A govemment's department ot transportation requires tire manufacturers to provide performance intormation on tire sidewalls to help prospective buyers make their purchasing decisions. One very important piece of information is the tread wear index. which indicates the tire's resistance to tread wear. A tire with a grade of 200 should last twice as long, on average, as a tire with a grade of 100. A consumer organization wants to test the actual tread wear index of a brand name of tires that claims "graded 200" on the sidewall of the tire. A random sample of n = 18 indicates a sample mean tread wear index of 195.6 and a sample standard deviation of 213. Complete parts (a) and (b) below. Click here to view p_age 1 of the table of the critical values of t.' Click here to View p_age 2 of the table of the critical values of t.2 a. Is there evidence that the population mean amount is dierent from a grade of 200? (Use a 0.01 level at signicance.) State the null and alternative hypotheses. Ho: [1(1) H1 : p (2) Identify the critical value(s). The critical value(s) is(are) . (Round to four decimal places as needed, Use a comma to separate answers as needed.) Determine the test statistic. The test statistic is . (Round to tour decrmal places as needed.) State the conclusion. (3) \"0 There is (4) evidence to conclude the population mean amount is difterent from a grade of 200. b. Determine the p-value and interpret its meaning. The pvalue is . (Round to four decimal places as needed.) Interpret the meaning of the p-value. Choose the correct answer below. 0 A. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 4.400 ounce below 200 it the null hypothesis is false. 0 B. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 4.400 ounce away from 200 if the null hypothesis is true. 0 C. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 4.400 ounce above 200 if the null hypothesis is false. 0 D. The p-value is the probability of not rejecting the null hypothesis when it is false. 1: Table of critical values of t (page 1) Print Critical Values of t For a particular number of degrees of freedom, entry represents the critical value of t corresponding to the cumulative probability (1 - a) and a specified upper-tail area (a). 0 Cumulative Probabilities 0.75 0.90 0.95 0.975 0.99 0.995 Degrees of Upper-Tail Areas Freedom 0.25 0.10 0.05 0.025 0.01 0.005 1.0000 3.0777 6.3138 12.7062 31.8207 63.6574 WN 0.8165 1.8856 2.9200 4.3027 6.9646 9.9248 0.7649 1.6377 2.3534 3.1824 4.5407 5.8409 0.7407 1.5332 2.1318 2.7764 3.7469 4.6041 0.7267 1.4759 2.0150 2.5706 3.3649 4.0322 0.7176 1.4398 1.9432 2.4469 3.1427 0.7111 3.7074 1.4149 1.8946 2.3646 2.9980 3.4995 0.7064 1.3968 1.8595 2.3060 2.8965 3.3554 0.7027 1.3830 1.8331 2.2622 2.8214 0.6998 3.2498 1.3722 1.8125 2.2281 2.7638 3.1693 0.6974 1.3634 1.7959 2.2010 2.7181 3.1058 0.6955 1.3562 1.7823 2.1788 2.6810 3.0545 0.6938 1.3502 1.7709 2.1604 2.6503 3.0123 0.6924 1.3450 1.7613 2.1448 15 2.6245 2.9768 0.6912 1.3406 1.7531 2.1315 2.6025 2.9467 16 0.6901 1.3368 1.7459 2.1199 2.5835 17 2.9208 0.6892 1.3334 1.7396 2.1098 18 2.5669 2.8982 0.6884 1.3304 1.7341 2.1009 2.5524 19 2.8784 0.6876 1.3277 1.7291 2.0930 2.5395 2.8609 20 0.6870 1.3253 1.7247 2.0860 2.5280 2.8453 21 0.6864 1.3232 22 1.7207 2.0796 2.5177 0.6858 2.8314 1.3212 1.7171 2.0739 2.5083 2.8188\fCumulative Probabilities 0.75 0.90 0.95 0.975 0.99 0.995 Degrees of Upper-Tail Areas Freedom 0.25 0.10 0.05 0.025 0.01 0.005 49 0.6795 1.2991 1.6766 2.0096 2.4049 2.6800 50 0.6794 1.2987 1.6759 2.0086 2.4033 2.6778 51 0.6793 1.2984 1.6753 2.0076 2.4017 2.6757 52 0.6792 1.2980 1.6747 2.0066 2.4002 2.6737 53 0.6791 1.2977 1.6741 2.0057 2.3988 2.6718 54 0.6791 1.2974 1.6736 2.0049 2.3974 2.6700 55 0.6790 1.2971 1.6730 2.0040 2.3961 2.6682 56 0.6789 1.2969 1.6725 2.0032 2.3948 2.6665 57 0.6788 1.2966 1.6720 2.0025 2.3936 2.6649 58 0.6787 1.2963 1.6716 2.0017 2.3924 2.6633 59 0.6787 1.2961 1.6711 2.0010 2.3912 2.6618 60 0.6786 1.2958 1.6706 2.0003 2.3901 2.6603 0.6785 1.2956 1.6702 1.9996 2.3890 2.6589 0.6785 1.2954 1.6698 1.9990 2.3880 2.6575 0.6784 1.2951 1.6694 1.9983 2.3870 2.6561 0.6783 1.2949 1.6690 1.9977 2.3860 2.6549 0.6783 1.2947 1.6686 1.9971 2.3851 2.6536 0.6782 1.2945 1.6683 1.9966 2.3842 NE 80898 82892 2.6524 0.6782 1.2943 1.6679 1.9960 2.3833 2.6512 0.6781 1.2941 1.6676 1.9955 2.3824 2.6501 0.6781 1.2939 1.6672 1.9949 2.3816 2.6490 0.6780 1.2938 1.6669 1.9944 2.3808 2.6479 0.6780 1.2936 1.6666 1.9939 2.3800 2.6469 0.6779 1.2934 1.6663 1.9935 2.3793 2.6459 73 0.6779 1.2933 1.6660 1.9930 2.3785 2.6449 74 0.6778 1.2931 1.6657 1.9925 2.3778 2.6439 75 0.6778 1.2929 1.6654 1.9921 2.3771 2.643075 0.6778 1.2929 1.6654 1.9921 2.3771 2.6430 76 0.6777 1.2928 1.6652 1.9917 2.3764 2.6421 0.6777 1.2926 1.6649 1.9913 2.3758 2.6412 78 0.6776 1.2925 1.6646 1.9908 2.3751 2.6403 79 0.6776 1.2924 1.6644 1.9905 2.3745 2.6395 80 0.6776 1.2922 1.6641 1.9901 2.3739 2.6387 81 0.6775 1.2921 1.6639 1.9897 2.3733 2.6379 82 0.6775 1.2920 1.6636 1.9893 2.3727 2.6371 83 0.6775 1.2918 1.6634 1.9890 2.3721 2.6364 84 0.6774 1.2917 1.6632 1.9886 2.3716 2.6356 85 0.6774 1.2916 1.6630 1.9883 2.3710 2.6349 86 0.6774 1.2915 1.6628 1.9879 2.3705 2.6342 0.6773 1.2914 1.6626 1.9876 2.3700 2.6335 88 0.6773 1.2912 1.6624 1.9873 2.3695 2.6329 89 0.6773 1.2911 1.6622 1.9870 2.3690 2.6322 90 0.6772 1.2910 1.6620 1.9867 2.3685 2.6316 91 0.6772 1.2909 1.6618 1.9864 2.3680 2.6309 92 0.6772 1.2908 1.6616 1.9861 2.3676 2.6303 93 0.6771 1.2907 1.6614 1.9858 2.3671 2.6297 94 0.6771 1.2906 1.6612 1.9855 2.3667 2.6291 95 0.6771 1.2905 1.6611 1.9853 2.3662 2.6286 96 0.6771 1.2904 1.6609 1.9850 2.3658 2.6280 97 0.6770 1.2903 1.6607 1.9847 2.3654 2.6275 98 0.6770 1.2902 1.6606 1.9845 2.3650 2.6269 99 0.6770 1.2902 1.6604 1.9842 2.3646 2.6264 100 0.6770 1.2901 1.6602 1.9840 2.3642 2.6259 110 0.6767 1.2893 1.6588 1.9818 2.3607 2.6213 120 0.6765 1.2886 1.6577 1.9799 2.3578 2.6174 OO 0.6745 1.2816 1.6449 1.9600 2.3263 2.5758 (1 ) (2) > (3) O Do not reject (4) O insufficient OO V NV = O Reject ooOO H A IA II O sufficient ooOO H IA IV