis

499 WordsFeb 25, 20122 Pages
Week7 Sample size &gt; 30  Approximately Normal (Central Lt Theorem) S = ∑(X - µ)2 / √(n-1) STDEV not P ±σ = 68.6% (For Z scale it will be 1Z, 2Z, 3Z  0,1  σ = 1) ±2σ = 95.4% ±3σ = 99.74% Even if the distribution isn’t normal, sampling distribution (X) will be normal (Std of mean error) σx = σ/√n E(X) and E(Xbar) = µ n α 1/σ n  σ Concentration around the mean (More precise) Estimation = Confidence interval  % CI α Z (Z – Confident statement) Margin of error = ±Z σ/√n Z = NORMINV([1+CP]/2, 0, 1) – std normal [1+CP]/2 = 0.5 + CP/2 [Left half + Rem] α – Error %  α% times the mean of a sample will be outside the interval (CI) n/N &lt; 0.1  correction can be ignored t – Population std not known =TINV(α, n-1) Confidence level α margin of error Infinite Population 1. Normal Method (Using Eqn) (i.e) (X – Z σx) &lt; µ &lt; (X+ Z σx), where σx = σ/√n [Note: The mean, std is 0,1. Even if µ and σ are given] (or) Z = NORM.INV( [1+CL]/2,0,1) 2) Excel Method [probability (Area-α), Mean (Pop), standard (sample)] Finite Population 1) Sample size (n &gt; 30) 2) Sample size (n &lt; 30) Population percentage interval (Percentage) p = x/n (x – No of bad/good___) P – success% as per our definition Normal method p – Zσp &lt; ᴨ &lt; p + Zσp Excel Method Lower Lt =NORM.INV(α/2, p, σp) Upper Lt =NORM.INV(1-[α/2], p, σp) Mention the rational 4 method upfront Z – no pop σ; n&gt;30  by central Lt theorem, Z theorem can be used Week 8 Believe µ is real mean &amp; build a model &amp; Test ur model by comparing the sample with it Take α% risk upfront (Type1 error – Alpha error) α = P(Reject H0 | H0 is true) = risk t function in excel is always a 2 tail test – for 1 tail test (Left or Right)  use 2α Population percentage interval P = µO