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?

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.