Problem

The mean weight of male dancers in a local modern dance company is at most $190 \mathrm{lbs}$. Express the null and alternative hypotheses in symbolic form for this claim.
\[
H_{0}: \mu
\]
\[
H_{1}: \mu
\]
Use the following codes to enter the following symbols:
\[
\begin{array}{l}
\geq \text { enter }> = \\
\leq \text { enter }< = \\
\neq \text { enter } !=
\end{array}
\]
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Answer

The null and alternative hypotheses in symbolic form for this claim are: \(H_{0}: \mu \leq 190\) and \(H_{1}: \mu > 190\)

Steps

Step 1 :The null hypothesis (H0) is a statement of no effect or no difference. It is the hypothesis that the researcher is trying to disprove. In this case, the null hypothesis would be that the mean weight of male dancers is equal to 190 lbs.

Step 2 :The alternative hypothesis (H1) is a statement that contradicts the null hypothesis. It is the hypothesis that the researcher believes to be true. In this case, the alternative hypothesis would be that the mean weight of male dancers is not equal to 190 lbs.

Step 3 :However, the question states that the mean weight is 'at most' 190 lbs. This implies that the mean weight could be less than or equal to 190 lbs, but not more. Therefore, the alternative hypothesis should reflect this by stating that the mean weight is more than 190 lbs.

Step 4 :The null and alternative hypotheses in symbolic form for this claim are: \(H_{0}: \mu \leq 190\) and \(H_{1}: \mu > 190\)

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