If, in a sample of n = 20 selected from a normal population, X = 60 and S = 20, what are the critical values of t if the level of significance, x, is 0.10, the null hypothesis, Ho, is =50, and the alternative hypothesis, H, is #50? Click here to view page 1 of the critical values for the t Distribution. Click here to view page 2 of the critical values for the t Distribution. The critical values of t are (Round to four decimal places as needed.) Critical Values for the t Distribution. 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). t 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 1.0000 3.0777 6.3138 12.7062 31.8207 63.6574 2345 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 10 11 12 13 14 15 67890225 879 0.7176 1.4398 1.9432 2.4469 3.1427 3.7074 0.7111 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 3.2498 0.6998 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 2.6245 2.9768 0.6912 1.3406 1.7531 2.1315 2.6025 2.9467 0.6901 1.3368 1.7459 2.1199 2.5835 2.9208 0.6892 1.3334 1.7396 2.1098 2.5669 2.8982 0.6884 1.3304 1.7341 2.1009 2.5524 2.8784 31 36 40 41 42 43 44 45 46 47 48 222222222228-23223233379*** 4 4 4 19 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 1.7207 2.0796 2.5177 2.8314 0.6858 1.3212 1.7171 2.0739 2.5083 2.8188 0.6853 1.3195 1.7139 2.0687 2.4999 2.8073 24 0.6848 1.3178 1.7109 2.0639 2.4922 2.7969 25 0.6844 1.3163 1.7081 2.0595 2.4851 2.7874 26 0.6840 1.3150 1.7056 2.0555 2.4786 2.7787 0.6837 1.3137 1.7033 2.0518 2.4727 2.7707 0.6834 1.3125 1.7011 2.0484 2.4671 2.7633 0.6830 1.3114 1.6991 2.0452 2.4620 2.7564 30 0.6828 1.3104 1.6973 2.0423 2.4573 2.7500 0.6825 1.3095 1.6955 2.0395 2.4528 2.7440 0.6822 1.3086 1.6939 2.0369 2.4487 2.7385 0.6820 1.3077 1.6924 2.0345 2.4448 2.7333 34 0.6818 1.3070 1.6909 2.0322 2.4411 2.7284 35 0.6816 1.3062 1.6896 2.0301 2.4377 2.7238 0.6814 1.3055 1.6883 2.0281 2.4345 2.7195 0.6812 1.3049 1.6871 2.0262 2.4314 2.7154 0.6810 1.3042 1.6860 2.0244 2.4286 2.7116 0.6808 1.3036 1.6849 2.0227 2.4258 2.7079 0.6807 1.3031 1.6839 2.0211 2.4233 2.7045 0.6805 1.3025 1.6829 2.0195 2.4208 2.7012 0.6804 1.3020 1.6820 2.0181 2.4185 2.6981 0.6802 1.3016 1.6811 2.0167 2.4163 2.6951 0.6801 1.3011 1.6802 2.0154 2.4141 2.6923 0.6800 1.3006 1.6794 2.0141 2.4121 2.6896 0.6799 1.3002 1.6787 2.0129 2.4102 2.6870 0.6797 1.2998 1.6779 2.0117 2.4083 2.6846 0.6796 1.2994 1.6772 2.0106 2.4066 2.6822 40 41 42 43 44 45 22222222222223247 7 7 7 7 25 0.6844 1.3163 1.7081 2.0595 2.4851 2.7874 26 0.6840 1.3150 1.7056 2.0555 2.4786 2.7787 0.6837 1.3137 1.7033 2.0518 2.4727 2.7707 28 0.6834 1.3125 1.7011 2.0484 2.4671 2.7633 29 0.6830 1.3114 1.6991 2.0452 2.4620 2.7564 30 0.6828 1.3104 1.6973 2.0423 2.4573 2.7500 31 0.6825 1.3095 1.6955 2.0395 2.4528 2.7440 0.6822 1.3086 1.6939 2.0369 2.4487 2.7385 33 0.6820 1.3077 1.6924 2.0345 2.4448 2.7333 0.6818 1.3070 1.6909 2.0322 2.4411 2.7284 35 0.6816 1.3062 1.6896 2.0301 2.4377 2.7238 36 0.6814 1.3055 1.6883 2.0281 2.4345 2.7195 0.6812 1.3049 1.6871 2.0262 2.4314 2.7154 38 0.6810 1.3042 1.6860 2.0244 2.4286 2.7116 39 0.6808 1.3036 1.6849 2.0227 2.4258 2.7079 0.6807 1.3031 1.6839 2.0211 2.4233 2.7045 0.6805 1.3025 1.6829 2.0195 2.4208 2.7012 0.6804 1.3020 1.6820 2.0181 2.4185 2.6981 0.6802 1.3016 1.6811 2.0167 2.4163 2.6951 0.6801 1.3011 1.6802 2.0154 2.4141 2.6923 0.6800 1.3006 1.6794 2.0141 2.4121 2.6896 46 0.6799 1.3002 1.6787 2.0129 2.4102 2.6870 47 0.6797 1.2998 1.6779 2.0117 2.4083 2.6846 48 0.6796 1.2994 1.6772 2.0106 2.4066 2.6822 Degrees of 0.25 0.10 0.05 0.025 0.01 0.005 Freedom Upper-Tail Areas 0.75 0.90 0.95 0.975 0.99 0.995 Cumulative Probabilities Critical Values for the t Distribution. Cumulative Probabilities 0.75 0.90 0.95 0.975 0.99 0.995 Degrees of Freedom Upper-Tail Areas 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 69 71 8 85888 TO 6882 F 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 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 61 0.6785 1.2956 1.6702 1.9996 2.3890 2.6589 62 0.6785 1.2954 1.6698 1.9990 2.3880 2.6575 63 0.6784 1.2951 1.6694 1.9983 2.3870 2.6561 64 0.6783 1.2949 1.6690 1.9977 2.3860 2.6549 65 0.6783 1.2947 1.6686 1.9971 2.3851 2.6536 66 0.6782 1.2945 1.6683 1.9966 2.3842 2.6524 67 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 70 0.6780 1.2938 1.6669 1.9944 2.3808 2.6479 0.6780 1.2936 1.6666 1.9939 2.3800 2.6469 Critical Values for the t Distribution. 98 99 100 FILAS 322222222228 0.6780 1.2936 1.6666 1.9939 2.3800 2.6469 72 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 2.6430 76 0.6777 1.2928 1.6652 1.9917 2.3764 2.6421 77 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 87 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 0.6770 1.2902 1.6606 1.9845 2.3650 2.6269 0.6770 1.2902 1.6604 1.9842 2.3646 2.6264 0.6770 1.2901 1.6602 1.9840 2.3642 2.6259 0.6775 1.2921 1.6639 1.9897 2.3733 2.6379 0.6775 1.2920 1.6636 1.9893 2.3727 2.6371 0.6775 1.2918 1.6634 1.9890 2.3721 2.6364 0.6774 1.2917 1.6632 1.9886 2.3716 2.6356 0.6774 1.2916 1.6630 1.9883 2.3710 2.6349 0.6774 1.2915 1.6628 1.9879 2.3705 2.6342 0.6773 1.2914 1.6626 1.9876 2.3700 2.6335 100 110 120 3222222222282 0.6773 1.2912 1.6624 1.9873 2.3695 2.6329 0.6773 1.2911 1.6622 1.9870 2.3690 2.6322 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 0.6772 1.2908 1.6616 1.9861 2.3676 2.6303 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 0.6771 1.2905 1.6611 1.9853 2.3662 2.6286 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 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 0.6770 1.2901 1.6602 1.9840 2.3642 2.6259 0.6767 1.2893 1.6588 1.9818 2.3607 2.6213 0.6765 1.2886 1.6577 1.9799 2.3578 2.6174 0.6745 1.2816 1.6449 1.9600 2.3263 2.5758 Degrees of Upper-Tail Areas Freedom 0.25 0.10 0.05 0.025 0.01 0.005 Cumulative Probabilities 0.75 0.90 0.95 0.975 0.99 0.995