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

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.

Step-by-step explanation:

Type I error is defined as the rejection of the true null hypothesis. It is also called as the 'false positive' conclusion or 'false positive' findings. The value of alpha or the significance level determines the probability of making the error type I.

In the context, it is given that for a gold piece to be of 18 karat , the piece of jewelry must be made of 75% of pure gold.

The null hypothesis is, H0: The proportion of metal that is gold is 75%

The alternative hypothesis is Ha: The proportion of metal that is gold is less than 75%.

Thus the type I error is when the gold shipment is made of 75% gold but the jewelry designer rejects the shipment thinking that the shipment is made of less than 75% gold.

Thus it shows the error of type I rejecting the null hypothesis.