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The problem is asking for the null and alternative hypotheses for a claim about the mean weight of male dancers.

Given:
- The claim is that the mean weight of male dancers is **less than 181 lbs**.

### Hypotheses
1. **Null Hypothesis (\( H_0 \))**: This represents the status quo or no effect. Since the claim is that the mean is less than 181 lbs, the null hypothesis will assume the opposite:
   \[
   H_0: \mu \geq 181
   \]

2. **Alternative Hypothesis (\( H_1 \))**: This represents the claim we want to test (that the mean weight is less than 181 lbs):
   \[
   H_1: \mu < 181
   \]

So, the hypotheses in symbolic form are:
- \( H_0: \mu \geq 181 \)
- \( H_1: \mu < 181 \)

Would you like a further explanation of hypothesis testing steps or have any questions?

### Related Questions
1. What does the alternative hypothesis signify in a hypothesis test?
2. How do we interpret the null hypothesis when testing a claim about a mean?
3. What are the common symbols used for inequality in hypothesis testing, and what do they represent?
4. How can we determine the type of hypothesis test needed (one-tailed vs. two-tailed)?
5. What is the importance of setting a significance level in hypothesis testing?

**Tip**: Always start with defining the null hypothesis as the default assumption before the claim.

The mean weight of male dancers in a local modern dance company is less than 181 lbs. Express the null and alternative hypotheses in symbolic form for this claim.

Learn how to express the null and alternative hypotheses for a claim about the mean weight of male dancers in a local dance company. This exercise covers essential concepts in hypothesis testing, including the use of inequality symbols and mean comparison.

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