The label of caviar cans of a certain brand states that they contain a net weight...

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The label of caviar cans of a certain brand states that they contain a net weight of 50 grams. It is given that the net weights of the cans are normally distributed with a standard deviation of 1.5 grams. To see whether the claim on the label is true, a sample of 36 cans is taken. The obtained sample mean of net weights is 49.5 grams. [Problem I] Test the null hypothesis that the average net weight of caviar cans is 50 grams against the alternative hypothesis that this average is smaller than 50 grams. Use a significance level of 5%. [20] [Problem II] Compute the power of the test in (b) if the actual average net weight of caviar cans is 49.3 grams. [20] Table 3-App B (pp. B-8/B-9) - Cumulative Standardized Normal Probabilities P(Z< 2) 0 09 0 0010 0. 03 0.00 -3.0 0.0013 -2.9 0.0019 -2.8 0 0026 -2.7 0.0035 -2.6 0.0047 -2.5 0 0082 -2.4 0 0082 -2.3 0 0107 -2.2 0.0139 0.01 00013 0 00 18 0 0025 0.05 0 0011 0 00 18 0 0022 0.06 0.07 0 0011 0.0011 0 0015 0.00 15 0 0021 0.02 0.0013 0.08 00010 0.04 0 0012 0.0012 -3.0 -2.9 -2.8 2.7 -2.6 2.5 -2.4 2.3 -2.2 0 0014 0 0020 0.0018 00017 0.0016 0.0014 0 0023 0 0032 0 0043 0 0057 0 0075 0 0099 0 0019 0.0028 0 0038 0 0048 0 0084 0 0084 0.0023 0.0031 0.0024 0.0021 00034 0.0033 0.0030 0 0029 0.0028 00027 0.0041 0.0055 0 0073 0 0098 0 0125 00122 0 0040 0 0054 00039 0 0037 0 0049 0 0068 0 0087 00045 0.0044 0.0038 0 0051 0 0052 0 0089 0.0000 0.0059 0 0080 00104 0 0088 0.0078 00102 00071 0 0094 0 0091 0.0089 00138 0.0132 00129 00119 0.0118 00113 00110 Table 3-AppB(pp. B-BB-9)- Cumulative 5tandardized Normal Probabilities P(Z< 2) 0.00 3.0 0.0013 0 0013 2.9 0 0019 000 18 2.8 0.0026 2,7 0.0035 2.6 0.0047 2.5 0.0062 2.4 0.0082 2.3 00107 2.2 0.0139 00138 0.0132 00129 2.1 0.0179 00174 2.0 0 0228 1.9 00287 00281 1.8 0.0369 1.7 0.0440 -1.6 0.0548 1.5 0 0868 1.4 00808 1.3 0.0968 1.2 01151 1.1 0.1357 1.0 0 1587 01502 0.9 0.1841 -0.8 02119 0.7 02420 -0.6 0.2743 -0.5 0.3085 -0.4 0.01 0.03 0.02 0.0013 00012 0.0012 00011 00011 0.0011 000 10 0.0018 0 0017 0 00 10 0 00 16 00015 0.0015 00014 0.0024 00023 0 0023 0 0022 00021 0.0033 00032 0.04 0.05 0.06 0.07 0.09 0 0010-3.0 00014 -2.9 00019 -2.8 0.0028 -2.7 0.0038 0.08 00025 00034 0.0021 00020 0 0045 0 0060 00080 00104 0.0031 00030 00029 0 0028 00027 0 0041 0.0055 00054 0.0052 0 0051 00049 0.0073 00071 0.0096 00094 00091 0 0089 00087 00084-2.3 0 0125 00122 00119 00116 00113 00110 -22 0.0162 00158 00154 0.0150 0.0148 00143-2.1 0.0044 00043 00040 00039 0 0038 0.0037 -2.6 -2.5 -2.4 0 0069 0 0057 00075 0.0102 00099 00048 0.0078 000e9 0 00C8 0 0068 00084 0.0170 00166 00222 00217 00212 00207 0.0274 00202 00197 00192 00188 00183 2.0 00250 0.0288 00202 00338 0.0329 00322 0.0250 0.0244 00239 00233 1,9 00294 1.8 00392 0.0384 00375 003671.7 00351 00344 00314 0.0307 00301 0.0427 00418 00526 00516 0.0843 00e30 0.0818 00778 0.0934 00438 0.0409 00401 0.0505 00537 0 0655 00783 00495 00485 00475 00465 004651.6 00608 00594 0.0582 00571 0 0708 00e94 00889 0.0853 00838 0 1020 0 1003 00784 0.0749 00738 00918 0.0901 00885 00559 -1.5 -1.4 00721 00951 01131 00681 00823 -1.3 01112 01093 0.1314 0.1539 01515 0.1492 01409 0 1448 0.1423 0 1401 0 1788 0.2061 0.2358 0.1075 0 1056 0 1038 0.1230 00985-1.2 01335 01292 0 1271 01251 0.1210 0.1190 01170 1.1 0.1379 -1.0 01814 0 1736 01711 0.2005 0.1977 0.2296 02208 0.1762 0 1685 0.1680 0.1835 0 1011 0.9 0 2090 0 2033 02327 0 1949 0.1922 0 1894 01887 -0.0 02389 02236 0.2208 02177 02148 0.7 02709 0.2876 02643 02981 0.2811 02578 02548 0.2514 02483 -0.6 02877 0.2843 02810 02776 02481 0 3050 0.30 15 02948 02912 -0.5 0 3228 03192 03158 0 3121-0.4 03483 -0.3 0 3859 -0.2 04286 04247 0 3448 03409 0.3 0 3821 03783 -0.2 04207 04108 0.1 04602 0.0 0.5000 0.0 0 5000 0.1 0.5398 05438 0.2 0.5793 05832 0.3 0.0179 0.4 0 6654 0.5 0 0915 0.6 07257 0.7 07580 0.8 0.7881 0.9 0.8169 1.0 0 8413 1.1 0 8643 1.2 08849 1.3 0.9032 0 9049 0 9oee 0 9082 1.4 09192 0 9207 1.5 08332 1.6 0 5452 1.7 09554 1.8 1.9 09713 2.0 0.9772 2.1 0.9821 2.2 0.9601 2.3 0 9693 24 09918 2.6 0 9938 0 3372 0 3336 0 3300 0 3264 0 3745 0370O7 0 4090 04483 0.3609 03632 04129 0.4522 0.4052 0.4013 0.4443 0.3594 0 3857 0 3520 0.3974 03936 0 3897 0.4325 0.4502 0 4404 04801 0.4364 -0.1 04960 0 5040 0.4920 0.5080 0.5478 04880 05120 0.4840 0.5160 05199 0.5557 05596 04761 04721 05239 0 6279 0 4681 04641 -0.0 0.0 0.5636 0.5075 05714 0 5763 0.5319 05369 05517 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5871 0.5910 0.5948 05987 06293 0.e331 06368 oe406 0 e020 0.60e4 08103 0 6443 08480 0.0809 0 e844 06141 06217 0 e255 08591 00950 06517 0C879 07224 0.0028 0.6700 06738 0 7054 07088 07123 0.7157 07190 0 7389 07422 07454 07486 07517 07549 06772 0 0985 07324 07019 07291 07357 0.7842 0.7673 07704 07734 07784 0.7939 07907 0 7995 0 B023 08051 07611 0.7794 07823 07852 0.7910 08188 0.8 0 8212 08238 0 264 0 8289 08315 0.8340 0 8305 O8389 0.9 0 8078 08106 08133 08438 0 8461 0 BC80 0 0888 08485 0 8508 08531 O8708 OB907 0 8925 0 8944 08902 0 8980 O8584 0.8577 O8599 0 Be21 1.0 0 8665 08809 0 8729 08749 08770 0 8790 O8810 08830 1.1 0 9015 O8997 1.2 0.9147 0912 09177 0 9099 09115 09131 0 8251 0 9382 09495 0.9691 0 9871 09678 09086 0 9093 0 9e99 09738 09744 09750 0 9750 09701 O 9793 09798 1.3 09308 09319 0.9222 0 9236 09265 0 9279 09292 09 406 09418 09429 0 9515 0.9525 09536 0 9599 09608 0.9816 0 9025 1.4 1.5 1.6 0 9C33 09345 09483 0.9357 09370 09394 09505 09441 09545 0 9474 09484 0 9564 0.9649 09673 09582 1.7 9841 0 9656 0 9004 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.0 2.9 3.0 09706 0 9719 09778 0 9720 09732 09767 0.9817 0.9857 0 9783 09788 09903 0.9808 0 9812 098 30 09828 09804 09896 09834 0.9838 0 982 09846 0 9850 0 9854 0 9871 0 9901 0 9925 0 9027 0 9929 0 9931 0 9932 0 9934 09943 09967 0 9875 09878 0.9904 09908 0 9909 0.9911 09913 0 9881 0 9884 09887 09890 0.9910 0.9898 0 9922 0.9941 0 9956 0 9967 09920 09936 09962 09940 0 9945 0 994 09948 0 9949 09951 0 9959 0 900 0 9909 09970 O. 9977 0 9978 09979 0 9979 0 9984 0 9888 0.04 2.6 9953 09355 09900 0.9902 0 9e3 09901 2.7 0.9965 2.8 0 9984 0.9974 9968 0 9971 O.9972 09973 9974 09975 09976 0 9977 09980 09986 09981 2.9 0 9981 3.0 09987 9987 0.00 09982 0 9982 09983 26660 09988 0 9984 0 9999 0.05 0 9985 0.9985 0666 06606O 60660 0.08 09986 09990 0.09 0.01 0.02 0.03 0.06 0.07 MacBook Air The label of caviar cans of a certain brand states that they contain a net weight of 50 grams. It is given that the net weights of the cans are normally distributed with a standard deviation of 1.5 grams. To see whether the claim on the label is true, a sample of 36 cans is taken. The obtained sample mean of net weights is 49.5 grams. [Problem I] Test the null hypothesis that the average net weight of caviar cans is 50 grams against the alternative hypothesis that this average is smaller than 50 grams. Use a significance level of 5%. [20] [Problem II] Compute the power of the test in (b) if the actual average net weight of caviar cans is 49.3 grams. [20] Table 3-App B (pp. B-8/B-9) - Cumulative Standardized Normal Probabilities P(Z< 2) 0 09 0 0010 0. 03 0.00 -3.0 0.0013 -2.9 0.0019 -2.8 0 0026 -2.7 0.0035 -2.6 0.0047 -2.5 0 0082 -2.4 0 0082 -2.3 0 0107 -2.2 0.0139 0.01 00013 0 00 18 0 0025 0.05 0 0011 0 00 18 0 0022 0.06 0.07 0 0011 0.0011 0 0015 0.00 15 0 0021 0.02 0.0013 0.08 00010 0.04 0 0012 0.0012 -3.0 -2.9 -2.8 2.7 -2.6 2.5 -2.4 2.3 -2.2 0 0014 0 0020 0.0018 00017 0.0016 0.0014 0 0023 0 0032 0 0043 0 0057 0 0075 0 0099 0 0019 0.0028 0 0038 0 0048 0 0084 0 0084 0.0023 0.0031 0.0024 0.0021 00034 0.0033 0.0030 0 0029 0.0028 00027 0.0041 0.0055 0 0073 0 0098 0 0125 00122 0 0040 0 0054 00039 0 0037 0 0049 0 0068 0 0087 00045 0.0044 0.0038 0 0051 0 0052 0 0089 0.0000 0.0059 0 0080 00104 0 0088 0.0078 00102 00071 0 0094 0 0091 0.0089 00138 0.0132 00129 00119 0.0118 00113 00110 Table 3-AppB(pp. B-BB-9)- Cumulative 5tandardized Normal Probabilities P(Z< 2) 0.00 3.0 0.0013 0 0013 2.9 0 0019 000 18 2.8 0.0026 2,7 0.0035 2.6 0.0047 2.5 0.0062 2.4 0.0082 2.3 00107 2.2 0.0139 00138 0.0132 00129 2.1 0.0179 00174 2.0 0 0228 1.9 00287 00281 1.8 0.0369 1.7 0.0440 -1.6 0.0548 1.5 0 0868 1.4 00808 1.3 0.0968 1.2 01151 1.1 0.1357 1.0 0 1587 01502 0.9 0.1841 -0.8 02119 0.7 02420 -0.6 0.2743 -0.5 0.3085 -0.4 0.01 0.03 0.02 0.0013 00012 0.0012 00011 00011 0.0011 000 10 0.0018 0 0017 0 00 10 0 00 16 00015 0.0015 00014 0.0024 00023 0 0023 0 0022 00021 0.0033 00032 0.04 0.05 0.06 0.07 0.09 0 0010-3.0 00014 -2.9 00019 -2.8 0.0028 -2.7 0.0038 0.08 00025 00034 0.0021 00020 0 0045 0 0060 00080 00104 0.0031 00030 00029 0 0028 00027 0 0041 0.0055 00054 0.0052 0 0051 00049 0.0073 00071 0.0096 00094 00091 0 0089 00087 00084-2.3 0 0125 00122 00119 00116 00113 00110 -22 0.0162 00158 00154 0.0150 0.0148 00143-2.1 0.0044 00043 00040 00039 0 0038 0.0037 -2.6 -2.5 -2.4 0 0069 0 0057 00075 0.0102 00099 00048 0.0078 000e9 0 00C8 0 0068 00084 0.0170 00166 00222 00217 00212 00207 0.0274 00202 00197 00192 00188 00183 2.0 00250 0.0288 00202 00338 0.0329 00322 0.0250 0.0244 00239 00233 1,9 00294 1.8 00392 0.0384 00375 003671.7 00351 00344 00314 0.0307 00301 0.0427 00418 00526 00516 0.0843 00e30 0.0818 00778 0.0934 00438 0.0409 00401 0.0505 00537 0 0655 00783 00495 00485 00475 00465 004651.6 00608 00594 0.0582 00571 0 0708 00e94 00889 0.0853 00838 0 1020 0 1003 00784 0.0749 00738 00918 0.0901 00885 00559 -1.5 -1.4 00721 00951 01131 00681 00823 -1.3 01112 01093 0.1314 0.1539 01515 0.1492 01409 0 1448 0.1423 0 1401 0 1788 0.2061 0.2358 0.1075 0 1056 0 1038 0.1230 00985-1.2 01335 01292 0 1271 01251 0.1210 0.1190 01170 1.1 0.1379 -1.0 01814 0 1736 01711 0.2005 0.1977 0.2296 02208 0.1762 0 1685 0.1680 0.1835 0 1011 0.9 0 2090 0 2033 02327 0 1949 0.1922 0 1894 01887 -0.0 02389 02236 0.2208 02177 02148 0.7 02709 0.2876 02643 02981 0.2811 02578 02548 0.2514 02483 -0.6 02877 0.2843 02810 02776 02481 0 3050 0.30 15 02948 02912 -0.5 0 3228 03192 03158 0 3121-0.4 03483 -0.3 0 3859 -0.2 04286 04247 0 3448 03409 0.3 0 3821 03783 -0.2 04207 04108 0.1 04602 0.0 0.5000 0.0 0 5000 0.1 0.5398 05438 0.2 0.5793 05832 0.3 0.0179 0.4 0 6654 0.5 0 0915 0.6 07257 0.7 07580 0.8 0.7881 0.9 0.8169 1.0 0 8413 1.1 0 8643 1.2 08849 1.3 0.9032 0 9049 0 9oee 0 9082 1.4 09192 0 9207 1.5 08332 1.6 0 5452 1.7 09554 1.8 1.9 09713 2.0 0.9772 2.1 0.9821 2.2 0.9601 2.3 0 9693 24 09918 2.6 0 9938 0 3372 0 3336 0 3300 0 3264 0 3745 0370O7 0 4090 04483 0.3609 03632 04129 0.4522 0.4052 0.4013 0.4443 0.3594 0 3857 0 3520 0.3974 03936 0 3897 0.4325 0.4502 0 4404 04801 0.4364 -0.1 04960 0 5040 0.4920 0.5080 0.5478 04880 05120 0.4840 0.5160 05199 0.5557 05596 04761 04721 05239 0 6279 0 4681 04641 -0.0 0.0 0.5636 0.5075 05714 0 5763 0.5319 05369 05517 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5871 0.5910 0.5948 05987 06293 0.e331 06368 oe406 0 e020 0.60e4 08103 0 6443 08480 0.0809 0 e844 06141 06217 0 e255 08591 00950 06517 0C879 07224 0.0028 0.6700 06738 0 7054 07088 07123 0.7157 07190 0 7389 07422 07454 07486 07517 07549 06772 0 0985 07324 07019 07291 07357 0.7842 0.7673 07704 07734 07784 0.7939 07907 0 7995 0 B023 08051 07611 0.7794 07823 07852 0.7910 08188 0.8 0 8212 08238 0 264 0 8289 08315 0.8340 0 8305 O8389 0.9 0 8078 08106 08133 08438 0 8461 0 BC80 0 0888 08485 0 8508 08531 O8708 OB907 0 8925 0 8944 08902 0 8980 O8584 0.8577 O8599 0 Be21 1.0 0 8665 08809 0 8729 08749 08770 0 8790 O8810 08830 1.1 0 9015 O8997 1.2 0.9147 0912 09177 0 9099 09115 09131 0 8251 0 9382 09495 0.9691 0 9871 09678 09086 0 9093 0 9e99 09738 09744 09750 0 9750 09701 O 9793 09798 1.3 09308 09319 0.9222 0 9236 09265 0 9279 09292 09 406 09418 09429 0 9515 0.9525 09536 0 9599 09608 0.9816 0 9025 1.4 1.5 1.6 0 9C33 09345 09483 0.9357 09370 09394 09505 09441 09545 0 9474 09484 0 9564 0.9649 09673 09582 1.7 9841 0 9656 0 9004 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.0 2.9 3.0 09706 0 9719 09778 0 9720 09732 09767 0.9817 0.9857 0 9783 09788 09903 0.9808 0 9812 098 30 09828 09804 09896 09834 0.9838 0 982 09846 0 9850 0 9854 0 9871 0 9901 0 9925 0 9027 0 9929 0 9931 0 9932 0 9934 09943 09967 0 9875 09878 0.9904 09908 0 9909 0.9911 09913 0 9881 0 9884 09887 09890 0.9910 0.9898 0 9922 0.9941 0 9956 0 9967 09920 09936 09962 09940 0 9945 0 994 09948 0 9949 09951 0 9959 0 900 0 9909 09970 O. 9977 0 9978 09979 0 9979 0 9984 0 9888 0.04 2.6 9953 09355 09900 0.9902 0 9e3 09901 2.7 0.9965 2.8 0 9984 0.9974 9968 0 9971 O.9972 09973 9974 09975 09976 0 9977 09980 09986 09981 2.9 0 9981 3.0 09987 9987 0.00 09982 0 9982 09983 26660 09988 0 9984 0 9999 0.05 0 9985 0.9985 0666 06606O 60660 0.08 09986 09990 0.09 0.01 0.02 0.03 0.06 0.07 MacBook Air