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To define the null and alternative hypotheses for this claim:

1. **Claim**: At least 51% of workers got their job through networking. This translates to the population proportion \( p \geq 51\% \).

### Hypotheses:
- **Null Hypothesis** \((H_0)\): \( p = 51\% \)
- **Alternative Hypothesis** \((H_1)\): \( p < 51\% \)

These hypotheses are set up for a one-tailed test to check if the proportion is less than 51%.

Would you like further details or have any questions?

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Here are some related questions to expand understanding:
1. How would the hypotheses change if the claim was "more than 51%"?
2. What is the significance level in hypothesis testing, and why is it important?
3. How can sample data be used to test these hypotheses?
4. What is a Type I error in the context of this hypothesis test?
5. How is the p-value used to make a decision in hypothesis testing?

**Tip:** In hypothesis testing, the null hypothesis \( H_0 \) often represents the status quo or a specific value to be tested against, while the alternative hypothesis \( H_1 \) reflects the new claim or suspicion being tested.

At least 51% of workers got their job through networking. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage).

Learn how to set up the null and alternative hypotheses for a claim that at least 51% of workers got their jobs through networking. This problem covers concepts in hypothesis testing for proportions, suitable for students in Grades 11-12.

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