https://file.aiquickdraw.com/mathbot/file/1730074181128ug7t8g37.jpg

Let's analyze and solve the questions presented in your image.

### Part (a): Defining Null and Alternative Hypotheses
The question states:
- **Claim:** The proportion of customers who check a bag with a weight exceeding the limit is 23.4%.
- **Your Belief:** You suspect the proportion is not 23.4%.

To express this belief statistically:
- **Null Hypothesis (H₀):** \( p = 0.234 \)
  - This hypothesis assumes that the actual proportion of customers who check bags over the weight limit is exactly 23.4%.
- **Alternative Hypothesis (H₁):** \( p \neq 0.234 \)
  - The alternative hypothesis indicates that the proportion differs from 23.4% (either higher or lower).

### Part (b): Type of Hypothesis Test
Since your belief is that the proportion is **not equal** to 23.4%, you are looking for any deviation, whether it is an increase or a decrease in this proportion.

- **Test Type:** A **two-tailed test** is appropriate because it checks for any significant difference in either direction (greater or less than 23.4%).

The correct answers are:
- **(a)** \( H_0: p = 0.234 \) and \( H_1: p \neq 0.234 \)
- **(b)** Two-tailed test

Would you like a detailed explanation of hypothesis testing steps, or do you have any questions about this topic?

---

Here are some additional questions to help deepen your understanding:
1. How would the hypothesis change if you believed the proportion was less than 23.4%?
2. What does it mean for a test to be one-tailed instead of two-tailed?
3. What are the common significance levels used in hypothesis testing?
4. How do you determine the critical values for a two-tailed test?
5. What would be the next steps if you were conducting this hypothesis test?

**Tip:** In a two-tailed test, the rejection regions are on both ends of the distribution, meaning it tests for any significant deviation from the null value in either direction.

An airline industry trade journal reports that the proportion of customers who check a bag with a weight in excess of the limit is 23.4%. You are not entirely convinced and believe that it is not 23.4%. Define your null and alternative hypotheses, and determine the type of hypothesis test that should be conducted.

This page explores hypothesis testing related to an airline industry report on the proportion of customers whose bag weight exceeds the 23.4% limit. Learn how to set up null and alternative hypotheses and conduct a two-tailed test for statistical accuracy.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation