Math Problem Statement
Solution
From the image you provided, we have a hypothesis testing problem regarding the proportion of female fish in a population. The claim is that "at most 54% are female," and a test is being conducted to evaluate this claim.
Hypotheses Setup:
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Null Hypothesis (H₀): This represents the claim that the proportion of female fish is at most 54%. Mathematically, this is stated as:
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Alternative Hypothesis (H₁ or Hₐ): This is the hypothesis that challenges the null. Since the test is about whether the proportion is greater than 54%, the alternative hypothesis is:
Thus, you should fill in the boxes as follows:
- Null Hypothesis (H₀):
- Alternative Hypothesis (H₁):
Do you need further clarification or details on hypothesis testing or the process of setting these up?
Here are 5 relative questions for further practice:
- What is the difference between a one-tailed and a two-tailed hypothesis test?
- How do you determine the appropriate significance level (α) for a hypothesis test?
- What is a Type I error in hypothesis testing, and how can it be minimized?
- How do you calculate the test statistic for a proportion hypothesis test?
- When should you use a z-test for proportions?
Tip: In hypothesis testing, always carefully distinguish between the null and alternative hypotheses, especially in one-tailed tests, to ensure your conclusions align with the initial claim.
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Proportions
Formulas
Null Hypothesis (H₀): p ≤ 0.54
Alternative Hypothesis (Hₐ): p > 0.54
Theorems
One-Tailed Test
Suitable Grade Level
Grades 11-12
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