A group of 25,000 design engineers was asked a series of questions concerning the importance of various attributes of a milling machine. The group had the following response to the question: "How important is it that the machine be capable of working with both hard and soft metals?"
a. What is the average response of this population?
b. What are the variance and standard deviation?
c. A sample of size 25 yielded the following numbers: 4, 4, 1, 2, 3, 5, 4, 2, 3, 3, 3, 4, 4, 4, 1, 1, 5, 5, 4, 1, 3, 4, 4, 5, 2. Determine the sample mean, the sample variance, and the sample standard deviation.
d. Calculate the standard error of the sample mean, σX. How would your calculation change if the sample size were 100 instead of 25? Why? Estimate σX using s instead of σ.
e. Repeat parts (a) and (b) assuming that half the population of 25,000 engineers responded "extremely important" and half responded "of no consequence."