A sample of 1200
computer chips revealed that 37%
of the chips do not fail in the first 1000
hours of their use. The company's promotional literature claimed that more than 34%
do not fail in the first 1000
hours of their use. Is there sufficient evidence at the 0.05
level to support the company's claim?

State the null and alternative hypotheses for the above scenario.

In this scenario, the company claims that more than 34% of their computer chips do not fail in the first 1000 hours of use. To test this claim, we can set up the null and alternative hypotheses as follows:

**Null Hypothesis (\(H_0\))**: The proportion of chips that do not fail in the first 1000 hours is equal to 34%.

\[
H_0: p = 0.34
\]

**Alternative Hypothesis (\(H_1\))**: The proportion of chips that do not fail in the first 1000 hours is greater than 34%.

\[
H_1: p > 0.34
\]

This is a one-tailed test, as the company is specifically claiming that the proportion is **greater than** 34%.

Would you like to go through the steps to test this hypothesis, or do you have any questions about the setup? Here are five related questions you might consider:

1. How do you calculate the test statistic for this hypothesis test?
2. What is the critical value for a one-tailed test at the 0.05 significance level?
3. How do you determine if the evidence is sufficient to reject the null hypothesis?
4. What does it mean to have a Type I error in this context?
5. How does the sample size affect the reliability of this test?

**Tip**: In hypothesis testing, carefully distinguishing between the null and alternative hypotheses is crucial for correctly interpreting the test results.

Explore hypothesis testing for proportions with a real-world example involving computer chips. Test if the company's claim that more than 34% of chips do not fail in the first 1000 hours is supported by statistical evidence. Learn about setting up null and alternative hypotheses, calculating test statistics, and interpreting results.

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