This problem is about testing whether a shipment meets the quality standard. Specifically, the goal is to determine if the proportion of defective circuits in the shipment exceeds 1%. Let’s carefully define the hypotheses:

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1. Parameter of interest:

• $p$ = true proportion of defective circuits in the shipment.

2. Null and alternative hypotheses:

• Null hypothesis ($H_0$): The shipment meets the quality requirement, meaning the proportion of defective circuits is less than or equal to 1%. $H_0: p \leq 0.01$

• Alternative hypothesis ($H_a$): The shipment is of inferior quality, meaning the proportion of defective circuits is greater than 1%. $H_a: p > 0.01$

This setup suggests a one-tailed test because the concern lies only in whether the defect rate exceeds 1%.

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Let me know if you need further details or calculations for this test!

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Relative Questions:

1. What sample size would be required to conduct this test with high precision?
2. How is the decision rule set for a hypothesis test like this (involving critical values or p-values)?
3. What is the significance level ($\alpha$) typically used in such quality control tests?
4. How would you calculate the test statistic for this hypothesis test using a sample proportion?
5. What is the role of Type I and Type II errors in this testing scenario?

Tip: In quality control, tests often use small significance levels (like 0.01) to minimize the risk of falsely accepting poor-quality batches (Type I error).