The Problem: A factory manufactures millions of steel rods. The rods are supposed to have a mean length of 24 cm. If there is evidence at a = 0.05 that the mean length for all rods is different from 24 cm the factory will be shut down and a costly maintenance procedure will ensue. If the mean length is different from 24 cm their customers will be unhappy and not use their rods anymore. A random sample of rods is taken and their lengths are in the file rods2024.xlIsx. o L P S. Find the mean and standard deviation of the lengths of the rods in the sample. Find a 95% confidence interval for the mean length of all manufactured rods. Interpret the confidence interval in context. Does this provide evidence that the mean length for all rods is different from 24 cm? Justify in a complete sentence. Based on your conclusion, would you recommend shutting down the factory? Justify! Of secondary interest is the proportion of rods produced that are greater than 24 cm. Using the same dataset. 6. Find the proportion of rods in the sample that are greater than 24 cm in length. 7. Find a 95% confidence interval for the proportion of all manufactured rods that are greater than 24 cm in length. 8. Interpret the confidence interval in context. 9. Does this provide evidence that the proportion of all rods that are greater than 24 cm is different from 60%? Justify in a complete sentence