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 not 500


b.
H0: average is more than 500

Ha: average is less than or equal to 500



c.
H0: average is less than or equal to 500

Ha: average is more than 500



d.
H0: average is more than or equal to 500

Ha: average is less than 500



e.
H0: average is equal to 500

Ha: average is not 500

In this scenario, Hilda is testing whether the average weight of chips in a bag is at least 500 grams, as advertised. This suggests a one-sided hypothesis test because the interest is in determining if the weight is **more than 500 grams** (alternative hypothesis) or **less than or equal to 500 grams** (null hypothesis).

The null hypothesis (\( H_0 \)) typically represents the status quo or the claim being tested. Since the advertisement claims at least 500 grams, we test whether the true average is 500 grams or less.

The alternative hypothesis (\( H_a \)) is what you are trying to prove—whether the average weight is more than 500 grams.

The correct choice is:

**c.**
- \( H_0 \): The average is less than or equal to 500 grams
- \( H_a \): The average is more than 500 grams

This matches the nature of the problem because you're testing whether the average weight exceeds 500 grams.

Would you like further details or explanations about this reasoning? Here are some related questions:

1. How do you calculate the test statistic for hypothesis testing?
2. What is the critical value for a 95% confidence level?
3. How does sample size affect the outcome of hypothesis testing?
4. What is a Type I error in hypothesis testing?
5. What is a Type II error in hypothesis testing?

**Tip:** The null hypothesis is always framed as a statement of equality (or inequality) and assumes the status quo, while the alternative hypothesis reflects the change or effect you want to detect.

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.

Options:
a.
H0: average is more than or equal to 500
Ha: average is not 500

b.
H0: average is more than 500
Ha: average is less than or equal to 500

c.
H0: average is less than or equal to 500
Ha: average is more than 500

d.
H0: average is more than or equal to 500
Ha: average is less than 500

e.
H0: average is equal to 500
Ha: average is not 500

Explore a hypothesis testing problem where a quality assurance manager tests if the average weight of chips in a bag is more than 500 grams. This problem covers key statistical concepts such as hypothesis testing, confidence intervals, and Z-tests, using real-world data of 25 bags with an average weight of 512.5 grams and a standard deviation of 18.45 grams.

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