Production Costs A manufacturer produces custom metal blanks that are used by its customers for computer-aided machining. The customer sends a design via computer (a 3-D blueprint), and the...

Production Costs A manufacturer produces custom metal blanks that are used by its customers for computer-aided machining. The customer sends a design via computer (a 3-D blueprint), and the manufacturer comes up with an estimated cost per unit, which is then used to determine a price for the customer. This analysis considers the factors that affect the cost to manufacture these blanks. The data for the analysis were sampled from the accounting records of 195 previous orders that were filled during the last 3 months. Formulate the regression model with
 as the cost per unit and
 as the material cost per unit.

(a) Does the material cost per unit explain statistically significant variation in the average cost of an order?

(b) A customer has called back with a revised order. Rather than use materials that cost $2 per unit, the customer prefers to use a cheaper material that reduces the cost to $1.60 per unit. Based on the fit of the indicated model, how should this reduction affect the average cost per unit ordered? Give your answer as a 95% confidence interval.

(c) Do you have any qualms about presenting this interval as a 95% confidence interval?