Confidence intervals for a mean (for studying the impact of confidence level)

The applet below allows one to visually investigate confidence intervals for a population mean. Specify the sample size n, the shape of the distribution (Normal or Right skewed), the true population mean (Mean) and the true population standard deviation (Std. Dev.). When you click the Simulate button, 100 separate samples of size n will be selected from a population with these population parameters. For each of the 100 samples, a 95% confidence interval and a 99% confidence interval are displayed in the plot to the right. Each of these intervals is computed using the t distribution. If an interval does not contain the true mean, it is displayed in red. Note that the 99% confidence interval is always wider than the 95% confidence interval. Additional simulations can be carried out by clicking the Simulate button multiple times. The cumulative number of times that each type of interval contains the true mean is also tabled. Press the Clear button to clear existing results and start a new simulation. Things to try with the applet:

  • Simulate at least 1000 intervals using samples of size 10 from a normal distribution with a Mean = 50 and Std. Dev. = 1. What proportion of the 95% confidence intervals contain 50? What proportion of the 99% confidence intervals contain 50?
  • Simulate at least 1000 intervals using samples of size 10 from a right skewed distribution with a Mean = 50 and Std. Dev. = 1. What proportion of the 95% confidence intervals contain 50? What proportion of the 99% confidence intervals contain 50?
  • Simulate at least 1000 intervals using samples of size 100 from a normal distribution with a Mean = 50 and Std. Dev. = 1. What proportion of the 95% confidence intervals contain 50? What proportion of the 99% confidence intervals contain 50?
  • Simulate at least 1000 intervals using samples of size 100 from a right skewed distribution with a Mean = 50 and Std. Dev. = 1. What proportion of the 95% confidence intervals contain 50? What proportion of the 99% confidence intervals contain 50?