The U.S. Mint has a specification that pennies have a mean weight of 2.5 g. Data Set 20 in Appendix B lists the weights (in grams) of 37 pennies manufactured after 1983. Those pennies have a mean weight of 2.49910 g and a standard deviation of 0.01648 g. Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5 g. Do the pennies appear to conform to the specifications of the U.S. Mint?

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Unless specified by your instructor, use either the traditional method or P-value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), critical value(s), and state the final conclusion that addresses the original claim.

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Data Set 20: Coin Weights (grams) The "pre-1983 pennies" were made after the Indian and wheat pennies, and they are 97% copper and 3% zinc. The "post-1983 pennies" are 3% copper and 97% zinc. The "pre-1964 silver quarters" are 90% silver and 10% copper. The "post-1964 quarters" are made with a copper-nickel alloy. 3.0630 3.0487 STATDISK: Minitab: Excel: TI-83/84 Plus: Text file names: Indian Wheat Pre-1983 Pennies Pennies Pennies 2.9149 3.1358 2.9753 3.1366 3.0755 3.1692 3.0476 3.1029 3.0377 3.1083 3.1141 3.0976 3.0862 3.0570 3.0765 3.1114 3.0965 3.0816 3.0054 3.1934 3.1461 3.0185 3.1267 3.1524 3.0786 3.0131 3.1535 3.0480 3.0050 3.0290 3.1038 3.0357 3.0064 3.0936 3.1031 3.0408 Data set name is Coins. Worksheet name is COINS.MTW. Workbook name is COINS.XLS. App name is COINS, and the file names are the same as for text files. Text file names are CPIND, CPWHT, CPPRE, CPPST, CPCAN, CQPRE, CQPST, CDOL. 3.0561 3.0994 3.1582 3.0406 3.0762 3.0398 3.1043 3.1274 3.0775 3.1038 3.1086 3.0586 3.0603 3.0502 3.1028 3.0522 3.0546 3.0185 3.0712 3.0717 3.0546 3.0817 3.0704 3.0797 3.0713 3.0631 3.0866 3.0763 3.1299 3.0846 3.0917 3.0877 2.9593 3.0966 2.9800 3.0934 3.1340 Post-1983 Canadian Pre-1964 Pennies Pennies Quarters 2.5113 2.4907 2.5024 2.5298 2.4950 2.5127 2.4998 2.4848 2.4823 2.5163 2.5222 2.5004 2.5248 2.5058 2.4900 2.5068 2.5016 2.4797 2.5067 2.5139 2.4762 2.5004 2.5170 2.4925 2.4876 2.4933 2.4806 2.4907 2.5017 2.4950 2.4973 2.5252 2.4978 2.5073 2.4658 2.4529 2.5085 3.2214 3.2326 2.4662 2.8357 3.3189 3.2612 3.2441 2.4679 2.7202 2.5120 6.2771 6.2371 6.1501 6.0002 6.1275 6.2151 6.2866 6.0760 6.1426 6.3415 6.1309 6.2412 6.1442 6.1073 6.1181 6.1352 6.2821 6.2647 6.29 08 6.1661 6.2674 6.2718 6.1949 6.2465 6.3172 6.1487 6.0829 6.1423 6.1970 6.2441 6.3669 6.0775 6.1095 6.1787 6.2130 6.1947 6.1940 6.0257 6.1719 6.3278 Post-1964 Dollar Coins Quarters 5.7027 5.7495 5.7050 5.5941 5.7247 5.6114 5.6160 5.5999 5.7790 5.6841 5.6234 5.5928 5.6486 5.6661 5.5361 5.5491 5.7239 5.6555 5.6063 5.5709 5.5591 5.5864 5.6872 5.6274 5.6157 5.6668 5.7198 5.6694 5.5454 5.6646 5.5636 5.6485 5.6703 5.6848 5.5609 5.7344 5.6449 5.5804 5.6010 5.6022 8.1008 8.1072 8.0271 8.0813 8.0241 8.0510 7.9817 8.0954 8.0658 8.1238 8.1281 8.0307 8.0719 8.0345 8.0775 8.1384 8.1041 8.0894 8.0538 8.0342