https://file.aiquickdraw.com/mathbot/file/1729999924641eawdcjeq.jpg

To analyze the hypothesis test setup from the image:

### Given:
- A trade journal reports that **16.7%** of customers check a bag exceeding the weight limit.
- You believe the true proportion is **less than 16.7%**.

### Solution:

#### Part (a): Null and Alternative Hypotheses
1. **Null Hypothesis (H₀)**: The proportion of customers checking bags over the weight limit is 16.7%.
   \[
   H_0: p = 16.7\%
   \]

2. **Alternative Hypothesis (H₁)**: The proportion of customers checking bags over the weight limit is less than 16.7%.
   \[
   H_1: p < 16.7\%
   \]

#### Part (b): Type of Hypothesis Test
Since your alternative hypothesis is testing for a value **less than** the reported 16.7%, this is a **left-tailed test**.

### Summary:
- **H₀:** \( p = 16.7\% \)
- **H₁:** \( p < 16.7\% \)
- **Type of test:** Left-tailed

Would you like additional details or have any questions?

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### Further Related Questions:
1. How do you determine whether a hypothesis test is left-tailed, right-tailed, or two-tailed?
2. What is the significance level, and how does it affect the test outcome?
3. How can sample size influence the results of a hypothesis test?
4. What are Type I and Type II errors in hypothesis testing, and how do they relate to this problem?
5. How do you calculate the p-value in a left-tailed test for a proportion?

### Tip:
For hypothesis testing, clearly identify the direction of your hypothesis to determine the appropriate tail (left, right, or two-tailed).

An airline industry trade journal reports that the proportion of customers that check a bag with a weight in excess of the limit is 16.7%. You are not entirely convinced. You believe that it is less than 16.7%. What would be your null and alternative hypotheses, and what type of hypothesis test should you conduct?

Explore hypothesis testing with proportions. Test whether the proportion of customers who check a bag over the weight limit is less than 16.7%. Understand null and alternative hypotheses and learn how to conduct a left-tailed test. Suitable for college-level statistics students.

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