Question

Generating a single confidence interval. The below image was generated using your book's Confidence Interval applet.(Link to book applets (Links to an external site.)Links to an external site.)

Using the default settings in the Confidence Interval applet (95% confidence level and n = 20), a SRS was drawn by clicking “Sample”. The resulting 95% confidence interval is displayed below.

Population Distribution -

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.

Answer 1

No, the span of the data is not larger than the span of confidence interval .

The 95% confidence interval is given by

$\bar{X}\pm 1.96*\sigma /\sqrt{n}$

That means 95% confidence interval includes the data which are within $1.96*\sigma /\sqrt{n}$ above or below the sample mean .The sample mean is shown by the black dot , and the confidence interval $(\bar{X}-1.96*\sigma /\sqrt{20}, \bar{X}+1.96*\sigma /\sqrt{20})$ is shown by the black line .

Confidence interval donot include the whole data , rather its equidistant spread around the sample mean .

By 95% confidence interval we mean we are 95% confident that the population mean is within this interval.

OR if we select number of samples of size 20 , 95% of the samples will have mean within this interval .