6.4 Generating a single confidence interval. Using the default settings in the Confidence Interval applet (95% confidence level and n = 20), click “Sample” to choose an SRS and display its confidence interval.

1. (a) Is the spread in the data, shown as yellow dots below the confidence interval, larger than the span of the confidence interval? Explain why this would typically be the case.

2. (b) For the same data set, you can compare the span of the confidence interval for different values of C by sliding the confidence level to a new value. For the SRS you generated in part (a), what happens to the span of the interval when you move C to 99%? What about 90%? Describe the relationship you find between the confidence level C and the span of the confidence interval.