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. You want to test if it is reasonable to conclude that machine 2 produces less (difference is positive) fraction of defective parts, using α= 0.03.

Let's assume you found a test statistic value less than critical value. What would be your conclusion?

Answer 1

There is evidence to conclude that both machines produce the same fraction of defective parts

Explanation:

Attached is the solution

Answer 2

Explanation:

Hello!

The objective of this exercise is to compare the proportion of defective parts produced by machine 1 and machine 2.

The parameter of study is the difference between the population proportion of defective parts produced by machine 1 and the population proportion of defective parts produced by machine 2, symbolically: p₁ - p₂

The hypotheses are:

H₀: p₁ - p₂ ≤ 0

H₁: p₁ - p₂ > 0

α: 0.03

This hypothesis test is one-tailed to the right, which means that you will reject the null hypothesis with high values of the statistic.

To test the difference of proportions you have to use a standard normal distribution, the critical value will be:

`Z_(1-\alpha )= Z_(1-0.03)= Z_(0.97)= 1.881`

The decision rule using the critical value approach is:

If
`Z_(H_0)` ≥ 1.881, the decision is to reject the null hypothesis.

If
`Z_(H_0)` < 1.881, the decision is to not reject the null hypothesis.

Considering the calculated
`Z_(H_0)` < 1.881, the decision is to not reject the null hypothesis. Using a significance level of 3%, you can conclude that the difference between the population proportion of defective plastic parts produced by machine 1 and the population proportion of defective plastic parts produced by machine 2 is at most zero.

I hope this helps!