Question

Simulate 100 confidence intervals with a 90% confidence level. Choose a sample size between 30 and 100. Look at your confidence intervals. Now increase the confidence level to 95%. Look at your confidence intervals. Finally, increase the confidence level to 99%. Look at your confidence intervals. How does the confidence level affect your confidence intervals?

Answer 1

Suppose, we simulate 100 confidence intervals with a 90% confidence level by using Excel or any other software with a specific sample size between 30 and 100. Suppose we select n=49. We simulate the confidence intervals based on the sample statistic values. Then again we did the same process by using a 95% confidence level instead of 90%. We have to do it again for the 99% confidence interval. After observing these simulated confidence intervals, it is observed that the width of the confidence intervals is increased when we increased the confidence level. The average width of the simulated confidence intervals with 95% level is more than the average width of the simulated confidence interval with 90% level. In the same way, the average width of the simulated confidence intervals with a 99% level is more than the average width of the simulated confidence interval with 95% level.

Example of simulated data is given for more explanation as below:

Example:
Sample Mean	10	10	10
Sample SD	2	2	2
Confidence level	90%	95%	99%
Sample size	49	49	49
df	48	48	48
Critical t value	1.6772	2.0106	2.6822
Standard error	0.2857	0.2857	0.2857
Margin of error	0.4792	0.5745	0.7663
Lower limit	9.5208	9.4255	9.2337
Upper limit	10.4792	10.5745	10.7663
Interval width	0.9584	1.1489	1.5327