## Lesson 13: Estimation with Confidence Intervals

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*

- Conduct a Simple Random Sample (SRS) of size
- 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]

Assignment:

**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.

Study:

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