To change the coordinates of a spatial data set to a new projection and coordinate system, first define the projection of the data frame. To confirm the change in projection has been applied, open a new data frame and add the exported shapefile. Notice the latitude and longitude coordinates at the bottom of the screen. Some databases default to the Geographic Coordinate system leaving the coverage looking a bit distorted. To change the coordinates of a spatial data set to a new projection and coordinate system, first define the projection of the data frame. Under 'Select a coordinate system', navigate down through the directories to select the appropriate projection as follows: Click OK to return to the map window. The warning prompt may pop up again but click 'Yes' and the new projection will be applied to the data frame. . Navigate to an appropriate directory, enter an appropriate name and click 'Save'. Click OK to the Export Data dialogue box. Source.