What is the best choice showing the null and alternative?

Hilda is a quality assurance manager. The product (bag of chips) is advertised to have **at least 500** gr of chips in each bag. She has taken a sample of **25 bags** of chips and has calculated the average as 512.5 gr. The sample's standard deviation is 18.45 gr. We need to be 95% certain.





a. 

H0: average is more than or equal to 500

Ha: average is less than 500




b. 

H0: average is equal to 500

Ha: average is not 500




c. 

H0: average is more than or equal to 500

Ha: average is not 500

d. 

H0: average is less than or equal to 500

Ha: average is more than 500




e. 

H0: average is more than 500

Ha: average is less than or equal to 500




The scenario describes a hypothesis test regarding the advertised claim that a bag of chips contains at least 500 grams. We need to identify the appropriate null and alternative hypotheses based on this claim.

### Key points to consider:
- The claim is that the weight of chips is **at least 500 grams**.
- Hilda is testing whether this claim is valid by sampling the bags.
- The hypothesis test should focus on **whether the weight is less than 500 grams** (to see if the claim is potentially false).

### Breakdown of the choices:

- **Null Hypothesis (H₀)**: This is the assumption we begin with, typically representing the status quo or the advertised claim. In this case, the company claims that the average weight is **at least 500 grams**, so the null hypothesis would be that the average weight is **greater than or equal to 500 grams**.
  
- **Alternative Hypothesis (Ha)**: This represents what we test for and is typically the opposite of the null. Hilda is checking whether the bags contain **less than 500 grams**, so the alternative hypothesis should reflect that possibility.

### Analysis of Choices:

a. **H₀: average is more than or equal to 500**
   **Ha: average is less than 500**  
   This is a **left-tailed test** setup. It fits the problem since the test is checking if the actual weight is less than 500 grams (challenging the claim).  
   - **Best Choice**!

b. **H₀: average is equal to 500**
   **Ha: average is not 500**  
   This setup is for a **two-tailed test**, which would test if the average is either higher or lower than 500. This is not the best choice since we are specifically concerned about the weight being less than 500 grams, not just different from 500.

c. **H₀: average is more than or equal to 500**
   **Ha: average is not 500**  
   This is also a **two-tailed test** and isn't the best fit for the question, which focuses on testing if the average is less than 500 grams.

d. **H₀: average is less than or equal to 500**
   **Ha: average is more than 500**  
   This setup represents a **right-tailed test** and is incorrect since the alternative hypothesis should be testing for **less than 500 grams**, not more.

e. **H₀: average is more than 500**
   **Ha: average is less than or equal to 500**  
   This setup is incorrect because it reverses the direction of the null and alternative hypotheses.

### Conclusion:
The best choice is **a**.

- **H₀: average is more than or equal to 500**
- **Ha: average is less than 500**

This represents a left-tailed test, which is appropriate given that Hilda wants to test if the bags contain less than the advertised amount.

Let me know if you'd like further explanation! Here are some related questions:

1. What are the differences between a one-tailed and two-tailed test?
2. How do we calculate the test statistic for this scenario?
3. What role does the sample size play in hypothesis testing?
4. How is the significance level chosen in hypothesis testing?
5. Why do we assume the null hypothesis to be true in hypothesis testing?

**Tip**: In hypothesis testing, the null hypothesis generally represents the established claim or assumption, while the alternative hypothesis tests for deviations from that claim.

What is the best choice showing the null and alternative? Hilda is a quality assurance manager. The product (bag of chips) is advertised to have at least 500 gr of chips in each bag. She has taken a sample of 25 bags of chips and has calculated the average as 512.5 gr. The sample's standard deviation is 18.45 gr. We need to be 95% certain.

Learn how to perform a hypothesis test for a quality assurance problem, where the claim is that each bag of chips contains at least 500 grams. Using a sample of 25 bags with an average of 512.5 grams and a standard deviation of 18.45 grams, we explore null and alternative hypotheses and conduct a left-tailed test.

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