A box of crayons comes with 4 colors: black, pink, purple, and green. According to the manufacturer, the color ratio in each production batch is 40% black, 30% pink, 15% purple, and 15% green. To test this claim, 500 crayons from 10 randomly selected boxes were sorted by color. The results were as follows
black: 180
pink: 170
purple: 80
green: 70
Does the observed data contradict the company's claim? Formulate and test the appropriate hypotheses at the 2.5% level of significance. Use the critical value approach