ChaPTER 9 Estimation from sample data to accompany Introduction to business statistics fourth edition by ronald M. Weiers Presentation by priscilla chaffe-Stengel Donald n. Stengel o The Wadsworth Group
CHAPTER 9 Estimation from Sample Data to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel © 2002 The Wadsworth Group
l Chapter 9- Learning objectives Explain the difference between a point and an interval estimate Construct and interpret confidence intervals. with a z for the population mean or proportion with a t for the population mean Determine appropriate sample size to achieve specified levels of accuracy and confidence o 2002 The Wadsworth Group
Chapter 9 - Learning Objectives • Explain the difference between a point and an interval estimate. • Construct and interpret confidence intervals: – with a z for the population mean or proportion. – with a t for the population mean. • Determine appropriate sample size to achieve specified levels of accuracy and confidence. © 2002 The Wadsworth Group
ll Chapter 9-Key terms ● Unbiased estimator· Confidence level Point estimates Accuracy Interval estimates Degrees of ● Interval limits freedom(df Confidence ° Maximum likely coefficient sampling error o 2002 The Wadsworth Group
Chapter 9 - Key Terms • Unbiased estimator • Point estimates • Interval estimates • Interval limits • Confidence coefficient • Confidence level • Accuracy • Degrees of freedom (df) • Maximum likely sampling error © 2002 The Wadsworth Group
LI Unbiased point estimates Population Sample Parameter Statistic Formula o mean, X x 2=2 n-x 2 Variance, o 12 Proportion,兀 p=x Successes n trials o 2002 The Wadsworth Group
Unbiased Point Estimates Population Sample Parameter Statistic Formula • Mean, µ • Variance, s 2 • Proportion, p x x = x i n –1 ( – )2 2 2 n x i x s s = p p = x successes n trials © 2002 The Wadsworth Group
l Confidence Interval: u, o Known where x= sample mean ASSUMPTION: o=population standard infinite population deviation n= sample size z= standard normal score for area in tail=a/2 /2 O/2 z x+z o 2002 The Wadsworth Group
Confidence Interval: µ, s Known where = sample mean ASSUMPTION: s = population standard infinite population deviation n = sample size z = standard normal score for area in tail = a/2 a 2 −a a 2 n x x z n x x z z z z s ×s × + + : – : – 0 x © 2002 The Wadsworth Group
l Confidence Interval: u, o Unknown where x= sample mean ASSUMPTION: s= sample standard Population deviation approximately n sample size normal and t=t-score for area infinite in tail=a/2 /2 O/2 t t x-t x+t o 2002 The Wadsworth Group
where = sample mean ASSUMPTION: s = sample standard Population deviation approximately n = sample size normal and t = t-score for area infinite in tail = a/2 df = n – 1 a 2 −a a 2 n s x x t n s x x t t t t × + × + : – : – 0 x Confidence Interval: µ, s Unknown © 2002 The Wadsworth Group
l Confidence Interval on t where p= sample proportion ASSUMPTION: n= sample size n°p≥5 z= standard normal score 1(1-p)≥5 for area in tail=a/2 and population infinite /2 O/2 2 2 0 P+2 o 2002 The Wadsworth Group
Confidence Interval on p where p = sample proportion ASSUMPTION: n = sample size n•p 5, z = standard normal score n•(1–p) 5, for area in tail = a/2 and population infinite a 2 −a a 2 n n z: –z 0 z p p p p z p p p p z (1– ) (1– ) : – × + × + © 2002 The Wadsworth Group
l Converting Confidence Intervals to Accommodate a finite population Mean o Proportion: x± or x o 2002 The Wadsworth Group
Converting Confidence Intervals to Accommodate a Finite Population • Mean: or • Proportion: –1 – 2 –1 – 2 N N n n s x t N N n n x z a s a –1 (1– ) – 2 N N n n p p p za © 2002 The Wadsworth Group
l Interpretation of Confidence intervals Repeated samples of size n taken from the same population will generate(1-a)% of the time a sample statistic that falls within the stated confidence interval OR We can be(1-a)% confident that the population parameter falls within the stated confidence interval o 2002 The Wadsworth Group
Interpretation of Confidence Intervals • Repeated samples of size n taken from the same population will generate (1–a)% of the time a sample statistic that falls within the stated confidence interval. OR • We can be (1–a)% confident that the population parameter falls within the stated confidence interval. © 2002 The Wadsworth Group
l Sample size Determination for u from an Infinite population Mean note o is known and e, the bound within which you want to estimate u, is given The interval half-width is e, also called the maximum likely error: Solving for n, we find: o 2002 The Wadsworth Group
Sample Size Determination for µ from an Infinite Population • Mean: Note s is known and e, the bound within which you want to estimate µ, is given. – The interval half-width is e, also called the maximum likely error: – Solving for n, we find: 2 2 2 e z n n e z s s = × = × © 2002 The Wadsworth Group
