7. Confidence Intervals for Proportion and Population Mean Based on Small Samples

Topics and Notes

1. Confidence interval for proportions
• a. Sampling distribution of sample proportion ($\hat{p}$)
• b. Margin of error: $E = CV\times \sqrt{\hat{p}(1-\hat{p})/n}$
• c. Steps for constructing confidence interval of proportion
• d. Tip: Draw the density curve for $\hat{p}$ and label given information on it then draw a density curve of standard normal density labelled with corresponding transformed information
2. Confidence interval of normal population mean - t confidence intervals
• a. Definition of t-distribution: degrees of freedom
• b. Finding critical value from t-table with a given degrees of freedom
• c. As the degrees of the t-distribution increase, the t-distribution approaches standard normal distribution.
• d. Sampling distribution of TS = $(\bar{x}- \mu)/(s/\sqrt{n})$: t-distribution with (n-1) degrees of freedom based on the following assumptions
•   ■ Population is normally distributed
•   ■ Population standard deviation is unknown (i.e., estimated from data)
•   ■ If sample size is less than 30, the t-critical value must be used.
• e. The same 5-step procedure applies to the t- CI for a normal population mean with unknown population variance
3. Lecture Note
• a. CI for normal population mean and population proportions HTML PDF

Practice and Interactive Apps

1. Practice exercises #07
2. [Optional]Read section 8.3 of Navidi's textbook
3. Interactive statistics learning apps
   • a. Normal CI for Means and Proportions INTERACTIVE APPS
   • b. t-CI for Normal Population Means INTERACTIVE APPS
   • c. C.I. Flowchart FLOWCHART

Weekly Assignments

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