A website reports that the mean weight of dancers in a local modern dance company is 141 lbs. Test the claim that the mean weight of dancers in the company is greater than 141 lbs.

Express the null and alternative hypotheses in symbolic form for this claim:

\[ H_0: \mu \leq 141 \]
\[ H_A: \mu > 141 \]

Express the null and alternative hypotheses in symbolic form for the following claim: the mean weight of female dancers in a local modern dance company is equal to 131 lbs. Note that the mean weight in the sample taken is 128 lbs.

\[ H_0: \mu = 131 \]
\[ H_1: \mu \neq 131 \]

Use the following codes to enter the following symbols:
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- ≤ enter \<=
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The null and alternative hypotheses for the claim that the mean weight of dancers in a modern dance company is greater than 141 lbs are H0: μ <= 141 and HA: μ > 141. For the claim that the mean weight of female dancers is equal to 131 lbs, the hypotheses are H0: μ = 131 and HA:μ != 131.

Explanation:

For the claim that the mean weight of dancers in a local modern dance company is greater than 141 lbs, we can write the null hypothesis and alternative hypothesis as follows:

H0:μ <= 141

HA: μ > 141

The null hypothesis, H0, is that the mean weight of the dancers is less than or equal to 141 lbs. The alternative hypothesis, HA, is that the mean weight of the dancers is greater than 141 lbs.

For the claim that the mean weight of female dancers in a local modern dance company is equal to 131 lbs, we can write the null and alternative hypotheses as follows:

H0: μ = 131

HA:μ != 131

The null hypothesis, H0, is that the mean weight of the female dancers is equal to 131 lbs. The alternative hypothesis, HA, is that the mean weight of the female dancers is not equal to 131 lbs.

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