class...

    public class ExceptionCreateExceptionRecord{
    public static void insertException(Map<string, string> param)
        {    
    	Exception__c newExcept              =   new Exception__c();
            newExcept.ExceptionTypeCode__c      =   param.get('ExceptionTypeCode__c');
            newExcept.RecordType.DeveloperName  =   'New Exception'; 
    		
    		
    test class
    
        @isTest(SeeAllData=true)
        public class TestExceptionCreateExceptionRecord {
           static testmethod void Exception(){
            map<String ,String> parm=new map<String,String>();
                parm.put('ExceptionTypeCode__c', 'open');                
                parm.put('entry2','Second entry'); 
           ExceptionCreateExceptionRecord excep=new ExceptionCreateExceptionRecord();   
            ExceptionCreateExceptionRecord.insertException(Parm);
    		
		
stacktrace

Class.ExceptionCreateExceptionRecord.insertException: line 7, column 1( newExcept.RecordType.DeveloperName  =   'New Exception'; )
Class.TestExceptionCreateExceptionRecord.Exception: line 8, column 1( ExceptionCreateExceptionRecord.insertException(Parm);)