BA 275 Quantitative Business Methods

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Presentation transcript:

BA 275 Quantitative Business Methods Agenda Statistical Inference: Confidence Interval Estimation Estimating the population mean m Margin of Error Sample Size Determination Quiz #4

Statistical Inference: Estimation Example: s = 15 n = 400 What is the value of m? Population Research Question: What is the parameter value? Example: m =? Sample of size n Tools (i.e., formulas): Point Estimator Interval Estimator

Central Limit Theorem (CLT) The CLT applied to Means

Example 2 (p.14) Suppose that the amount of time teenagers spend weekly at part-time jobs is normally distributed with a standard deviation of 20 minutes. A random sample of 100 observations is drawn and the sample mean is computed as 125 minutes. Determine the 92% confidence interval estimate of the population mean.

Example 4 (p.14) A company that produces universal remote controls wanted to determine the number of remote control devices American homes contain. The company hired a statistician to survey 24 randomly selected homes and determine the number of remote controls. The sample mean and sample standard deviation were 4.46 and 7.30, respectively. Estimate with 99% confidence the average number of remote controls in the United States.

Critical Values of t (p.41) ∞

Example (CyberStats) A university administrator wanted to estimate the average number of times students at her university drank alcohol in the past month. A random sample of 92 students was surveyed by phone. The average number of times students in the sample drank was 5.6 times with a standard deviation of 6 times. Calculate a 95% confidence interval for the average number of times all students at the university drank alcohol in the past month.

Factors Affecting the Width of a Confidence Interval Sample Size Confidence Level Standard Deviation

What does “95% confidence” mean? “95% Confidence” is a short way of saying “We use a method that gives correct results 95% of the time.”

Margin of Error (B) Margin of Error (how good is your point estimate?)

Relations among B, n, and a B (margin of error) N (sample size) Fixed Confidence Level (e.g., 90%, 95%) Fixed

Estimation in Practice Determine a confidence level (say, 95%). How good do you want the estimate to be? (define margin of error) Use formulas (p.14) to find out a sample size that satisfies pre-determined confidence level and margin of error.

Example (p.14) An auditor is sampling inventory items in order to estimate the mean age of the items. (a “population mean” problem!) The auditor believes that the standard deviation is about 28. How large a sample is required to estimate the mean age to within 1 day? Assume that the confidence level is to be 99%.

Example (p.14) An auditor is sampling inventory items in order to estimate the mean age of the items. (a “population mean” problem!) The auditor believes that almost all of the ages will be between 30 and 130 days. How large a sample is required to estimate the mean age to within 1 day? Assume that the confidence level is to be 99%.

Example (p.14) An auditor is sampling inventory items in order to estimate the mean age of the items. (a “population mean” problem!) The auditor believes that almost all of the ages will be between 30 and 130 days. How large a sample is required to estimate the mean age to within 1 day? Assume that the confidence level is to be 90%.