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Answer :
To express the null and alternative hypotheses for the claim that the mean weight of female dancers in a local modern dance company is at least 143 lbs, let's break it down step-by-step:
1. Understand the Claim: The claim is that the mean weight is at least 143 lbs. In hypothesis testing, "at least" refers to being greater than or equal to a certain value.
2. Formulate the Hypotheses:
- Null Hypothesis (H₀): The null hypothesis is typically a statement of no effect or no difference, and it is what we seek to test against. In this case, the null hypothesis would be that the mean weight of female dancers is at least 143 lbs. Symbolically, we represent this as:
- H₀: μ ≥ 143
- Alternative Hypothesis (H₁): The alternative hypothesis is what you might accept if the null hypothesis is rejected. It reflects a contrasting statement to the null hypothesis. For this scenario, the alternative hypothesis would be that the mean weight is less than 143 lbs. Symbolically, we represent this as:
- H₁: μ < 143
3. Summary:
- Null Hypothesis (H₀): μ ≥ 143
- Alternative Hypothesis (H₁): μ < 143
These hypotheses help test whether the mean weight of the dancers is statistically different from 143 lbs in the context of the given claim.
1. Understand the Claim: The claim is that the mean weight is at least 143 lbs. In hypothesis testing, "at least" refers to being greater than or equal to a certain value.
2. Formulate the Hypotheses:
- Null Hypothesis (H₀): The null hypothesis is typically a statement of no effect or no difference, and it is what we seek to test against. In this case, the null hypothesis would be that the mean weight of female dancers is at least 143 lbs. Symbolically, we represent this as:
- H₀: μ ≥ 143
- Alternative Hypothesis (H₁): The alternative hypothesis is what you might accept if the null hypothesis is rejected. It reflects a contrasting statement to the null hypothesis. For this scenario, the alternative hypothesis would be that the mean weight is less than 143 lbs. Symbolically, we represent this as:
- H₁: μ < 143
3. Summary:
- Null Hypothesis (H₀): μ ≥ 143
- Alternative Hypothesis (H₁): μ < 143
These hypotheses help test whether the mean weight of the dancers is statistically different from 143 lbs in the context of the given claim.
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