Conducting hypothesis tests for the difference between two means with summary data

This tutorial covers the steps for conducting hypothesis tests 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 Conducting hypothesis tests for the difference between two means with raw data.

Performing a two-sample hypothesis test

Is there a significant difference in the average size of four-bedroom homes listed for sale in the two cities? This can be tested by conducting a hypothesis test for the difference between the mean square footage of four-bedroom homes listed for sale in each location. To compute the appropriate two-sample T hypothesis test results, 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, the Hypothesis test for μ_{1} - μ_{2} is selected by default. Leave the null value at 0 to directly compare the two means. The alternative hypothesis can be changed to > or < , but for this scenario leave the alternative hypothesis at ≠ since the goal is to detect any type of difference. Click Compute! to view the hypothesis test results. The output table provides various statistics from this test including the test statistic and the P-value.

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