The multinomial variable payment preference takes the values credit card, debit card, and check. Now, suppose we know that 50% of the customers in our population prefer to pay by credit card, 20% prefer debit card, and 30% prefer to pay by check. We have taken a sample from our population, and would like to determine whether it is representative of the population. The sample of size 200 shows 125 customers preferring to pay by credit card, 25 by debit card, and 50 by check. Test whether the sample is representative of the population, using α = 0.05.