Lesson 16: Estimation with Confidence Intervals

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October 24, 2016 at 10:00 am  •  Posted in f16-busad265 by  •  0 Comments

Mon, Oct 24

Review:

  • Sampling Distributions

Presentation:

  • How to Estimate a Population Mean (μ)
    • Conduct a Simple Random Sample (SRS) of size n
    • Calculate the sample mean, x-bar = (∑x)/n
    • If n is sufficiently large (≥30), we can assume x-bar is Normally distributed
    • Estimate of the population mean, μ = x-bar (point estimate)
    • Estimate of the population standard deviation, σ = s/(√n)
    • Estimate margin of error, m = z*σ  (use z = 1.96 for 95% confidence)
    • Estimate with confidence interval for μ = x-bar ± m
  • Watch video
  • Example: A sample of size n = 400 produced the sample mean, x-bar = 36.0 and sample standard deviation, s = 9.0. Construct a 95% confidence interval to estimate the population mean.
    • n = 400
    • x-bar = 36.0
    • s = 9.0
    • m = 1.96*(9/(√400)) = 0.882
    • Estimate for μ = 36.0 ± 0.882
    • 95% confidence interval: [35.118, 36.882]

Activity:

  • Problem 1. A sample of size n = 100 produced the sample mean, x-bar = 16.0 and sample standard deviation, s = 3.0. Construct a 95% confidence interval to estimate the population mean.
  • Problem 2. An operation manager at a large plant observed 120 workers assembling an electronic component. The average time needed for assembly was 16.2 minutes with a standard deviation of 3.6 minutes. Construct a 95% confidence interval to estimate the mean assembly time.
  • Problem 3. A computer technician installs new hard drives on 64 different computers. The average installation time is 42 minutes with a standard deviation of 5 minutes. Construct a 95% confidence interval for the mean installation time.
  • Problem 4. A research firm conducted a survey of regular smokers to estimate the average amount spent per week on cigarettes. A sample of 49 regular smokers revealed average spending on cigarettes to be $21.55 with a standard deviation of $5.21. Construct a 95% confidence interval to estimate mean weekly cigarette spending.

Assignment:

  • Read pp. 353-362, Introduction to Inference and Estimating with Confidence

 

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