(20 points)Engineers at a tire manufacturing corporation wish to test a new tire material for incresed durability. To test the tires under realistic road conditions, new front tires are mounted on each of 11 company cars, one tire made with a production material and the other with the experimental material. After a fixed period, the 11 pairs were measured for wear. The amount of wear for each tire(in mm) is shown in the table: Test, at the 1% level of significance, the hypothesis that the mean wear with the experimental material is less than that for the production material.(Assume the population follow a normal distribution) (a)Set up the null and alternative hypothesis. (b)Report the value of test statistic.(Assume the population follow a normal distribution with equal variance) (c)Find the P-value and make your conclusion at Car Production Experimental 1 5.1 5.0 2 6.5 6.5 3 3.6 3.1 4 3.5 3.7 5 5.7 4.5 6 5.0 4.1 7 6.4 5.3 8 4.7 2.6 9 3.2 3.0 10 3.5 3.5 11 6.4 5.1 = 0.01