0.75 0.90 0.95 0.975 0.99 0.995 Upper-Tail Areas Degrees of Freedom 0.25 0.10 0.05 0.025 0.01 0.0051 1.0000 3.0777 6.3138 12.7062 31.8207 63.65742 0.8165 1.8856 2.9200 4.3027 6.9646 9.92483 0.7649 1.6377 2.3534 3.1824 4.5407 5.84094 0.7407 1.5332 2.1318 2.7764 3.7469 4.60415 0.7267 1.4759 2.0150 2.5706 3.3649 4.03226 0.7176 1.4398 1.9432 2.4469 3.1427 3.70747 0.7111 1.4149 1.8946 2.3646 2.9980 3.49958 0.7064 1.3968 1.8595 2.3060 2.8965 3.35549 0.7027 1.3830 1.8331 2.2622 2.8214 3.249810 0.6998 1.3722 1.8125 2.2281 2.7638 3.169311 0.6974 1.3634 1.7959 2.2010 2.7181 3.105812 0.6955 1.3562 1.7823 2.1788 2.6810 3.054513 0.6938 1.3502 1.7709 2.1604 2.6503 3.012314 0.6924 1.3450 1.7613 2.1448 2.6245 2.976815 0.6912 1.3406 1.7531 2.1315 2.6025 2.946716 0.6901 1.3368 1.7459 2.1199 2.5835 2.920817 0.6892 1.3334 1.7396 2.1098 2.5669 2.898218 0.6884 1.3304 1.7341 2.1009 2.5524 2.878419 0.6876 1.3277 1.7291 2.0930 2.5395 2.860920 0.6870 1.3253 1.7247 2.0860 2.5280 2.845321 0.6864 1.3232 1.7207 2.0796 2.5177 2.831422 0.6858 1.3212 1.7171 2.0739 2.5083 2.818823 0.6853 1.3195 1.7139 2.0687 2.4999 2.807324 0.6848 1.3178 1.7109 2.0639 2.4922 2.796925 0.6844 1.3163 1.7081 2.0595 2.4851 2.787426 0.6840 1.3150 1.7056 2.0555 2.4786 2.778727 0.6837 1.3137 1.7033 2.0518 2.4727 2.770728 0.6834 1.3125 1.7011 2.0484 2.4671 2.763329 0.6830 1.3114 1.6991 2.0452 2.4620 2.756430 0.6828 1.3104 1.6973 2.0423 2.4573 2.750031 0.6825 1.3095 1.6955 2.0395 2.4528 2.744032 0.6822 1.3086 1.6939 2.0369 2.4487 2.738533 0.6820 1.3077 1.6924 2.0345 2.4448 2.733334 0.6818 1.3070 1.6909 2.0322 2.4411 2.728435 0.6816 1.3062 1.6896 2.0301 2.4377 2.723836 0.6814 1.3055 1.6883 2.0281 2.4345 2.719537 0.6812 1.3049 1.6871 2.0262 2.4314 2.715438 0.6810 1.3042 1.6860 2.0244 2.4286 2.711639 0.6808 1.3036 1.6849 2.0227 2.4258 2.707940 0.6807 1.3031 1.6839 2.0211 2.4233 2.704541 0.6805 1.3025 1.6829 2.0195 2.4208 2.701242 0.6804 1.3020 1.6820 2.0181 2.4185 2.698143 0.6802 1.3016 1.6811 2.0167 2.4163 2.695144 0.6801 1.3011 1.6802 2.0154 2.4141 2.692345 0.6800 1.3006 1.6794 2.0141 2.4121 2.689646 0.6799 1.3002 1.6787 2.0129 2.4102 2.687047 0.6797 1.2998 1.6779 2.0117 2.4083 2.684648 0.6796 1.2994 1.6772 2.0106 2.4066 2.6822Critical Values of t. Cumulative Probabilities 0.75 0.90 0.95 0.975 0.99 0.995 Upper-Tail Areas Degrees of Freedom 0.25 0.10 0.05 0.025 0.01 0.00549 0.6795 1.2991 1.6766 2.0096 2.4049 2.680050 0.6794 1.2987 1.6759 2.0086 2.4033 2.677851 0.6793 1.2984 1.6753 2.0076 2.4017 2.675752 0.6792 1.2980 1.6747 2.0066 2.4002 2.673753 0.6791 1.2977 1.6741 2.0057 2.3988 2.671854 0.6791 1.2974 1.6736 2.0049 2.3974 2.670055 0.6790 1.2971 1.6730 2.0040 2.3961 2.668256 0.6789 1.2969 1.6725 2.0032 2.3948 2.666557 0.6788 1.2966 1.6720 2.0025 2.3936 2.664958 0.6787 1.2963 1.6716 2.0017 2.3924 2.663359 0.6787 1.2961 1.6711 2.0010 2.3912 2.661860 0.6786 1.2958 1.6706 2.0003 2.3901 2.660361 0.6785 1.2956 1.6702 1.9996 2.3890 2.658962 0.6785 1.2954 1.6698 1.9990 2.3880 2.657563 0.6784 1.2951 1.6694 1.9983 2.3870 2.656164 0.6783 1.2949 1.6690 1.9977 2.3860 2.654965 0.6783 1.2947 1.6686 1.9971 2.3851 2.653666 0.6782 1.2945 1.6683 1.9966 2.3842 2.652467 0.6782 1.2943 1.6679 1.9960 2.3833 2.651268 0.6781 1.2941 1.6676 1.9955 2.3824 2.650169 0.6781 1.2939 1.6672 1.9949 2.3816 2.649070 0.6780 1.2938 1.6669 1.9944 2.3808 2.647971 0.6780 1.2936 1.6666 1.9939 2.3800 2.646972 0.6779 1.2934 1.6663 1.9935 2.3793 2.645973 0.6779 1.2933 1.6660 1.9930 2.3785 2.644974 0.6778 1.2931 1.6657 1.9925 2.3778 2.643975 0.6778 1.2929 1.6654 1.9921 2.3771 2.643076 0.6777 1.2928 1.6652 1.9917 2.3764 2.642177 0.6777 1.2926 1.6649 1.9913 2.3758 2.641278 0.6776 1.2925 1.6646 1.9908 2.3751 2.640379 0.6776 1.2924 1.6644 1.9905 2.3745 2.639580 0.6776 1.2922 1.6641 1.9901 2.3739 2.638781 0.6775 1.2921 1.6639 1.9897 2.3733 2.637982 0.6775 1.2920 1.6636 1.9893 2.3727 2.637183 0.6775 1.2918 1.6634 1.9890 2.3721 2.636484 0.6774 1.2917 1.6632 1.9886 2.3716 2.635685 0.6774 1.2916 1.6630 1.9883 2.3710 2.634986 0.6774 1.2915 1.6628 1.9879 2.3705 2.634287 0.6773 1.2914 1.6626 1.9876 2.3700 2.633588 0.6773 1.2912 1.6624 1.9873 2.3695 2.632989 0.6773 1.2911 1.6622 1.9870 2.3690 2.632290 0.6772 1.2910 1.6620 1.9867 2.3685 2.631691 0.6772 1.2909 1.6618 1.9864 2.3680 2.630992 0.6772 1.2908 1.6616 1.9861 2.3676 2.630393 0.6771 1.2907 1.6614 1.9858 2.3671 2.629794 0.6771 1.2906 1.6612 1.9855 2.3667 2.629195 0.6771 1.2905 1.6611 1.9853 2.3662 2.628696 0.6771 1.2904 1.6609 1.9850 2.3658 2.628097 0.6770 1.2903 1.6607 1.9847 2.3654 2.627598 0.6770 1.2902 1.6606 1.9845 2.3650 2.626999 0.6770 1.2902 1.6604 1.9842 2.3646 2.6264100 0.6770 1.2901 1.6602 1.9840 2.3642 2.6259110 0.6767 1.2893 1.6588 1.9818 2.3607 2.6213120 0.6765 1.2886 1.6577 1.9799 2.3578 2.6174infinity 0.6745 1.2816 1.6449 1.9600 2.3263 2.5758 If, in a sample of n = 30 selected from a normal population, X= 57 and S=20, what is your statistical decision if the level of significance, a, is 0.10, thenull hypothesis, Ho, is μ = 50, and the alternative hypothesis, H₁, is µ #50?Click here to view page 1 of the table of the critical values of t. Click here to view page 2 of the table of the critical values of t.………Determine 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, ISTAT.ISTAT =(Round to four decimal places as needed.)State your statistical decision. Choose the correct answer below.OA. The test rejects the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from μ = 50.OB. The test does not reject the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from μ = 50.OC. The test does not reject the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from μ = 50.OD. The test rejects the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from μ = 50.

Question

0.75	0.90	0.95	0.975	0.99	0.995	Upper-Tail Areas					Degrees of Freedom	0.25	0.10	0.05	0.025	0.01	0.0051	1.0000	3.0777	6.3138	12.7062	31.8207	63.65742	0.8165	1.8856	2.9200	4.3027	6.9646	9.92483	0.7649	1.6377	2.3534	3.1824	4.5407	5.84094	0.7407	1.5332	2.1318	2.7764	3.7469	4.60415	0.7267	1.4759	2.0150	2.5706	3.3649	4.03226	0.7176	1.4398	1.9432	2.4469	3.1427	3.70747	0.7111	1.4149	1.8946	2.3646	2.9980	3.49958	0.7064	1.3968	1.8595	2.3060	2.8965	3.35549	0.7027	1.3830	1.8331	2.2622	2.8214	3.249810	0.6998	1.3722	1.8125	2.2281	2.7638	3.169311	0.6974	1.3634	1.7959	2.2010	2.7181	3.105812	0.6955	1.3562	1.7823	2.1788	2.6810	3.054513	0.6938	1.3502	1.7709	2.1604	2.6503	3.012314	0.6924	1.3450	1.7613	2.1448	2.6245	2.976815	0.6912	1.3406	1.7531	2.1315	2.6025	2.946716	0.6901	1.3368	1.7459	2.1199	2.5835	2.920817	0.6892	1.3334	1.7396	2.1098	2.5669	2.898218	0.6884	1.3304	1.7341	2.1009	2.5524	2.878419	0.6876	1.3277	1.7291	2.0930	2.5395	2.860920	0.6870	1.3253	1.7247	2.0860	2.5280	2.845321	0.6864	1.3232	1.7207	2.0796	2.5177	2.831422	0.6858	1.3212	1.7171	2.0739	2.5083	2.818823	0.6853	1.3195	1.7139	2.0687	2.4999	2.807324	0.6848	1.3178	1.7109	2.0639	2.4922	2.796925	0.6844	1.3163	1.7081	2.0595	2.4851	2.787426	0.6840	1.3150	1.7056	2.0555	2.4786	2.778727	0.6837	1.3137	1.7033	2.0518	2.4727	2.770728	0.6834	1.3125	1.7011	2.0484	2.4671	2.763329	0.6830	1.3114	1.6991	2.0452	2.4620	2.756430	0.6828	1.3104	1.6973	2.0423	2.4573	2.750031	0.6825	1.3095	1.6955	2.0395	2.4528	2.744032	0.6822	1.3086	1.6939	2.0369	2.4487	2.738533	0.6820	1.3077	1.6924	2.0345	2.4448	2.733334	0.6818	1.3070	1.6909	2.0322	2.4411	2.728435	0.6816	1.3062	1.6896	2.0301	2.4377	2.723836	0.6814	1.3055	1.6883	2.0281	2.4345	2.719537	0.6812	1.3049	1.6871	2.0262	2.4314	2.715438	0.6810	1.3042	1.6860	2.0244	2.4286	2.711639	0.6808	1.3036	1.6849	2.0227	2.4258	2.707940	0.6807	1.3031	1.6839	2.0211	2.4233	2.704541	0.6805	1.3025	1.6829	2.0195	2.4208	2.701242	0.6804	1.3020	1.6820	2.0181	2.4185	2.698143	0.6802	1.3016	1.6811	2.0167	2.4163	2.695144	0.6801	1.3011	1.6802	2.0154	2.4141	2.692345	0.6800	1.3006	1.6794	2.0141	2.4121	2.689646	0.6799	1.3002	1.6787	2.0129	2.4102	2.687047	0.6797	1.2998	1.6779	2.0117	2.4083	2.684648	0.6796	1.2994	1.6772	2.0106	2.4066	2.6822Critical Values of t.							Cumulative Probabilities						0.75	0.90	0.95	0.975	0.99	0.995	Upper-Tail Areas					Degrees of Freedom	0.25	0.10	0.05	0.025	0.01	0.00549	0.6795	1.2991	1.6766	2.0096	2.4049	2.680050	0.6794	1.2987	1.6759	2.0086	2.4033	2.677851	0.6793	1.2984	1.6753	2.0076	2.4017	2.675752	0.6792	1.2980	1.6747	2.0066	2.4002	2.673753	0.6791	1.2977	1.6741	2.0057	2.3988	2.671854	0.6791	1.2974	1.6736	2.0049	2.3974	2.670055	0.6790	1.2971	1.6730	2.0040	2.3961	2.668256	0.6789	1.2969	1.6725	2.0032	2.3948	2.666557	0.6788	1.2966	1.6720	2.0025	2.3936	2.664958	0.6787	1.2963	1.6716	2.0017	2.3924	2.663359	0.6787	1.2961	1.6711	2.0010	2.3912	2.661860	0.6786	1.2958	1.6706	2.0003	2.3901	2.660361	0.6785	1.2956	1.6702	1.9996	2.3890	2.658962	0.6785	1.2954	1.6698	1.9990	2.3880	2.657563	0.6784	1.2951	1.6694	1.9983	2.3870	2.656164	0.6783	1.2949	1.6690	1.9977	2.3860	2.654965	0.6783	1.2947	1.6686	1.9971	2.3851	2.653666	0.6782	1.2945	1.6683	1.9966	2.3842	2.652467	0.6782	1.2943	1.6679	1.9960	2.3833	2.651268	0.6781	1.2941	1.6676	1.9955	2.3824	2.650169	0.6781	1.2939	1.6672	1.9949	2.3816	2.649070	0.6780	1.2938	1.6669	1.9944	2.3808	2.647971	0.6780	1.2936	1.6666	1.9939	2.3800	2.646972	0.6779	1.2934	1.6663	1.9935	2.3793	2.645973	0.6779	1.2933	1.6660	1.9930	2.3785	2.644974	0.6778	1.2931	1.6657	1.9925	2.3778	2.643975	0.6778	1.2929	1.6654	1.9921	2.3771	2.643076	0.6777	1.2928	1.6652	1.9917	2.3764	2.642177	0.6777	1.2926	1.6649	1.9913	2.3758	2.641278	0.6776	1.2925	1.6646	1.9908	2.3751	2.640379	0.6776	1.2924	1.6644	1.9905	2.3745	2.639580	0.6776	1.2922	1.6641	1.9901	2.3739	2.638781	0.6775	1.2921	1.6639	1.9897	2.3733	2.637982	0.6775	1.2920	1.6636	1.9893	2.3727	2.637183	0.6775	1.2918	1.6634	1.9890	2.3721	2.636484	0.6774	1.2917	1.6632	1.9886	2.3716	2.635685	0.6774	1.2916	1.6630	1.9883	2.3710	2.634986	0.6774	1.2915	1.6628	1.9879	2.3705	2.634287	0.6773	1.2914	1.6626	1.9876	2.3700	2.633588	0.6773	1.2912	1.6624	1.9873	2.3695	2.632989	0.6773	1.2911	1.6622	1.9870	2.3690	2.632290	0.6772	1.2910	1.6620	1.9867	2.3685	2.631691	0.6772	1.2909	1.6618	1.9864	2.3680	2.630992	0.6772	1.2908	1.6616	1.9861	2.3676	2.630393	0.6771	1.2907	1.6614	1.9858	2.3671	2.629794	0.6771	1.2906	1.6612	1.9855	2.3667	2.629195	0.6771	1.2905	1.6611	1.9853	2.3662	2.628696	0.6771	1.2904	1.6609	1.9850	2.3658	2.628097	0.6770	1.2903	1.6607	1.9847	2.3654	2.627598	0.6770	1.2902	1.6606	1.9845	2.3650	2.626999	0.6770	1.2902	1.6604	1.9842	2.3646	2.6264100	0.6770	1.2901	1.6602	1.9840	2.3642	2.6259110	0.6767	1.2893	1.6588	1.9818	2.3607	2.6213120	0.6765	1.2886	1.6577	1.9799	2.3578	2.6174infinity	0.6745	1.2816	1.6449	1.9600	2.3263	2.5758 If, in a sample of n = 30 selected from a normal population, X= 57 and S=20, what is your statistical decision if the level of significance, a, is 0.10, thenull hypothesis, Ho, is μ = 50, and the alternative hypothesis, H₁, is µ #50?Click here to view page 1 of the table of the critical values of t. Click here to view page 2 of the table of the critical values of t.………Determine 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, ISTAT.ISTAT =(Round to four decimal places as needed.)State your statistical decision. Choose the correct answer below.OA. The test rejects the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from μ = 50.OB. The test does not reject the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from μ = 50.OC. The test does not reject the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from μ = 50.OD. The test rejects the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from μ = 50.

Accepted Answer

Given information:
Population mean is specified as μ=50.
Sample mean is x¯=57.
Sample standard…