Math Problem Statement

A scientist claims that in a population of fish, at most 54% are female. A test is conducted to test the claim. Identify the null hypothesis and the alternative hypothesis.

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:

  • Null Hypothesis (H₀): This represents the claim that the proportion of female fish is at most 54%. Mathematically, this is stated as: H0:p0.54H_0: p \leq 0.54

  • 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: Ha:p>0.54H_a: p > 0.54

Thus, you should fill in the boxes as follows:

  • Null Hypothesis (H₀): p0.54p \leq 0.54
  • Alternative Hypothesis (H₁): p>0.54p > 0.54

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:

  1. What is the difference between a one-tailed and a two-tailed hypothesis test?
  2. How do you determine the appropriate significance level (α) for a hypothesis test?
  3. What is a Type I error in hypothesis testing, and how can it be minimized?
  4. How do you calculate the test statistic for a proportion hypothesis test?
  5. 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