Question: Manufacturing and Product Development 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 wash cycle was recorded. The summary statistics are x¯ = 37.8 and σ = 5.9. Assume the underlying distribution of main wash cycle times is normal.
a. Find a 90% confidence interval for the true mean wash cycle time. Write a Solution Trail for this problem.
b. Interpret the confidence interval found in part (a).
c. 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.