
A sample of 13001300 computer chips revealed that 24%24% of the chips fail in the first 10001000 hours of their use.  The company's promotional literature states that 26%26% of the chips fail in the first 10001000 hours of their use.  The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage.  State the null and alternative hypotheses.

To test the claim that the actual percentage of computer chips that fail in the first 1000 hours is different from the stated percentage, we can set up the null and alternative hypotheses as follows:

1. **Null Hypothesis (\(H_0\))**: The actual percentage of computer chips that fail in the first 1000 hours is equal to the stated percentage. Mathematically, this is expressed as:
   \[
   H_0: p = 0.26
   \]
   where \( p \) is the true proportion of chips that fail within the first 1000 hours.

2. **Alternative Hypothesis (\(H_a\))**: The actual percentage of computer chips that fail in the first 1000 hours is different from the stated percentage. This is a two-tailed test because we are interested in deviations in either direction. Mathematically, this is expressed as:
   \[
   H_a: p \neq 0.26
   \]

In summary:

- \( H_0: p = 0.26 \)
- \( H_a: p \neq 0.26 \)

Would you like details or have any questions?

Here are 5 relative questions that expand on the previous information:

1. What is the significance level (\(\alpha\)) commonly used in hypothesis testing?
2. How do you calculate the test statistic for a hypothesis test about a proportion?
3. What is a p-value, and how is it used in hypothesis testing?
4. How do you interpret the results of a hypothesis test in the context of quality control?
5. What are Type I and Type II errors in hypothesis testing, and how do they relate to this scenario?

**Tip:** When performing a hypothesis test, always check the assumptions and conditions for the test to ensure valid results.

A sample of 1300 computer chips revealed that 24% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 26% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. State the null and alternative hypotheses.

Test the hypothesis that the actual percentage of computer chips failing in the first 1000 hours differs from the stated 26%. This problem covers hypothesis testing concepts, including null and alternative hypotheses for proportions. Suitable for college-level statistics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation