A VP of manufacturing claims that more than 3% of items produced using a certain assembly line are is defective. A random sample of 100 items from the assembly line had 4 defectives. At the 5% level of significance, which of the following would be part of the standardized decision rule?

To determine whether the claim made by the VP of manufacturing can be supported or not, we can use a hypothesis test. In this case, we want to test whether the true proportion of defective items produced using the assembly line is greater than 3%.

Let's set up the hypotheses:
- Null hypothesis (H0): The true proportion of defective items is 3% or less. (P ≤ 0.03)
- Alternative hypothesis (Ha): The true proportion of defective items is greater than 3%. (P > 0.03)

Next, we need to calculate the test statistic, which in this case is the z-score. The formula for the z-score in this case is:

z = (p̂ - P) / √(P(1-P)/n)

where:
- p̂ is the sample proportion of defectives
- P is the proportion claimed by the VP (0.03)
- n is the sample size

Plugging in the values from the question, we have:
p̂ = 4/100 = 0.04
P = 0.03
n = 100

Next, we can calculate the z-score:
z = (0.04 - 0.03) / √(0.03(1-0.03)/100)

Once we have the z-score, we can compare it to the critical value to make our decision. The critical value is determined based on the desired level of significance (in this case, 5%) and whether the alternative hypothesis is one-tailed (greater than) or two-tailed.

Since we are testing if the proportion is greater than 3%, this is a one-tailed test. We can find the critical value from a standard normal distribution table or by using statistical software.

The standardized decision rule will depend on the critical value, but it will likely be expressed as:
- If z > critical value, reject the null hypothesis (support the alternative hypothesis).
- If z ≤ critical value, fail to reject the null hypothesis (do not support the alternative hypothesis).

Therefore, the standardized decision rule will involve comparing the calculated z-score to the critical value based on the desired significance level of 5%.