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BA 275 Quantitative Business Methods

BA 275 Quantitative Business Methods. Quiz #2 Sampling Distribution of a Statistic Statistical Inference: Confidence Interval Estimation Introduction Estimating the population mean m Examples. Agenda. Central Limit Theorem (CLT). The CLT applied to Means. Example 1.

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BA 275 Quantitative Business Methods

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  1. BA 275Quantitative Business Methods • Quiz #2 • Sampling Distribution of a Statistic • Statistical Inference: Confidence Interval Estimation • Introduction • Estimating the population mean m • Examples Agenda

  2. Central Limit Theorem (CLT) • The CLT applied to Means

  3. Example 1 • The dean of a B-school claims that the average weekly income of graduates of her school one year after graduation is $600. • If the dist. of weekly incomes is normal with a std of $100, • Q1. What is the prob. of one randomly selected graduate has an avg weekly income of less than $550? • Q2. What is the prob. of 64 randomly selected graduates have an avg weekly income of less than $550? • Q3. If the dist. of weekly incomes is UNKNOWN, but the std is believed to be $100, can we still answer the above two questions?

  4. Example 2

  5. Example 3 • The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 15. A random sample of 400 salespeople was taken and the mean number of cars sold annually was found to be 75. Find the 95% confidence interval estimate of the population mean. Interpret the interval estimate.

  6. Statistical Inference: Estimation Example: s = 10,000 n = 100 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

  7. 100(1-a)% Confidence Interval for the Mean • If s is known (or n is large): Section 6.1 • If s is unknown (or n is small): Section 7.1

  8. Practice Problems (Za/2) • What are the values of za/2 for 86%, 92%, and 97% confidence intervals? • Which of the three intervals is wider?

  9. Example 3 (continued) • The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 15. A random sample of 400 salespeople was taken and the mean number of cars sold annually was found to be 75. Find the 90% confidence interval estimate of the population mean. Interpret the interval estimate. • Za/2=?

  10. Example 4 • 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.

  11. Standard Normal Probabilities (Table A)

  12. Standard Normal Probabilities (Table A)

  13. Answer Key to the Examples used • Example 1 • Q1: 0.3086; Q2: 0.0000; Q3: only Q2 because of the central limit theorem • Example 2 • Q1: 0.281; Q2: 0.1251; Q3: 0.0000; Q4: Yes to all because the population distribution is normal. • Example 3: 75 ± 1.96 x (15 / SQRT(400) ) • Practice Problems: For 86%, za/2 = 1.47; For 92%, za/2 = 1.75; For 97%, za/2 = 2.17 • Example 3: 75 ± 1.645 x (15 / SQRT(400) ) • Example 4: 125 ± 1.75 x (20 / SQRT(100) )

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