Math Problem Statement

Which of the following correctly states H0 and Ha? The problem involves hypothesis testing for a claim about the proportion of consumers who stopped buying a product due to environmental concerns. The claim is that more than 26% have stopped buying.

Solution

From the image, you are working on a hypothesis testing problem, specifically about the proportion of people who have stopped buying a product due to environmental concerns. The question appears to involve identifying the null hypothesis (H0H_0) and alternative hypothesis (HaH_a) and performing hypothesis testing.

Breakdown of Problem

  1. Claim: "More than 26% of consumers have stopped buying a product due to environmental concerns."

    • The alternative hypothesis (HaH_a) corresponds to the claim.
    • The null hypothesis (H0H_0) typically states the opposite or reflects no significant change.
  2. Hypotheses:

    • Null Hypothesis (H0H_0): p0.26p \leq 0.26
    • Alternative Hypothesis (HaH_a): p>0.26p > 0.26 (claim is "more than 26%").

From the choices in your image, the correct option appears to be:
C. H0:p=0.26H_0: p = 0.26, Ha:p>0.26H_a: p > 0.26

If you'd like, I can help solve the entire problem by finding the critical values, test statistic, or rejection region.

Do you want to proceed further with detailed calculations? Here are some questions to guide further learning:

  1. How do you determine the critical value in a one-tailed hypothesis test for proportions?
  2. What formula should you use to calculate the standardized test statistic?
  3. How does the significance level (α=0.03\alpha = 0.03) affect the rejection region?
  4. How do you interpret the results of this hypothesis test in the context of the problem?
  5. How can sample size influence the reliability of the test results?

Tip: Always start hypothesis testing by clearly stating your null and alternative hypotheses, as they form the foundation for the test!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Proportions
Statistical Testing

Formulas

z = (p̂ - p0) / √(p0(1-p0)/n)

Theorems

Central Limit Theorem

Suitable Grade Level

Grades 11-12 or Introductory College