Theory-Based Approach
The previous method works pretty well but only for 95% confidence intervals. To be able to change the confidence level and to obtain a more precise calculation for the confidence interval, we will use a one-sample t-interval.
| Validity Conditions:
The one-sample t-interval is only considered valid if we have a reasonably symmetric sample distribution or at least 20 observations and the sample distribution is not strongly skewed. |
(h) Do you consider these conditions met for these data? Explain.
(i) Use the Theory-Based Inference applet to calculate a 95% confidence interval. How does it compare to the 2SD interval?
(j) Use the Theory-Based Inference applet to calculate a 99% confidence interval. How does it compare to the interval in (i)? (Look at both midpoint and width.) Is this what you expected? Explain.
