Business Statistics: Confidence Intervals and Estimation of Population Mean and Proportion, Assignments of Business Statistics

Download Business Statistics: Confidence Intervals and Estimation of Population Mean and Proportion and more Assignments Business Statistics in PDF only on Docsity! BA 253: Business Statistics 10/08/08 Today Confidence Intervals (Chapter 8) Fri More CI (Ch 8) Start ICE 6 Mon (10/13) No class! Finish ICE 6 Weds(10/15) No class! Project Proposal  Collect HW 4. Chapter 8  Previously, we assumed μ and σ were known, then found that the sample mean x was approximately normal for n ≥ 30.  Reality Check: Why estimate μ if we already know it???  What if we do not know μ, but want a good estimate for it? Ex: Survey 50 people about how much they spend on gas per week. x = $37, s = $19. Is μ ≈ x = $37? How close is the population mean to the sample mean?  With 95% certainty, what is the population mean? o Point Estimate: μ = x = $37. o Confidence Interval: μ is in x ± E = ………… o There is a 95% chance that the population mean is in 37 ± 5 = ($32, $42).  Require more certainty? Interval gets bigger.  Got more data? Interval gets smaller.  What if we want the error to only be ± $1? How many samples n do we need? o E = ………. n = ………. = 1381. Ex: n = 100, x = $1200, s = $425.  What is the 98% confidence interval for μ?  How many samples are required to know μ within ± $50? Ex: Same survey as before. With higher gas prices, have you considered switching to a more fuel efficient vehicle? p = 37/50 = 74% = 0.74  Is p = p = 74%?  With 95% certainty, what is p?  Point Estimate: p = 74%.  Confidence Interval: p ± E = …… = 74% ± 12% = (61%, 85%)  How many data necessary to know p within ± 5%?  E = ……, solve for n, = 303  What if we didn’t know p ? Then assume p = ½.  At 95% confidence, how many samples n necessary to know a proportion within ± 5%? ± 1%?  Quick estimate Fill in……….. Average Proportion Point Estimate Confidence Interval