Question

Two different types of injection-molding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discolored. Two random samples, each of size 300, are selected, and 15 defective parts are found in the sample from machine 1 while 8 defective parts are found in the sample from machine 2.

What would be the possible result of making a type I error?
Is it reasonable to conclude that both machines produce the same fraction of defective parts, using α = 0.05?

Answer 1

A type I error occurs when the null hypothesis is rejected when it is actually true.

To determine if both machines produce the same fraction of defective parts, perform a hypothesis test with an alpha level of 0.05.

A type I error in hypothesis testing occurs when the null hypothesis is rejected when it is actually true. In this case, it would mean concluding that both machines produce the same fraction of defective parts when they actually don't.

To determine if it is reasonable to conclude that both machines produce the same fraction of defective parts, we can perform a hypothesis test.

With an alpha level of 0.05, we can calculate the p-value using the normal approximation to the binomial distribution.

Once we have the p-value, we can compare it to the alpha level.

If the p-value is less than the alpha level, we reject the null hypothesis. If the p-value is greater than the alpha level, we fail to reject the null hypothesis.