Color coding is often used in manufacturing operations to display production status or to identify/prioritize materials. For example, suppose "green" status indicates that an assembly line is operating normally, "yellow" indicates it is down waiting on personnel for set up or repair, "blue" indicates it is down waiting on materials to be delivered, and "red" indicates an emergency condition. Management has set realistic goals whereby the assembly line should be operating normally 80% of the time, waiting on personnel 9% of the time, waiting on materials 9% of the time, and in an emergency condition 2% of the time. Based on 250 recent status records, the status was green 185 times, yellow 24 times, blue 32 times, and red 9 times.

a. State the appropriate null and alternative hypotheses to test if the proportions of assembly line statuses differ from the goals set by management.

b. Calculate the value of the test statistic.

c. Use Excel's CHISQ.DIST.RT function to calculate the p-value.

d. Are management's goals being met at α = 0.05? Will your conclusion change at α = 0.01?