Question 1 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
To be considered 18-karat (18K) gold, a piece of jewelry must be made of 75% pure gold. The higher the karats, the more valuable a piece of jewelry. A jewelry designer is purchasing a large quantity of 18K gold from a new supplier. To see if the new supplier is being dishonest about the karat rating in the shipment, the designer melts a random sample of the gold and conducts a hypothesis test with H0: The proportion of metal that is gold is 75%, and Ha: The proportion of metal that is gold is less than 75%. What is a Type I error and its consequence in this context?
Answer
A
The gold shipment truly is made of less than 75% gold, but the designer concludes that it is made of 75% gold. The designer will reject the shipment of gold and miss out on an honest business relationship with the supplier.
B
The gold shipment truly is made of less than 75% gold, but the designer concludes that it is made of 75% gold. The designer will accept the shipment of gold and produce inferior jewelry.
C
The gold shipment truly is made of 75% gold, but the designer concludes that it is made of less than 75% gold. The designer will reject the shipment of gold and miss out on an honest business relationship with the supplier.
D
The gold shipment truly is made of 75% gold, but the designer concludes that it is made of less than 75% gold. The designer will accept the shipment of gold and produce inferior jewelry.