Critical Values of t 32 1.3086 1.6939 2.0369 2.4487 2.7385 66 1.2945 1.6683 1.9966 2.3842 2.6524 (1-tailed probabilities) 2 of 2 ID: MST.FET.HT.PAHT.02.0010A [3 marks] 33 1.3077 1.6924 2.0345 2.4448 2.7333 67 1.2943 1.6679 1.9960 2.3833 2.6512 34 68 A psychologist has developed an aptitude test which consists of a series of mathematical and vocabulary problems. They want to test the hypothesis that the mean test grees of 1.2941 1.6676 1.9955 2.3824 2.6501 reedom t.100 .050 t.025 t.010 t.005 1.3070 1.6909 2.0322 2.4411 2.7284 score is 63.0. 35 1.6896 2.0301 2.4377 2.7238 69 1.2939 1.6672 1.9949 2.3816 2.6490 A random sample of 40 people have taken the test and their results recorded: 3.0777 6.3138 12.7062 31.8207 63.6574 36 1.3055 1 5 1.6883 2.0281 2.4345 2.7195 70 .2938 1.6669 1.9944 2.3808 2.6479 2 1.8856 2.9200 4.3027 6.9646 9.9248 37 1.3049 1.6871 2.0262 2.4314 2.7154 1.2936 1.6666 1.9939 2.3800 2.6469 88 52 80 77 74 57 69 73 56 70 Download the data 3 1.6377 2.3534 3.1824 4.5407 5.8409 38 1.3042 1.6860 2.0244 2.4286 2.7116 72 .2934 1.6663 1.9935 2.3793 2.6459 57 66 72 94 76 63 58 81 52 90 1.5332 2.1318 2.7764 3.7469 4.6041 39 1.3036 1.6849 2.0227 2.4258 2.7079 73 1.2933 1.6660 1.9930 2.3785 2.6449 73 68 46 63 63 92 87 41 61 56 1.4759 2.0150 2.5706 3.3649 40 74 .2931 1.6657 1.9925 2.3778 2.6439 83 60 66 48 65 47 64 99 95 59 1.3031 1.6839 2.0211 2.4233 2.7045 1.4398 1.9432 2.4469 3.1427 3.7074 41 1.3025 1.6829 2.0195 2.4208 2.7012 75 1.2929 1.6654 1.9921 2.3771 2.6430 You may find this Student's t distribution table useful throughout this question. 1.4149 1.8946 2.3646 2.9980 3.4995 42 1.3020 1.6820 2.0181 2.4185 76 1.2928 1.6652 1.9917 2.3764 2.6421 1.3968 1.8595 2.3060 a) Calculate the test statistic (t) for the hypothesis test. Give your answer to 4 decimal places. 2.8965 3.3554 43 1.3016 1.6811 2.0167 2.4163 2.6951 77 1.2926 1.6649 1.9913 2.3758 2.6412 1.3830 1.8331 2.2622 2.8214 3.2498 t =[ 44 1.3011 1.6802 2.0154 2.4141 2.6923 78 1.2925 1.6646 1 1.9908 2.3751 2.6403 10 1.3722 1.8125 2.2281 2.7638 3.1693 45 .3006 1.6794 2.0141 2.4121 2.6896 79 1.2924 1.6644 1.9905 2.3745 2.6395 b) A level of significance of a = 0.05 is to be used for the test. The P-value for this test statistic is v than the level of significance. 11 1.3634 1.7959 2.2010 2.7181 3.1058 46 1.3022 1.6787 2.0129 2.4102 2.6870 80 1.2922 1.6641 1.9901 2.3739 2.6387 c) The result of this test is that the null hypothesis is less 12 1.3562 1.7823 2.1788 2.6810 3.0545 47 1.2998 1.6779 2.0117 2.4083 2.6846 81 1.2921 1.6639 1.9897 2.3733 2.6379 greater 13 1.3502 1.7709 2.1604 2.6503 3.0123 48 1.2994 1.6772 2.0106 2.4066 2.6822 82 1.2920 1.6636 1.9893 2.3727 2.6371 14 1.3450 1.7613 2.1448 2.6245 2.9768 49 1.2991 1.6766 2.0096 2.4049 2.6800 83 1.2918 1.6634 1.9890 2.3721 2.6364 15 1.3406 1.7531 2.1315 2.6025 2.9467 50 1.2987 1.6759 2.0086 2.4033 2.6778 84 1.2917 1.6632 1.9886 2.3716 2.6356 rejected 16 1.3368 1.7459 2.1199 2.5835 2.9208 51 1.2984 1.6753 2.0076 2.4017 2.6757 85 .2916 1.6630 1.9883 2.3710 2.6349 not rejected 17 1.3334 1.7396 2.1098 2.5669 2.8982 52 1.2980 1.6747 2.0066 2.4002 2.6737 86 .2915 1.6628 1.9879 2.3705 2.6342 18 1.3304 1.7341 2.1009 2.5524 2.8784 53 1.2977 1.6741 2.0057 2.3988 2.6718 87 1.2914 1.6626 1.9876 2.3700 2.6335 19 1.3277 1.7291 2.0930 2.5395 2.8609 54 1.2974 1.6736 2.0049 2.3974 2.6700 88 1.2912 1.6624 1.9873 2.3695 2.6329 20 1.3253 1.7247 2.0860 2.5280 2.8453 55 1.2971 1.6730 2.0040 2.3961 2.6682 89 1.2911 1.6622 1.9870 2.3690 2.6322 21 1.3232 1.7207 2.0796 2.5177 2.8314 56 1.2969 1.6725 2.0032 2.3948 2.6565 90 1.2910 1.6620 1.9867 2.3685 2.6316 22 1.3212 1.7171 2.0739 2.5083 2.8188 57 1.2966 1.6720 2.0025 2.3936 2.6649 91 1.2909 1.6618 1.9864 2.3680 2.6309 23 1.3195 1.7139 2.0687 2.4999 2.8073 58 1.2963 1.6716 2.0017 2.3924 2.6633 92 1.2908 1.6616 1.9861 2.3676 2.6303 24 1.3178 1.7109 2.0639 2.4922 2.7969 59 1.2961 1.6711 2.0010 2.3912 2.6618 93 1.2907 1.6614 1.9858 2.3671 2.6297 25 1.3163 1.7081 2.0595 2.4851 2.7874 60 1.2958 1.6706 2.0003 2.3901 2.6603 94 1.2906 1.6612 1.9855 2.3667 2.6291 26 1.3150 1.7056 2.0555 2.4786 2.7787 61 1.2956 1.6702 1.9996 2.3890 2.6589 95 1.2905 1.6611 1.9853 2.3662 2.6286 27 1.3137 1.7033 2.0518 3 2.4727 2.7707 62 1.2954 1.6698 1.9990 2.3880 2.6575 96 1.2904 1.6609 1.9850 2.3658 2.6280 28 1.3125 1.7011 2.0484 2.4671 2.7633 63 1.2951 1.6694 1.9983 2.3870 2.6561 97 .2903 1.6607 1.9847 2.3654 2.6275 29 1.3114 1.6991 2.0452 2.4620 2.7564 64 1.2949 1.6690 1.9977 2.3860 2.6549 98 .2902 1.6606 1.9845 2.3650 2.6269 30 1.3104 1.6973 2.0423 2.4573 2.7500 65 1.2947 1.6686 1.9971 1 2.3851 2.6536 99 .2902 1.6604 1.9842 2.3646 2.6264 31 1.3095 1.6955 65 2.0395 2.4528 2.7740 66 1.2945 1.6683 1.9966 2.3842 2.6524 100 .2901 1.6602 1.9840 2.3642 2.6259