The mean time to assemble a product as found from a sample of size 40 is 10.4 minutes. The standard deviation of the assembly times is known to be 1.2 minutes.
(a) Find a two-sided 90% confidence interval for the mean assembly time, and interpret it.
(b) Find a two-sided 99% confidence interval for the mean assembly time, and interpret it.
(c) What assumptions are needed to answer parts (a) and (b)?
(d) The manager in charge of the assembly line believes that the mean assembly time is less than 10.8 min. Can he make this conclusion at a significance level α of 0.05?