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.