A typical washing machine has several different cycles, including soak, wash, and rinse. The energy consumption of a washing machine is linked to the length of each cycle. A random sample of 21 washing machines was obtained, and the length (in minutes) of each washing cycle was recorded. The summary statistics are = 37.8 and = 5.9. Assume the underlying distribution of the main wash cycle times is normal. i. Find a 90% confidence interval for the true mean wash cycle time. ii. Interpret the confidence interval found in part (a) iii. Suppose a 95% confidence interval for the true mean wash cycle time is constructed. Would this interval be smaller or larger than the interval in part (a)? Justify your answer.