6. Confidence Intervals Based on Normal Distributions

Topics and Notes

1. Concept of confidence interval (CI) for population mean ($\mu$)
• a. Point estimate vs interval estimate
• b. The logic of confidence intervals
• c. Concepts of confidence interval of population mean
•   ■ Confidence level ($1- \alpha$) and critical value ($CV = Z_{\alpha/2}$)
•   ■ Standard error of sample mean ($\bar{x}$)
•   ■ Margin of error ($E = CV \times s/\sqrt{n}$)
•   ■ structure of CI ($\bar{x} - E, \bar{x} + E$)
2. Steps for constructing a confidence interval of population means
• a. Identify confidence level (default 1 - $\alpha$ = 0.95)
• b. Find the critical value (CV) from the normal distribution table
• c. Calculate the margin of error: $E = CV s/\sqrt{n}$
• d. Write the CI explicitly: ($\bar{x} - E, \bar{x} + E$)
• e. Interpret confidence interval
3. Implementing confidence interval for a population mean: large sample case
4. Lecture Note
• Confidence Intervals: Logic and Framework
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Practice and Interactive Apps

1. Practice exercises #06 WEB LINK
2. [Optional]Read section 8.1 and 8.2 of Navidi's textbook
3. Normal CI for Means and Proportions INTERACTIVE APPS

Weekly Assignments

1. This week's Assignment (Weekly quiz)
   • a. Available on D2L: 12:00 PM, Thursday
   • b. Due: 11:30 PM, Sunday