You have been studying the effects of different fertilizers on the growth of certain produce. In the latest instalment of your experiment, you are testing Quebec's own "Gro-Haut" fertilizer and its effects on carrots. From the sample of carrots that you have measured, you calculate an average length of 24 cm with a standard deviation of 4. Please construct a confidence interval for the mean length of the carrots using Gro-Haut in the following circumstances:
a) Sample size = 35, confidence level = 98%.
b) Sample size = 15, confidence level = 90%.
c) What would be the minimum sample needed to estimate the population mean of the length of carrots using Gro-Haut to within 1.5 cm with 99% confidence?