Parents of teenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was $679. For 23 teenage girls, it was $559. From past years, it is known that the population standard deviation for each group is $180. Determine whether or not you believe that the mean cost for auto insurance for teenage boys is greater than that for teenage girls under the assumption that auto insurance costs in the respective populations are normally distributed. Please also state if the assumption of normal distribution was essential for solving this question. You will need to present the answer in the format that shows all the steps of hypothesis testing For example: Given? Step1: what is the parameter of interest? Provide notation. 'Nhat is the hypothesis of interest? Step2: Viihat method would you use to test the above hypothesis (stating the name of the function used in TIcalculator will suffice)? Provide brief reasoning for your choice. Step3: If using the pvaluemethod, then provide the name and value of the test statistic. If using the CI-method, then provide the name for the type of interval and its value. Step4: What do you conclude? Provide reasoning for your conclusion. ~II~II~II~IHD