"A manufacturer of handheld calculators receives large shipments of printed circuits from a supplier. It is too costly and time-consuming to inspect all incoming circuits, so when each shipment arrives, a sample is selected for inspection. A shipment is defined to be of inferior quality if it contains more than 1% defective circuits."

what is the p =  

Give the null and alternative hypothesis.

H0 :    


Ha : 


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:

---

### 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%.

---

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

---

**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).

A manufacturer of handheld calculators receives large shipments of printed circuits from a supplier. It is too costly and time-consuming to inspect all incoming circuits, so when each shipment arrives, a sample is selected for inspection. A shipment is defined to be of inferior quality if it contains more than 1% defective circuits.

what is the p =  

Give the null and alternative hypothesis.

H0 :    

Ha :

Understand how to perform hypothesis testing on the proportion of defective circuits in a shipment. This problem includes setting up null and alternative hypotheses for testing if the defect rate exceeds 1%, using statistical formulas and concepts relevant to quality control. Ideal for college students or advanced high school statistics learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation