Computing confidence intervals for the difference between two means with summary data
This tutorial covers the steps for computing confidence intervals for the difference between two means in StatCrunch. This example will compare randomly sampled four-bedroom homes listed for sale in the two adjoining cities of Bryan, Texas, and College Station, Texas. A random sample of 15 homes from Bryan, Texas was found to have a mean square footage of 2842 square feet and a sample standard deviation of 831 square feet. A random sample of 15 homes from College Station, Texas was found to have a mean square footage of 2751 square feet and a sample standard deviation of 774 square feet. This tutorial will cover using two-sample T methods with the sample size and the summary information above from both samples. A very similar approach can be used for two-sample Z methods that are appropriate for situations with larger sample sizes and/or known standard deviations. To compute two-sample results using the corresponding raw data set with individual values, see Computing confidence intervals for the difference between two means with raw data.
Calculating a confidence interval for difference in means
StatCrunch can create a confidence interval for the difference in the average size of four-bedroom homes listed for sale in the two cities. For this example, choose the Stat > T Stats > Two Sample > With Summary menu option. Under Sample 1, enter 2842 for the Sample mean, 831 for the Sample std. dev., and 15 for the Sample size. Under Sample 2, enter 2751 for the Sample mean, 774 for the Sample std. dev., and 15 for the Sample size. Under Perform, choose Confidence interval for μ1 - μ2. By default, StatCrunch has a value of 0.95 for the Level input which will produce a 95% confidence interval for the difference between the two means. Enter 0.99 for this input to produce a 99% confidence interval instead and click Compute!. The results below show a 99% confidence interval for the difference in mean square footage of four-bedroom homes in the two cities with "L. Limit" representing the lower limit and "U. Limit" representing the upper limit of this confidence interval.