A particular brand of tires claims that its deluxe tire averagesat least 50,000 miles before it needs to be replaced. From paststudies of this tire, the standard deviation is known to be 8,000.A survey of owners of that tire design is conducted. Of the 28tires surveyed, the mean lifespan was 46,500 miles with a standarddeviation of 9,800 miles. Using alpha = 0.05, is the data highlyconsistent with the claim? Note: If you are using a Student'st-distribution for the problem, you may assume that the underlyingpopulation is normally distributed. (In general, you must firstprove that assumption, though.) A.) State the distribution to usefor the test. (Round your answers to two decimal places.) B.) Whatis the test statistic? (If using the z distribution round youranswers to two decimal places, and if using the t distributionround your answers to three decimal places.) C.) What is thep-value? (Round your answer to four decimal places.) D.) Indicatethe correct decision (\"reject\" or \"do not reject\" the nullhypothesis), the reason for it, and write an appropriateconclusion. (i) Alpha (Enter an exact number as an integer,fraction, or decimal.) E.) Construct a 95% confidence interval forthe true mean. Sketch the graph of the situation. Label the pointestimate and the lower and upper bounds of the confidence interval.(Round your lower and upper bounds to the nearest wholenumber.)