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 minus alpha and a specified upper-tail area alpha. 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 0.0051 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 A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sampleof 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.155 ounces, with a sample standard deviation of 0.056ounce. Complete parts (a) and (b).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 Distributiona. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.01 level of significance.)State the null and alternative hypotheses.Hoi HH₁: H▼(Type integers or decimals.)...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 four decimal places as needed.)State the conclusion.Ho. There isevidence to conclude the population mean amount is different from 8.17 ounces. A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sampleof 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.155 ounces, with a sample standard deviation of 0.056ounce. Complete parts (a) and (b).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(Kouna to Tour decimal places as needea.)State the conclusion.evidence to conclude the population mean amount is different from 8.17 outices.Ho. There isb. Determine the p-value and interpret its meaning.The p-value is.(Round to four decimal places as needed.)Interpret the meaning of the p-value. Choose the correct answer below.OA. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.015 ounce above 8.17 if the null hypothesis isfalse.OB. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.015 ounce away from 8.17 if the nullhypothesis is true.OC. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.015 ounce below 8.17 if the null hypothesis isfalse.D. The p-value is the probability of not rejecting the null hypothesis when it is false.

Question

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 minus alpha and a specified upper-tail area alpha.							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	0.0051	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 A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sampleof 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.155 ounces, with a sample standard deviation of 0.056ounce. Complete parts (a) and (b).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 Distributiona. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.01 level of significance.)State the null and alternative hypotheses.Hoi HH₁: H▼(Type integers or decimals.)...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 four decimal places as needed.)State the conclusion.Ho. There isevidence to conclude the population mean amount is different from 8.17 ounces. A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sampleof 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.155 ounces, with a sample standard deviation of 0.056ounce. Complete parts (a) and (b).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(Kouna to Tour decimal places as needea.)State the conclusion.evidence to conclude the population mean amount is different from 8.17 outices.Ho. There isb. Determine the p-value and interpret its meaning.The p-value is.(Round to four decimal places as needed.)Interpret the meaning of the p-value. Choose the correct answer below.OA. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.015 ounce above 8.17 if the null hypothesis isfalse.OB. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.015 ounce away from 8.17 if the nullhypothesis is true.OC. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.015 ounce below 8.17 if the null hypothesis isfalse.D. The p-value is the probability of not rejecting the null hypothesis when it is false.

Accepted Answer

Given that:
Population mean, μ=8.17
Sample size, n = 50
Sample mean, x¯=8.155
Sample standard…