 |
7. Confidence Intervals for Proportion and Population Mean Based on Small Samples
Topics and Notes
- 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
- 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
- Lecture Note
- a. CI for normal population mean and population proportions
HTML
PDF
Practice and Interactive Apps
- Practice exercises #07
- [Optional]Read section 8.3 of Navidi's textbook
- Interactive statistics learning apps
|
|
|
