To calculate the p-value, we'll use the z-value obtained from the hypothesis test.

P-value Calculation

• We previously calculated the z-value as $z = 2.00$.
• The p-value for a two-tailed test is the probability that the test statistic is at least as extreme as the observed value, under the null hypothesis.

For a standard normal distribution, you can find the p-value using a z-table or a calculator:

1. Find the area to the right of $z = 2.00$:

   • The area to the right of $z = 2.00$ is approximately 0.0228.

2. Since this is a two-tailed test, the p-value is twice this area: $\text{p-value} = 2 \times 0.0228 = 0.0456$

Conclusion with p-value

• If $\text{p-value} \leq \alpha$ (0.05), we reject the null hypothesis.
• Here, $\text{p-value} = 0.0456$, which is less than 0.05.

Therefore, the p-value supports our earlier conclusion to reject the null hypothesis. This indicates that there is significant evidence to suggest the mean content of the cans is different from 12.00 oz.

---

Do you need further clarification on the p-value, or any other part of the hypothesis test? Here are some related questions:

1. How do you interpret the p-value in context?
2. How would the result change if the p-value were slightly higher, say 0.06?
3. What if the test were one-tailed instead of two-tailed? How would that affect the p-value?
4. What are the assumptions behind using a z-test for hypothesis testing?
5. How do p-values relate to confidence intervals?

Tip: A small p-value (typically less than 0.05) indicates strong evidence against the null hypothesis, while a large p-value suggests weak evidence against it.