A company supplying candy to school vending machines needs to know about candy preferences of middle school and high school age students. A random sample of 400 students was taken. The company wants to know if there is any relationship between the candy choices and the age of students. After performing a chi-square test of independence, the chi-square test statistic = 24.68. The appropriate critical value for df and desired alpha level = 11.34. Is there sufficient evidence to reject the null hypothesis? Explain.

World systems manufactures an optical switch that it uses in its final product. world systems incurred the following manufacturing costs when it produced 74 comma 000 units last​ year: ​(click the icon to view the manufacturing​ costs.) another company has offered to sell world systems the switch for $ 13.50 per unit. the world systems prepared an outsourcing decision analysis to show the cost per unit of making the switches versus the cost per unit of buying​ (outsourcing) the switches. ​(click the icon to view the outsourcing decision​ analysis.) world systems needs 86 comma 000 optical switches next year​ (assume same relevant​ range). by outsourcing​ them, world systems can use its idle facilities to manufacture another product that will contribute $ 140 comma 000 to operating​ income, but none of the fixed costs will be avoidable. should world systems make or buy the​ switches? show your analysis.