Question: Production standards for a bottling plant require that a machine produce bottle caps with a mean diameter of 1.80 cm. A production inspector checked a random sample of 80 caps to determine if the machine settings need adjustment. He found that the mean diameter of the caps in the sample was 1.82 cm with a standard deviation of 0.06 cm. Does this data indicate that the mean diameter of the caps does not equal the required standard, and the machine settings need to be adjusted? Use a 1% level of significance. Be sure to carry out the 7-step hypothesis-testing procedure and compute the p value.