Pleаse nоte thаt this questiоn cоnsists of six pаrts. You may use MINITAB to double check your final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question. An electric vehicle manufacturing company claims that on average batteries last for 340 miles on a full charge. Recently, the company has been getting many complaints about the need to charge the vehicles after less than 340 miles. Company would like to see if the true average mileage could possibly be well short of their quoted claim. They collected data from a random sample of 51 electric vehicles manufactured by the company. The average mileage per full charge for the sampled vehicles was 330 miles with a standard deviation 25 miles per full charge. Set up the appropriate null and alternative hypotheses for testing the company’s question to address the customers' complaints. Use proper notations when setting up and . Are the conditions to carry out the above stated test are satisfied? In addition to stating yes or no, explain how you check whether they were satisfied for this problem. Calculate the test statistic. Show your calculations. Calculate the p-value for the test. You MUST clearly write down the probability statement for the p-value for the test. You may use the appropriate table included in this exam or MINITAB to find the final numerical value of this p-value. Write the final conclusion in the context of the problem using 5% significance level. Instead of doing the above hypothesis test, suppose the company wanted to obtain an interval estimation for the true proportion of vehicles that do not last 340 miles on a full charge. In the sample of 51 vehicles, battery did not last for 340 miles on a full charge for 38 vehicles. Obtain a 95% confidence interval for the true proportion of vehicles that do not last 340 miles on a full charge.